Running head: MULTIPLEX LEXICAL NETWORK 1
1Quantifying the interplay of semantics and phonology during failures of word retrieval by people
2 with aphasia using a multiplex lexical network
3
4 Nichol Castro*1,2, Massimo Stella*3,4, and Cynthia S. Q. Siew5
5
6 1Georgia Institute of Technology, 2University of Washington, 3University of Southampton,
7 4Complex Science Consulting, 5National University of Singapore
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9
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11 Author Note
12 Nichol Castro, Department of Speech and Hearing Sciences, University of Washington;
13Massimo Stella, Complex Science Consulting, Italy; Cynthia S. Q. Siew, Department of
14Psychology, National University of Singapore. *These authors contributed equally.
15 This research was supported in part by a Ruth L. Kirschstein NRSA Institutional
16Research Training Grant from the National Institute on Aging (T32AG000175) and a Ruth L.
17Kirschstein NRSA Individual Fellowship Grant from the National Institute on Deafness and
18Other Communication Disorders (F32DC017074) to Nichol Castro, an EPSRC Doctoral
19Training Centre grant (EP/G03690X/1) to Massimo Stella, and an Overseas Postdoctoral
20Fellowship from the National University of Singapore to Cynthia S. Q. Siew.
21 Correspondence concerning this article should be addressed to Nichol Castro,
22Department of Speech and Hearing Sciences, University of Washington, [email protected] (or)
23Massimo Stella, Complex Science Consulting, Italy, [email protected]
24 Abstract MULTIPLEX LEXICAL NETWORK 2
25Investigating instances where lexical selection fails can lead to deeper insights into the cognitive
26machinery and architecture supporting successful word retrieval and speech production. In this
27paper, we utilized a multiplex lexical network approach that combines semantic and
28phonological similarities among words to model the structure of the mental lexicon. Network
29measures at different levels of analysis (degree, network distance, and closeness centrality) were
30used to investigate the influence of network structure on picture naming accuracy and errors by
31people with Anomic, Broca’s, Conduction, and Wernicke’s aphasia. Our results reveal that word
32retrieval is influenced by the multiplex lexical network structure in at least two ways – (i) the
33accuracy of production and error type on incorrect productions were influenced by the degree
34and closeness centrality of the target word, and (ii) error type also varied in terms of network
35distance between the target word and produced error word. Taken together, the analyses
36demonstrate that network science techniques, particularly the use of the multiplex lexical
37network to simultaneously represent semantic and phonological relationships among words,
38reveal how the structure of the mental lexicon influences language processes beyond traditionally
39examined psycholinguistic variables. We propose a framework for how the multiplex network
40approach allows for understanding the influence of mental lexicon structure on word retrieval
41processes, with an eye toward a better understanding the nature of clinical impairments like
42aphasia.
43
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45 MULTIPLEX LEXICAL NETWORK 3
461. Introduction
47 Word retrieval failures and speech errors do not occur at random. A close examination of
48such retrieval failures is vital for understanding normal and impaired speech and language
49processes (Baars, 1992). Indeed, word retrieval failures and speech errors are generally viewed,
50in part, as by-products of disruptions in the spreading activation process in the mental lexicon
51(e.g., Dell, Schwartz, Martin, Saffran, & Gagnon, 1997; Foygel & Dell, 2000; Levelt, Roelofs, &
52Meyer, 1999). Although errors may be due to disruptions in the process of spreading activation,
53it is important to also consider how the structure of the mental lexicon influences that process.
54We argue that gaps in our understanding of word retrieval, and particularly instances of failures,
55will continue to persist if investigations of spreading activation processes do not include a careful
56examination of the mental lexicon structure. This view is in line with several researchers who
57have pointed out that current limitations in fully understanding the mental lexicon and language
58processes are in part due to our inability to clearly define the structure of the mental lexicon
59(Jones, Willits, & Dennis, 2015; Sousa & Gabriel, 2015; Steyvers & Tenenbaum, 2005).
60Therefore, this paper adds to the growing body of research in cognitive network science (see
61reviews Baronchelli, Ferrer-i-Cancho, Pastor-Satorras, Chater, & Christiansen, 2013; Siew,
62Wulff, Beckage, & Kenett, 2019) by explicitly quantifying the large-scale structure of the mental
63lexicon as a multiplex language network (e.g., Castro & Stella, 2019; Siew & Vitevitch, 2019;
64Stella & Brede, 2016) and testing the influence of that network structure on word retrieval.
65Given that word retrieval failures are infrequent in typical adults, we focus on picture naming
66accuracy and errors made on incorrect trials by people with aphasia who often have significant
67word retrieval impairments to test the limits of this network model approach.
681.1. Models of typical and impaired word retrieval MULTIPLEX LEXICAL NETWORK 4
69 Most models of word retrieval describe three levels of word representation: a conceptual/
70semantic level, a lemma (or word) level, and a phonological level (see review Levelt, 1999). A
71network-like architecture is used to represent information in each level via nodes, and these
72nodes are connected to each other across levels. For example, several conceptual/semantic nodes
73have converging connections to a specific lemma node, which in turn has diverging connections
74to individual phoneme nodes (see Figure 1, left).
75
76Figure 1. The architecture of the interactive activation model (left) and a simplified depiction of 77the multiplex lexical network (right). In the interactive activation model (Dell et al., 1997), 78semantic nodes connect to word nodes and word nodes connect to phoneme nodes. The blue 79shaded nodes reflect shared semantic features between dog, cat, and rat. Note that there is no 80label as to what those shared features are in the interactive activation model. In the (simplified) 81multiplex lexical network, two networks are represented: a semantic network in blue and a 82phonological network in red, with semantic and phonological word form nodes connected 83between the separate networks as indicated by the dotted lines. Red phonological links represent 84a difference of one phoneme between connected pairs of words. Note that two shades of blue 85semantic links are used to highlight two different types of semantic relations existing between 86the words dog, cat, and rat. For example, the darker blue lines reflect shared features, like ‘is an 87animal’, ‘has a tail’, etc., while the lighter blue lines reflect free association cue-response pairs 88(i.e., dog-cat and cat-rat may be commonly provided free association pairs, but not dog-rat). 89
90 In order to retrieve a word, current models enact a process of spreading activation to
91bring semantic, lemma, and phonological information to conscious awareness. Spreading MULTIPLEX LEXICAL NETWORK 5
92activation processes have been articulated by several investigators (e.g., Anderson, 1983; Collins
93& Loftus, 1975), all hypothesizing three fundamental aspects: (i) activation spreads from one
94node to other related nodes (e.g., from a concept node to a lemma node), (ii) an entity must
95accumulate enough activation to either reach a particular threshold and/or hold the highest
96activation level in order to be “activated”, and (iii) activation diminishes in strength over time
97and over successive processing steps. Word retrieval failures and speech errors can occur at any
98one of these points during the spread of activation (e.g., a semantically related word receives
99more activation than a target word, resulting in a “semantic” error).
100 Despite these fundamental aspects of spreading activation processes, there are two types
101of models that differ in how activation spreads in the aforementioned cognitive architecture (see
102review Levelt, 1999): serial models and interactive activation models. As an example, consider a
103confrontation (i.e., picture) naming task where an image activates conceptual/semantic nodes.
104Serial models posit that the conceptual/semantic nodes transmit activation to relevant lemma
105nodes and it is only after lemma selection that activation is then transmitted to that lemma’s
106phonological nodes; in other words, activation spreads in a single direction with no feedback of
107activation from the phonological level to the lemma level (Levelt et al., 1999). On the other
108hand, interactive activation models begin with the transmission of activation from the
109conceptual/semantic level to the lemma level and further to the phonological level, but allows for
110the “upward” influence of phonological information on lemma selection (Dell & O’Seaghdha,
1111992). Unlike serial models, lemmas in interactive activation models can receive activation from
112both semantic and phonological levels (c.f. Rapp & Goldrick, 2000). Given that interactive
113activation models have been most prominently investigated in the literature with respect to the
114analysis of word retrieval failures by people with aphasia, whereas serial models have been MULTIPLEX LEXICAL NETWORK 6
115prominently used in the chronometric analysis of word retrieval (Levelt et al., 1991), the
116remainder of this paper focuses on the comparison between the class of interactive activation
117models and the multiplex network approach.
118 Aphasia is a disorder of language, often as the result of a left hemisphere stroke.
119Although there are several sub-types of aphasia related to deficits in language production and/or
120comprehension, word retrieval failures are a common feature. Thus, the study of word retrieval
121failures and limits of current models has benefited from research conducted with this unique
122participant sample. The leading hypothesis for word retrieval failures in aphasia is a primary
123breakdown in access-related deficits (Mirman & Britt, 2014); specifically, there is an impairment
124in the maintenance and/or transmission of spreading activation in the lexicon that underlies word
125retrieval (Martin & Dell, 2019). In particular, interactive activation models (Abel, Huber, & Dell,
1262009; Dell & O’Seaghdha, 1992; Dell et al., 1997; Foygel & Dell, 2000; Martin & Dell, 2019)
127have been influential in the study of word retrieval by focusing on the distribution of error types
128(e.g., semantically or phonologically related errors to a target word) that an individual with
129aphasia might produce in a confrontation naming or word repetition task.
130 For example, Foygel and Dell (2000) showed that by modifying certain parameters of
131their interactive activation model (e.g., “lesioning” links between the conceptual/semantic and
132the lemma levels to disrupt the spread of activation in the system), they were able to not only
133simulate the error distributions of individuals with aphasia, but also predict the locus of their
134word retrieval impairment (i.e., impairment in the semantic system or the phonological system).
135In comparing three types of aphasia, Conduction, Anomic, and Wernicke’s aphasia, Foygel and
136Dell were able to correlate the locus of impairment predicted by their model and hallmarks of
137these classic aphasia sub-types. Specifically, people with Anomic aphasia, who are often deemed MULTIPLEX LEXICAL NETWORK 7
138to be more mildly impaired, had relatively intact semantic and phonological systems compared to
139the other two types of aphasia. In contrast to people with Anomic aphasia, people with
140Conduction aphasia had greater phonological impairment aligning with classification requiring
141phonological deficits in repetition and production tasks, whereas people with Wernicke’s aphasia
142had greater semantic impairment aligning with classification requiring greater comprehension
143difficulties in repetition and production tasks (Foygel & Dell, 2000).
1441.2. Multiplex network representation of the mental lexicon
145 Although the interactive activation model has been influential in better understanding the
146processes underlying word retrieval (i.e., spreading activation), we propose that a complete
147understanding of word retrieval requires accounting for the structural influence of word
148representations in the mental lexicon. Indeed, Foygel and Dell (2000)’s work highlight the
149importance of considering the connections between words in the mental lexicon. Therefore, this
150paper draws on techniques from network science to quantify the similarity structure of word
151representations in the mental lexicon using a multiplex network framework.
152 In the multiplex lexical network studied by Stella and colleagues (Castro & Stella, 2019;
153Stella, 2018; Stella, Beckage, Brede, & De Domenico, 2018; Stella & De Domenico, 2018),
154nodes represent words (or lemmas) and are connected to each other on four layers, where each
155layer represents a different type of word-word similarity link. Three layers represent semantic
156relationships through free association (e.g., DOG-CAT, where the cue DOG elicited the response
157CAT in a free associate task), synonym sets (e.g., COUCH-SOFA, where COUCH and SOFA
158have similar meaning), and generalizations (e.g., FURNITURE-CHAIR, where CHAIR is a type
159of FURNITURE), and one layer represents phonological relationships through a one-phoneme
160edit distance rule (e.g., MAT-RAT). Note that the same set of nodes are represented in each MULTIPLEX LEXICAL NETWORK 8
161layer. Such an architecture allows for within-layer connectivity based on specific word-word
162similarity relations and between-layer connectivity reflecting the multiple linguistic features
163associated with a given word. Importantly, the multiplex lexical network conceptually resembles
164long-standing verbal descriptions of the mental lexicon (e.g., Collins & Loftus, 1975), as well as
165more modern computational models of word retrieval (Dell & O’Seaghdha, 1992; Levelt et al.,
1661999), both of which describe separate but connected semantic and phonological systems. In
167what follows, we discuss how the multiplex lexical network is structurally compatible with the
168interactive activation model and provides new ways of investigating instances of word retrieval
169failures (see Figure 1, right).
170 One difference between the architecture of the multiplex lexical network and the
171interactive activation model is the explicit definition of semantic relationships between words. In
172the interactive activation model, the conceptual/semantic nodes are not explicitly defined.
173Instead, each word is connected to 10 arbitrary semantic nodes (see Dell et al., 1997, Table 2, p.
174808). In contrast, the multiplex lexical network explicitly defines the number and type of
175semantic relations among words, in line with the previous literature on semantic memory
176representations in typical adults and people with aphasia (e.g., De Deyne & Storms, 2008;
177Erdeljac & Sekuliç, 2008; Sigman & Cecchi, 2002; Steyvers & Tenenbaum, 2005). Although
178other types of semantic relations may be important (e.g., features; McRae & Cree, 2005), the
179current formulation of the multiplex lexical network provides an explicit way of defining
180semantic relations.
181 An even more significant difference between the multiplex lexical network and the
182interactive activation model is simply the size of lexicon that is represented. Thousands of words,
183as well as the semantic and phonological relationships between all of these words, can be readily MULTIPLEX LEXICAL NETWORK 9
184represented in the multiplex lexical network, whereas existing models typically consider a very
185small set of lemmas. Specifically, the interactive activation model (Dell et al., 1997), and the
186class of models that followed (e.g., Abel et al., 2009; Foygel & Dell, 2000; Martin & Dell,
1872019), only has 6 lemmas. Recall that this model has been used to explain the distribution of
188speech errors made by persons with aphasia; therefore, the lemmas included in the model are
189related to the target word, as well as related and unrelated “error” words (e.g., 1 target lemma,
190plus 1 semantically related lemma, 1 phonologically related lemma, 1 “mixed” lemma that is
191both semantically and phonologically related, and 2 unrelated lemmas). Given that Dell and
192colleagues focus on investigating the parameters of spreading activation processes (i.e.,
193“lesioning” connections in the model to disrupt the spread of activation), their analyses have
194focused on the level of the individual; specifically, the overall picture naming behavior of an
195individual person.
196 Thus, one key limitation of models implementing a small lexicon is the inability to (i)
197investigate specific properties of the error word itself (i.e., an item-level analysis rather than a
198person-level analysis), and (ii) uncover the relationship between the error word and the intended
199target word. In this paper, we leverage on the fact that the multiplex lexical network
200representation naturally encodes word-word similarities among thousands of words, allowing
201researchers to conduct a more fine-grained analysis into the nature of the errors themselves. The
202next section will highlight different local and global network structure properties shown to
203influence word retrieval in typical adults and people with aphasia.
2041.3. Network structure influences word retrieval
205 The application of network science to the study of language representation and process is
206not novel (see reviews Baronchelli et al., 2013; Beckage & Colunga, 2015; Siew et al., 2019; MULTIPLEX LEXICAL NETWORK 10
207Vitevitch, Goldstein, Siew, & Castro, 2014). However, much of this work has focused almost
208exclusively on “single-layer” networks (i.e., a network with only one type of link; semantic only
209or phonological only); although network measures can be readily extrapolated from single-layer
210to multiplex networks. In this section, we describe three structural features of a network (i.e.,
211degree, network distance, closeness centrality; see Figure 2) and briefly discuss prior literature
212showing that these structural features influence various aspects of word retrieval when assuming
213a process of spreading activation in the networks.
214 First, we briefly discuss the body of psycholinguistic research focused on investigating a
215local network measure called degree (also called neighborhood density in the psycholinguistic
216literature; Luce & Pisoni, 1998; see review Vitevitch & Luce, 2016). Degree is simply the
217number of immediately connected “neighbors” of a particular node (i.e., a word), In Figure 2, the
218node for book has seven immediate connections, and thus has a degree of seven. The degree of
219words in semantic and phonological networks influences several language processes (e.g., De
220Deyne, Navarro, & Storms, 2013; Vitevitch & Luce, 2016), including how quickly and
221accurately typical adults (Vitevitch, 2002) and people with aphasia (Gordon, 2002; Vitevitch &
222Castro, 2015) produce words. In the context of spreading activation, words with higher degree
223(i.e., many immediate connections) accumulate activation more quickly from their many
224neighbors than words with lower degree (i.e., few immediate connections), leading to less
225errorful production. MULTIPLEX LEXICAL NETWORK 11
226
227Figure 2. A portion of the free association network depicting network measures of degree, 228closeness centrality, and shortest path length. Degree is the number of immediate connections, 229(e.g., the node for “book” has a degree of seven). Closeness centrality captures how close a node 230is to all other nodes in the network and is represented by the size of a node. Larger nodes have 231greater closeness centrality than smaller nodes (e.g., the node for “write” has high closeness 232centrality whereas the node for “meaning” has low closeness centrality). Path length refers to the 233number of edges between a pair of nodes, specifically the shortest path length between a pair of 234nodes. For example, the length of the shortest path length between the node for “letter” and the 235node for “sentence” is two (but note that there are other possible paths between the two nodes 236that are longer). 237
238 Another network measure shown to influence word retrieval is network distance, which
239quantifies the relationship between a specific pair of nodes in the network by computing the
240length of the shortest path connecting two nodes. For example, Figure 2 depicts the shortest path
241in red from the node for LETTER to the node for SENTENCE, which has a network distance of
242two. Note that it is possible to traverse from LETTER to SENTENCE using other paths;
243however, the shortest path would be the most efficient path for spreading activation (Collins &
244Loftus, 1975). Recently, Kenett, Levi, Anaki, and Faust (2017) showed that semantic relatedness MULTIPLEX LEXICAL NETWORK 12
245judgements were influenced by the network distance between two words in a semantic network
246of free associations, giving ecological validity to this network measure. Pairs of words separated
247by few links in the semantic network (i.e., pairs of words that were relatively close in the
248network) were rated as more semantically similar to each other than pairs of words separated by
249many links (i.e., pairs of words that were relatively far in the network). Theoretically, this
250measure has important implications for the spread and decay of activation: Words that are close
251to an activated word would receive more activation than words that are farther from an activated
252word, since activation decays over successive steps.
253 Lastly, the global network measure of closeness centrality captures the average distance
254of a node to all other nodes in the network, by considering the length of the shortest paths
255between a target node and all other nodes in the network. Note that this measure is an extension
256of network distance, which only considers the length of the (single) shortest path between a
257specific pair of nodes. Figure 2 depicts the closeness centrality of words through the size of
258nodes. For example, the node for WRITE has high closeness centrality, whereas the node for
259MEANING has low closeness centrality. Recent reports show that closeness centrality of words
260in the phonological network influences lexical decision in typical adults (Goldstein & Vitevitch,
2612017) and picture naming in typical adults and people with aphasia (Vitevitch & Castro, 2015).
262Nodes with high closeness centrality tend to reside on “short cut” paths in the network (i.e., short
263paths that connect distant nodes), whereas nodes with low closeness centrality tend to reside on
264the periphery of a network and are connected to other nodes via long paths (Holme, 2005). Thus,
265in terms of spreading activation, high closeness centrality words would receive more activation
266than low closeness centrality words because their location on short-cut paths allows for more
267activation to accumulate. On the other hand, words with low multiplex closeness centrality MULTIPLEX LEXICAL NETWORK 13
268would not receive enough activation because they are too distant from other words in the
269network and activation would have diminished over long network paths.
2701.4. Specific research aims
271 Although some psycholinguistic models are able to account for the influence of local
272structural effects on word retrieval (i.e., the influence of degree as in Dell & Gordon, 2003), it is
273not yet clear how those models in their present form would account for the influence of global
274structural effects on word retrieval (i.e., closeness centrality; e.g., Castro & Stella, 2019).
275Additionally, as noted previously, current models do not consider the relationship between target
276words and produced errors, whereas the measure of network distance may prove informative in
277this respect. Thus, we propose that network science methods enable language researchers to
278model the structure of the mental lexicon in a qualitatively intuitive and quantitatively precise
279manner, permitting continued investigations into how the structure of word representations in the
280mental lexicon influences word retrieval.
281 In this paper, we sought to extend upon the growing body of research examining the role
282of mental lexicon structure on language processes as described above by considering the
283influence of a lexical multiplex network structure on confrontation naming performance
284(accuracy and errors on incorrect trials) by people with aphasia. Our approach differs
285significantly from typical investigations into word retrieval failures, which focus on person-level
286analysis of error distributions (Dell et al., 1997; Foygel & Dell, 2000). Instead, we capitalize on
287the fact that the large-scale multiplex lexical network contains representations of thousands of
288words, as well as the semantic and phonological relationships among those words, to conduct a
289more fine-grained analysis of item-level confrontation naming data. MULTIPLEX LEXICAL NETWORK 14
290 To better understand the influence of the multiplex lexical network structure on word
291retrieval, we conducted a series of archival analyses on existing confrontation naming data by
292people with aphasia. In Section 3, we replicate and extend upon the findings of Castro and Stella
293(2019), who found that the global multiplex network measure of closeness centrality influenced
294successful word retrieval by people with Broca’s and Wernicke’s aphasia. In Sections 4 and 5,
295we consider a novel item-level analysis of errors on incorrect naming trials to consider the
296influence of the target word’s network structure (Section 4) and the influence of the connectivity
297in the network between a target word and an error word (Section 5). In all of these analyses, we
298compare the relative contributions of single-layer and multiplex variants of degree, network
299distance, and closeness centrality to assess the relative influence of the entire multiplex lexical
300network in relation to the additive contribution of individual network layers on word retrieval
301and speech errors. Finally, in Section 6 we propose a theoretical account for the influence of a
302multiplex network structure on the accuracy and error types associated with word retrieval and
303provide concluding remarks in Section 7.
3042. General Method
3052.1. Materials
3062.1.1. Aphasic Confrontation Naming Database
307 We acquired confrontation naming data by people with aphasia from the Moss Aphasia
308Psycholinguistic Project Database (MAPPD; Mirman et al., 2010). Classification of aphasia sub-
309type was provided in the database. We included data from 131 people with Anomic aphasia, 64
310people with Broca's aphasia, 53 people with Conduction aphasia, and 38 people with Wernicke's
311aphasia, which includes the aphasia sub-types analyzed in Foygel and Dell (2000) and Castro
312and Stella (2019). Furthermore, the inclusion of several different types of aphasia varying in type MULTIPLEX LEXICAL NETWORK 15
313and severity of deficits was to instantiate the notion that aphasia primarily impairs access to the
314mental lexicon, not its structure. (Mirman & Britt, 2014). Even though these sub-types of
315aphasia are hallmarked by differential impairment in comprehension and/or production abilities,
316based on the results of Castro and Stella (2019) we hypothesized that the underlying multiplex
317lexical network structure would have the same direction of influence on word retrieval,
318regardless of the person’s aphasia classification.
319 We focused our analyses on the Philadelphia Naming Test (PNT; Roach, Schwartz,
320Martin, Grewal, & Brecher, 1996), which is a 175-item picture naming test. Note that we only
321considered 139 of the target words due to the multiplex lexical network construction outlined
322below (see Supplementary Materials). The database contained codes for accuracy (‘correct’ or
323‘incorrect’) and error type according to the “model” response coding scheme (Mirman, Strauss,
324et al., 2010), which categorizes errors into five types based on relatedness to the target word:
325semantic, formal (or phonological), mixed (i.e., both semantically and phonologically related),
326nonword, and unrelated. Note that responses not falling into these categories (e.g., no response
327on a trial) are not considered in this coding scheme (Mirman, Strauss, et al., 2010). We followed
328this narrower coding scheme to remain consistent with what has been used in previous reports
329analyzing the interactive model of word production (Dell & O’Seaghdha, 1991; Dell et al., 1997;
330Foygel & Dell, 2000). Table 1 provides the percentage of trials for each scoring code.
331
332 MULTIPLEX LEXICAL NETWORK 16
333Table 1.
334Percentage of Correct and Errors for each Sub-type of Aphasia considering only trials for the 335139 PNT target words in the multiplex lexical network. 336 % of “Model” Errors % of % of Aphasia Unclassified Correct Semantic Formal Mixed Nonword Unrelated Sub-Type Errors Anomic 83.3% 3.1% 1.6% 1.7% 2.7% 0.7% 6.8% Broca’s 56.7% 5.1% 4.3% 2.5% 8.7% 4.9% 18.0% Conduction 65.8% 2.6% 7.5% 1.7% 10.5% 2.5% 9.5% Wernicke’s 45.0% 4.6% 8.6% 2.5% 14.0% 8.3% 16.9% 337* Unclassified Errors refer to the catch-all for all remaining incorrect responses not accounted for 338by the 5 error types used in the “model” coding scheme (e.g., no response; Mirman et al., 2010). 339
340 We briefly define error code criteria as obtained from
341https://mrri.org/wp-content/uploads/2016/01/PNT-Glossary-of-Terms_scoring-guide.pdf, which
342provides additional details on error coding. A semantic error code is given when the error
343response is related to the target word through synonym, category coordinate, superordinate,
344subordinate, associated, or diminutive relations. A formal error code is given when the error
345response is phonologically similar to the target word through sharing of: a) stressed vowel,
346initial, or final phoneme, b) two or more phonemes in any position (except unstressed vowels), or
347c) one or more phonemes at a corresponding syllable and word position. A mixed error code is
348given when the error response meets the criteria for a formal error (as outlined above) AND has
349an obvious semantic relation to the target (as outlined above). A nonword error code is given
350when the nonword is phonologically similar to the target (as outlined above). And, an unrelated
351error code is given when the response does not meet the criteria as semantically or
352phonologically related (as outlined above), including responses that have only a visual relation to
353the target and responses that are perseverations of previous naming trials.
3542.1.2. Multiplex Network Construction MULTIPLEX LEXICAL NETWORK 17
355 We represented the semantic and phonological similarities among words in the mental
356lexicon of the average adult native English speaker as a multiplex lexical network, as in previous
357studies (Castro & Stella, 2019; Stella, 2018; Stella et al., 2018; Stella & De Domenico, 2018).
358Figure 3 provides a depiction of the multiplex lexical network, where words are connected
359differently on each layer, but a particular node is connected to itself across each layer. Note that
360we do not make assumptions about the directionality of traversing the layers, nor the hierarchy of
361layers, in contrast to what one might expect in models that restrict the movement of spreading
362activation processes (e.g., Levelt et al., 1999; Rapp & Goldrick, 2000).
363 MULTIPLEX LEXICAL NETWORK 18
364Figure 3. The multiplex lexical network. There are four layers in the multiplex lexical network 365where nodes represent words in the mental lexicon. Words are connected within each layer 366according to free associations, synonyms, generalizations, or phonological similarities (i.e., intra- 367layer edges). Note that a word is connected to itself across all the layers (i.e., inter-layer edges). 368
369 The multiplex lexical network includes 8,531 words/nodes. Given that the multiplex
370lexical network captures several different types of word-word similarity relations, we rely upon
371the union of words across existing databases. Specifically, we obtained data from the Edinburgh
372Associative Thesaurus (Coltheart, 1981) and Wolfram (2018)’s Language WordData. Nodes in
373the multiplex lexical network were connected on at least one of four layers: free association,
374synonym, generalizations, and phonological similarity. (Wolfram, 2018). Free associations were
375obtained from the Edinburgh Associative Thesaurus (Coltheart, 1981), whereas synonyms,
376taxonomic dependencies, and phonological transcriptions were obtained from Wolfram’s
377Language WordData (Wolfram, 2018). The free association layer connected cue words based on
378participant responses during a free association task (e.g., cloud – rain). We did not consider the
379weighting (i.e., frequency of cue-response pairs) or directionality (i.e., asymmetric cue-response
380pairs; e.g., DOG leads to BONE, but BONE does not lead to DOG) of these edges following
381previous studies (e.g., Kenett, Anaki, & Faust, 2014; Kenett et al., 2017). The synonym layer
382connected synonymous words (e.g., character – nature). Note that synonym relations in
383WordData are obtained from WordNet 3.0 (Miller, 1995), which determines synsets (or groups
384of synonymous words) based on overlap in definitions and conceptual relations. The
385generalization layer connected words that exhibit a category-exemplar relationship (e.g., blue –
386color); again we did not consider weighting or directionality related to the relative position in the
387categorical hierarchy between the pair of words. Finally, the phonological layer connected words
388differing by only one phoneme through addition, substitution, or deletion (Luce & Pisoni, 1998;
389e.g., cat-cab) following the commonly studied phonological network of Vitevitch (2008). MULTIPLEX LEXICAL NETWORK 19
3902.1.3. Psycholinguistic Properties of Target Words
391 We obtained three psycholinguistic variables known to influence word retrieval for the
392139 PNT target words: frequency, length, and age of acquisition. Log word frequency was
393obtained from Opensubtitles dataset (Brysbaert & New, 2009), which contains a large corpus of
394subtitles from English movies and TV series. The target words had a mean log word frequency
395of 8.30 (SD = 1.44; ranging from 5.19 to 13.59). Word length was measured as the number of
396phonemes and obtained from Wolfram’s Language WordData (Wolfram, 2018). The target
397words had a mean length of 4.90 (SD = 1.47; ranging from 3 to 10). Age of acquisition was
398obtained from Kuperman, Stadthagen-Gonzalez, and Brysbaert (2012), who conducted a large-
399scale study gathering self-reported age of acquisition ratings for English words by adult native
400speakers via Amazon Mechanical Turk. The target words had a mean age of acquisition of 4.77
401(SD = 1.25; ranging from 2.50 to 8.85).
4023. Predicting Picture Naming Accuracy
403 We first analyzed accuracy of confrontation naming. This analysis extends upon that of
404Castro and Stella (2019), who found that multiplex closeness centrality was a stronger predictor
405of picture naming accuracy than the combination of single-layer closeness centrality predictors
406(i.e., association, synonym, generalization, and phonological closeness centrality) in individuals
407with Broca’s and Wernicke’s aphasia. In the present analysis, we assess the influence of both
408local network structure (i.e., degree) and global network structure (i.e., closeness centrality)
409measure, and consider additional sub-types of aphasia (i.e., Anomic, Broca’s, Conduction, and
410Wernicke’s aphasia).
4113.1. Method MULTIPLEX LEXICAL NETWORK 20
412 For the 139 PNT target words analyzed, we obtained two network measures, degree and
413closeness centrality, on each individual network layer (i.e., single-layer network measures) and
414computed a multiplex variant of each network measure (i.e., multiplex network measure). This
415allowed us to consider the individual influence of each network layer, as well as the combined,
416interactive influence of the entire multiplex lexical network. Table 2 provides the mean, standard
417deviation, and range for each single-layer and multiplex variant of degree and closeness
418centrality.
419
420Table 2.
421Mean, standard deviation, and range of single-layer and multiplex variants of degree and 422closeness centrality for the 139 PNT target items. 423 Network Measure Mean (SD) Range Association Degree 4.77 (31.94) 0.00 – 242.00 Synonym Degree 3.59 (4.54) 0.00 – 26.00 Generalization Degree 11.49 (10.70) 0.00 – 59.00 Phonological Degree 8.89 (8.67) 0.00 – 35.00 Multidegree 51.68 (40.86) 2.00 – 301.00 Association Closeness Centrality 0.29 (0.06) 0.00 – 0.37 Synonym Closeness Centrality 0.21 (0.25) 0.00 – 1.00 Generalization Closeness Centrality 0.25 (0.06) 0.00 – 0.32 Phonological Closeness Centrality 0.15 (0.12) 0.00 – 1.00 Multiplex Closeness Centrality 0.34 (0.02) 0.25 – 0.41 424
425 Degree is a local network measure, which is simply determined by counting the number
426of immediate edges for a given node. We computed degree of a word on each layer. For the
427multiplex variant, we computed multidegree, which is simply the sum of degree on all layers
428(Battiston, Nicosia, & Latora, 2017; Bianconi, 2018). MULTIPLEX LEXICAL NETWORK 21
429 Closeness centrality is a global network measure that captures how a node is connected to
430the rest of the network (Borgatti, 2005). Closeness centrality ci for node i in a given network with
431N connected nodes is defined as:
N c = i , (1) ∑ dij j 432
433where dij is the shortest path connecting nodes i and j. We calculated closeness centrality of a
434word on each individual layer by only considering the shortest path using edges for a particular
435layer. For the multiplex variant, we computed the average shortest path length by considering all
436edges in all layers at the same time. Closeness centrality ranges from 0 to 1, with higher values
437indicating greater centrality within the network.
4383.2. Statistical Analysis
439 We used a binomial logistic crossed-effects regression model to predict the probability of
440correct picture naming (i.e., correct vs incorrect) on a given trial for a given participant using the
441“lme4” package in R (Bates, Mächler, Bolker, & Walker, 2015). We tested several models in
442three stages by using a hierarchical model building procedure using Chi-Square tests (see
443Appendix 3) to determine the appropriate random effect structure and the constellation of fixed
444effects most critical for predicting picture naming accuracy. Fixed effects included single-layer
445and multiplex variants of degree and closeness centrality, while controlling for the expected
446influences of psycholinguistic variables. All predictors were z-scored prior to conducting the
447analyses.
4483.3. Results
449 The final model for predicting the probability of correct picture naming (i.e., correct vs
450incorrect) included fixed effects of word frequency, word length, age of acquisition, MULTIPLEX LEXICAL NETWORK 22
451generalization degree, multidegree, phonological closeness centrality, and multiplex closeness
452centrality, with random intercepts of diagnosis, subjects, and words. Table 3 provides the model
453output. Relevant to consideration of the multiplex lexical network, we found that both
454multidegree and multiplex closeness centrality were significant predictors of picture naming
455accuracy. Specifically, the odds of correct picture naming increased by 1.26 as multiplex
456closeness centrality increased by one standard deviation and 1.22 as multidegree increased by
457one standard deviation, holding all other variables constant. That is, pictures whose names were
458more central in the multiplex lexical network or had more immediate connections (regardless of
459edge type) were more likely to be named correctly than pictures whose names were less central
460in the multiplex network or had fewer immediate connections.
461
462Table 3.
463Final logistic crossed-effects regression model predicting correct picture naming from 464psycholinguistic variables, diagnosis, and single-layer and multiplex variants of degree and 465closeness centrality. 466 Fixed Effects Est. (log odds) St. Err. p-Value Intercept 0.633 0.473 0.180 Word Frequency 0.036 0.066 0.589 Word Length -0.114 0.055 0.040 Age of Acquisition -0.287 0.049 < .0001 Generalization Degree -0.265 0.073 0.0002 Multidegree 0.204 0.095 0.032 Phonological Closeness Centrality 0.075 0.039 0.056 Multiplex Closeness Centrality 0.231 0.099 0.020 467
Random Effects Variance St. Dev. Subject: Intercept 2.009 1.417 Diagnosis: Intercept 0.852 0.923 Word: Intercept 0.254 0.504 468
469 MULTIPLEX LEXICAL NETWORK 23
4703.4. Discussion
471 These results replicate and extend upon the findings of Castro and Stella (2019). First, we
472replicate the finding that multiplex closeness centrality has a facilitative influence on picture
473naming across several different types of aphasia. Recall that closeness centrality captures how
474central a word is in the network relative to all other words, which will influence the amount of
475activation that a word is likely to receive, with multiplex closeness centrality considering
476simultaneously the semantic and phonological connectivity of a word in the network. Our results
477reflect one of the fundamental aspects of spreading activation: namely, activation diminishes in
478strength over time and successive processing steps. That is, low closeness centrality words are at
479a disadvantage as such words do not receive enough activation needed for successful word
480retrieval, particularly for individuals with aphasia who may have deficits in the transmission of
481spreading activation (Martin & Dell, 2019).
482 Additionally, we provide novel evidence that multidegree facilitates picture naming
483accuracy. Recall that degree captures the number of immediate “neighbors,” or connections of a
484given word, with multidegree considering simultaneously semantic and phonological
485connectivity of a word in the network. There are two ways by which high multidegree may
486facilitate word retrieval: 1) having more neighbors leads to a greater number of pathways
487available for accumulating activation, and/or 2) converging activation from semantic and
488phonological neighbors of the target word reduces the likelihood of selecting an incorrect word.
489 Together, the results of this analysis predicting confrontation naming accuracy add to the
490growing body of evidence that the structure of a multiplex lexical network, at both local and
491global levels of analysis, contributes to word retrieval processes. However, understanding word
492retrieval processes also requires consideration of what happens when the process is disrupted. MULTIPLEX LEXICAL NETWORK 24
493Therefore, the remainder of this paper will focus on how the multiplex network structure
494influences words that are selected as “errors” on incorrect naming trials.
4954. Predicting Error Type on Incorrect Productions
496 Recall that the interactive activation model can help explain error distribution patterns for
497a specific person by determining the locus (i.e., within the semantic or phonological system) of
498their impairment (i.e., a person-level analysis; Foygel & Dell, 2000). This type of classification
499has significant implications for assigning certain individuals to appropriate treatment paradigms
500(e.g., a semantically impaired person would receive a semantic-based treatment, whereas a
501phonologically impaired person would receive a phonologically-based treatment). However, the
502interactive activation model cannot further our understanding in how the large-scale structure of
503word representations influences the type of error produced on incorrect trials (i.e., an item-level
504analysis). In the following analysis, we consider whether local and global network measures
505(degree and closeness centrality) of the target word influence the type of errors people with
506aphasia make for a target word.
5074.1. Method
508 Recall that the dataset from MAPPD includes five types of error codes: semantic, formal,
509mixed, nonword, and unrelated. As an initial attempt at understanding how network structure
510influences picture naming errors, we chose to focus on semantic, (e.g., camera for the target
511picture BINOCULARS), formal (e.g., zero for the target picture ZEBRA), and mixed (e.g., cattle
512for the target picture CAMEL) error types since they most closely correspond to the semantic
513and phonological layers considered in our multiplex lexical network. We did not analyze
514nonwords because they are not represented in the multiplex lexical network (i.e., nodes represent
515word lemmas). Although unrelated words may include single-word responses, we did not MULTIPLEX LEXICAL NETWORK 25
516analyze them because it is not always clear what an unrelated error reflects. Specifically, coding
517an unrelated error includes perseverations (i.e., producing a response given earlier in testing), as
518well as responses that have some visual relation to the target (e.g., producing the word ‘tie’ in
519response to the picture ‘waterfall’; https://mrri.org/wp-content/uploads/2016/01/PNT-Glossary-
520of-Terms_scoring-guide.pdf).
5214.2. Statistical Analysis
522 We used a multinomial regression model to predict the probability of error type
523(semantic, formal, or mixed) on a given incorrect picture naming trial of a given participant
524using “mlogit” in R (Croissant, 2012). (NB: We do not report a crossed-effects multinomial
525regression model given the complexity of the random effects structure and issues of data
526sparsity, even when attempted within a Bayesian framework; Bates, Kliegl, Vasishth, & Baayen,
5272015; Eager & Roy, 2017). We again tested several models in three stages by using a
528hierarchical model building procedure using Chi-Square tests (see Appendix 3) to determine
529which constellation of predictors were most critical for predicting error type on incorrect trials.
530Predictors considered included single-layer and multiplex variants of degree and closeness
531centrality, while controlling for the effects of psycholinguistic variables and diagnosis. All
532predictors were z-scored prior to conducting the analyses.
5334.3. Results
534 Our final model for predicting the error type on incorrect trials included word frequency,
535word length, age of acquisition, diagnosis (with Anomic as the reference group), association
536degree, synonym degree, phonological degree, multidegree, association closeness centrality,
537synonym closeness centrality, generalization closeness centrality, and multiplex closeness
538centrality. Table 4 provides the final model output. MULTIPLEX LEXICAL NETWORK 26
539 Of the network measures, association degree, multidegree, and multiplex closeness
540centrality had the largest regression coefficients across error type comparisons, holding all other
541variables constant. Specifically, the results indicated that as association degree increased by one
542standard deviation, the odds of semantic errors increased relative to mixed errors by 7.92 and the
543odds of formal errors increased relative to mixed errors by 4.13. On the other hand, as
544multidegree increased by one standard deviation, the odds of mixed errors increased relative to
545semantic errors by 17.15 and increased relative to formal errors by 8.23. Finally, as multiplex
546closeness centrality increased by one standard deviation, the odds of semantic errors increased
547relative to mixed errors by 2.25 and the odds of formal errors increased relative to mixed errors
548by 2.54.
5494.4. Discussion
550 Our results provide novel evidence that the structure of target words in the multiplex
551lexical network influences the types of errors people with aphasia produce for that given target
552word. These findings indicate that picture names with higher association degree and higher
553multiplex closeness centrality elicited more semantic and formal errors as compared to mixed
554errors, but picture names with higher multidegree elicited more mixed errors as compared to
555semantic and formal errors. These results suggest that semantic and formal errors are more
556influenced by network properties that capture separate layers of information, whereas mixed
557errors are more influenced by network properties that capture the overlap across layers of
558information. For example, although association degree reflects primarily semantic neighbors, this
559also includes phonologically related neighbors (N.B.: There was no explicit instruction during
560the free association task for participants to only provide semantically related responses to cue
561words). Thus, in the case of higher association degree, an error is likely to reflect either a MULTIPLEX LEXICAL NETWORK 27
562semantically or phonologically related neighbor. In contrast, multidegree captures neighbors that
563are both semantically and phonologically related. Thus, mixed errors are more likely to emerge
564as multidegree increases given the selection of neighbors that share both semantic and
565phonological relations.
566 Additionally, although multiplex closeness centrality is a network measure that
567simultaneously considers semantic and phonological layers in its computation, this measure is a
568global network measure that likely captures the initial search process of the network across
569semantic and phonological paths. Although a target word with high multiplex closeness
570centrality may benefit during spreading activation resulting in fewer errors made (as shown in
571Section 3), in the situation where an error is made, residing along many short-cut paths across
572layers increases the likelihood of producing either a semantically or phonologically related error
573(depending on which layer the search process terminates on) rather than a mixed error.
574
575 MULTIPLEX LEXICAL NETWORK 28
576 MULTIPLEX LEXICAL NETWORK 29
577Table 4.
578Final multinomial regression model predicting error type on incorrect picture naming trials from psycholinguistic variables, 579diagnosis, and single-layer and multiplex network measures of degree, and closeness centrality. Semantic v. Mixed Formal v. Mixed Est. (log odds) Std. Err. p-Value Est. (log odds) Std. Err. p-Value Intercept 0.720 0.076 < .0001 0.074 0.085 0.386 Word Frequency -0.136 0.064 0.035 -0.265 0.063 < .0001 Word Length -0.288 0.063 < .0001 0.005 0.062 0.925 Age of Acquisition -0.217 0.048 < .0001 -0.053 0.045 0.239 Broca (v. Anomic) 0.200 0.115 0.083 0.637 0.123 < .0001 Conduction (v. Anomic) -0.250 0.126 0.048 1.519 0.122 < .0001 Wernicke (v. Anomic 0.040 0.115 0.724 1.221 0.117 < .0001 Association Degree 2.072 0.234 < .0001 1.425 0.220 < .0001 Synonym Degree 0.227 0.073 0.001 0.227 0.068 0.0008 Phonological Degree 0.401 0.084 < .0001 0.529 0.078 < .0001 Multidegree -2.843 0.279 < .0001 -2.108 0.263 < .0001 Association Closeness Centrality -0.169 0.070 0.015 -0.189 0.069 0.006 Synonym Closeness Centrality -0.115 0.046 0.012 0.049 0.043 0.255 Generalization Closeness Centrality 0.004 0.057 0.933 0.199 0.061 0.001 Multiplex Closeness Centrality 0.810 0.124 < .0001 0.932 0.125 < .0001 MULTIPLEX LEXICAL NETWORK 30
5805. Predicting Error Type on Incorrect Productions using Network Distance
581 It is important to note that the prior two analyses (Sections 3 and 4) focused on
582investigating how the network properties of the target word affected the probability of correct
583naming and the likelihood of error types on incorrect trials. Particularly concerning is the small
584McFadden’s pseudo-R2 of our final multinomial model in Section 4 predicting error types
585(0.094), which indicates that a substantial proportion of variance in the data is unaccounted for.
586However, we may gain a more complete picture of word retrieval mechanisms by considering
587how the target word is connected to the produced error. A recent paper by Kenett et al. (2017)
588suggests that network distance, a metric quantifying the shortest path between two specific nodes
589in a network, could be a viable measure to consider given that network distance was able to
590reliably capture the magnitude of conceptual relatedness between two words. That is, participants
591judged the similarity of two words, and these behavioral results correlated with the network
592distance measure as calculated from a semantic network. We sought to investigate network
593distance in our data by first following best practices in statistics (Grimmett & Stirzaker, 2001) by
594examining the validity of network distance in our data. We compared the network distance
595between empirically generated target-error pairs to a random null model (see Appendix 2). We
596found that network distance between empirical target-error pairs was not random, indicating that
597this measure of network distance could be included as an additional predictor in the previous
598multinomial regression model predicting the type of error on incorrect trials produced by people
599with aphasia.
6005.1. Method
601 In this analysis, we had to further restrict the data to consider trials in which both the
602target and error words were located in the multiplex lexical network because we cannot calculate MULTIPLEX LEXICAL NETWORK 31
603network distance between a target word and a produced error if one or both of the words are not
604located in the multiplex lexical network. Given that this analysis is an extension of Section 4,
605Table 5 provides a depiction of the available data analyzed here in comparison to Section 4, with
606an approximate loss of 22% of the error analysis data.
607
608Table 5.
609Number and Percentage of Empirical Target-Error Pairs available for analysis depending on 610whether the target and error words were located in the multiplex lexical network. 611 Aphasia Anomic Broca’s Conduction Wernicke’s Sub-Type Error Type S F M S F M S F M S F M # Trials (Target + 573 299 293 476 381 200 261 789 171 437 732 209 Error in Network) # Trials (Target Only 789 401 420 596 512 289 346 991 219 529 984 285 in Network) % of data analyzed in 73 70% 75% 70% 80% 75% 69% 80% 80% 78% 80% 74% comparison % to Section 4 612*S = semantic error, F = formal error, M = mixed error 613
614 In network science, network distance is determined by considering the shortest path
615between nodes in the network. However, two nodes can be disconnected, resulting in an infinite
616value. In order to avoid this issue, we defined network distance as the inverse of the shortest path
617between two nodes. In this way, network distance can range from 0 (i.e., disconnected nodes) to
6181 (i.e., adjacently connected nodes). In our data, we obtained the network distance between a
619target word and the produced error word considering edges in each individual layer (i.e., single-
620layer network distance), as well as considering all edges simultaneously (i.e., multiplex network MULTIPLEX LEXICAL NETWORK 32
621distance. Table 6 provides the mean, standard deviation, and range of network distance between
622target-error pairs on each layer and on the multiplex network.
623
624Table 6.
625Mean, standard deviation, and range of single-layer and multiplex variants of network distance 626between target-error pairs. 627 Network Measure Mean (SD) Range Association Network Distance 0.31 (0.16) 0.00 – 1.00 Synonym Network Distance 0.09 (0.11) 0.00 – 1.00 Generalization Network Distance 0.24 (0.11) 0.00 – 1.00 Phonological Network Distance 0.17 (0.15) 0.00 – 1.00 Multiplex Network Distance 0.38 (0.11) 0.17 – 1.00 628
6295.2. Statistical Analysis
630 We extended upon the prior multinomial regression model in Section 4, by including an
631additional stage of model testing (see Appendix 2). Specifically, we tested whether the inclusion
632of network distance (single-layer and multiplex) between target-error pairs significantly
633contributed to the multinomial regression model predicting the probability of error type
634(semantic, formal, or mixed) on incorrect picture naming trials, while controlling for
635psycholinguistic variables, diagnosis, and network measures of degree and closeness centrality.
6365.3. Results
637 Our final model for predicting the type of error made on incorrect trials included word
638frequency, word length, age of acquisition, diagnosis (with Anomic as the reference group),
639association degree, synonym degree, phonological degree, multidegree, association closeness
640centrality, synonym closeness centrality, generalization closeness centrality, multiplex closeness
641centrality, association network distance, synonym network distance, generalization network
642distance, phonological network distance, and multiplex network distance. Table 7 provides the MULTIPLEX LEXICAL NETWORK 33
643model output. Critically, we found that inclusion of all network distance measures explained
644significantly more variance in predicting error types than the final regression model of Study 2,
645with an R2 gain of 0.235.
646 Network distance on all layers and the multiplex lexical network significantly influenced
647error type on incorrect picture naming trials. As distance between target-error pairs decreased on
648the association layer by 1 standard deviation, the odds of mixed errors increased relative to
649semantic errors by 1.34 and increased relative to formal errors by 1.56, keeping all other
650variables constant. As distance between target-error pairs decreased on the synonym layer by 1
651standard deviation, the odds of semantic and mixed errors were not different, but the odds of
652formal errors increased relative to mixed errors by 1.25, keeping all other variables constant. As
653distance between target-error pairs decreased on the generalization layer by 1 standard deviation,
654the odds of semantic errors increased relative to mixed errors by 1.15, while the odds of mixed
655errors increased relative to formal errors by 1.17, keeping all other variables constant. As
656distance between target-error pairs decreased on the phonological layer by 1 standard deviation,
657the odds of mixed errors increased relative to sematic errors by 1.20, while the odds of formal
658errors increased relative to mixed errors by 5.44, keeping all other variables constant. Finally, as
659distance between target-error pairs decreased on the multiplex network by 1 standard deviation,
660the odds of semantic and mixed errors were not different, but the odds of mixed errors increased
661relative to formal errors by 5.67, keeping all other variables constant.
6625.4. Discussion
663 These results demonstrate the importance of considering not just the lexical and structural
664properties of the target word, but also the way in which the target word and produced error are
665connected in the mental lexicon. One way of interpreting these results is to focus on how mixed MULTIPLEX LEXICAL NETWORK 34
666errors differ from semantic and formal errors, given that mixed errors reflect the combination of
667both. Mixed errors were more likely than formal errors when target-error pairs were close on the
668association layer or given the entire multiplex network, whereas formal errors were more likely
669than mixed errors when target-error pairs were close on the phonological and synonym layers. In
670regard to semantic errors, mixed errors were more likely when target-error pairs were close on
671the association and phonological layers, whereas semantic errors were more likely than mixed
672errors when target-error pairs were close on the generalization layer. Notably, the interactive
673activation model, and other models of word retrieval, cannot account for these results given their
674inability to model connections between specific pairs of words given their small lexicon sizes.
675Table 7.
676Final multinomial regression model predicting error type on incorrect picture naming trials 677from psycholinguistic variables, diagnosis, and single-layer and multiplex network measures of 678degree, closeness centrality, and network distance. Semantic v. Mixed Formal v. Mixed Est. (log odds) Std. Err. p-Value Est. (log odds) Std. Err. p-Value Intercept 0.723 0.085 < .0001 -0.068 0.109 0.535 Word Frequency -0.206 0.068 0.002 -0.256 0.074 0.0006 Word Length -0.302 0.069 < .0001 0.560 0.077 < .0001 Age of Acquisition -0.197 0.048 < .0001 -0.109 0.056 0.053 Broca’s (v. Anomic) 0.230 0.117 0.049 0.559 0.150 0.0001 Conduction (v. Anomic) -0.220 0.128 0.086 1.252 0.148 < .0001 Wernicke (v. Anomic) 0.053 0.117 0.647 0.992 0.142 < .0001 Association Degree 2.079 0.237 < .0001 1.259 0.272 < .0001 Synonym Degree 0.255 0.075 0.0007 0.115 0.085 0.175 Phonological Degree 0.428 0.084 < .0001 0.235 0.099 0.018* Multidegree -2.939 0.284 < .0001 -2.137 0.321 < .0001 Association Closeness Centrality -0.075 0.084 0.371 0.050 0.086 0.557 Synonym Closeness Centrality -0.121 0.047 0.010 -0.112 0.052 0.032 Generalization Closeness Centrality -0.023 0.063 0.708 0.437 0.079 < .0001 Multiplex Closeness Centrality 0.981 0.132 < .0001 1.418 0.146 < .0001 Association Network Distance -0.293 0.097 0.002 -0.448 0.102 < .0001 Synonym Network Distance -0.070 0.044 0.115 0.227 0.063 0.0003 Generalization Network Distance 0.145 0.054 0.007 -0.159 0.075 0.033 Phonological Network Distance -0.188 0.070 0.007 1.694 0.083 < .0001 Multiplex Network Distance 0.090 0.097 0.350 -1.736 0.111 < .0001 679 MULTIPLEX LEXICAL NETWORK 35
680 6816. General Discussion
682 Quantifying the structure of the mental lexicon and its influence on language processes
683remains an open challenge for cognitive science (Baronchelli et al., 2013; Beckage & Colunga,
6842015; Siew et al., 2019). In this paper, we applied computational and mathematical tools from
685network science to quantify the mental lexicon structure as a multiplex lexical network, which
686simultaneously represents semantic and phonological relationships between words, and
687examined the influence of this structure on confrontation naming performance (accuracy and
688errors) by people with aphasia. Our analyses revealed a complex pattern of results; although in
689the remainder of this paper we focus our discussion on the most significant patterns that were
690obtained from the measures computed from the multiplex lexical network and discuss how our
691results contribute to psycholinguistic theory regarding word retrieval processes.
6926.1. A framework for the influence of multiplex lexical network structure on picture naming
693performance.
694 We propose a framework that maintains the three fundamental aspects of spreading
695activation, following the interactive activation model. That is, spreading activation is
696implemented within the multiplex lexical network as the main mechanism driving word retrieval,
697specifically: (i) activation spreads across edges in the network from one node to other related
698nodes, (ii) a node must accumulate enough activation to either reach a particular threshold and/or
699hold the highest activation level in order to be “activated,” and (iii) activation diminishes in
700strength over time and successive processing steps in the network.
701 Although we align with these fundamental aspects of spreading activation, there is a
702major difference in the implementation of spreading activation within our framework as
703compared to the interactive activation model. Consider word retrieval in response to a picture MULTIPLEX LEXICAL NETWORK 36
704(i.e., confrontation naming). The class of models put forth by Dell and colleagues adopts a two-
705step process of retrieval. The stimulus (i.e., picture) introduces a jolt of activation to all the
706relevant semantic nodes in the semantic layer, which then spreads to lemma nodes and onward to
707phoneme nodes in an interactive fashion. A second jolt of activation is assigned to the lemma
708node that has the highest activation level when lexical selection occurs, and again activation is
709allowed to spread interactively across the layers. In contrast, we suggest a simpler process
710whereby during word retrieval, the stimulus (i.e., a picture) introduces a jolt of activation in both
711the semantic and phonological systems, initiating spreading activation separately but also
712simultaneously in the semantic and phonological layers of the multiplex lexical network.
713Importantly, this activation is not merely spread interactively (as in a simple diffusion process)
714between and within the layers; rather activation spreads in parallel in the various layers of the
715multiplex lexical network and activation patterns in any layer has the ability to inform activation
716patterns in another layer in a rapid, dynamic fashion until activation patterns settle on a given
717word. Such a process is consistent with the findings of the extensive body of research on parallel
718distributed processing models (Nadeau, 2012).
719 Additionally, we hypothesize that our implementation of spreading activation in a
720multiplex network could address one limitation of the interactive activation model, namely the
721small, consistent underprediction of mixed errors as reported by Foygel and Dell (2000, p. 211).
722The authors suggested that this might be due to the composition of the neighborhood of 6
723lexemes, which does not allow sufficient opportunities for the occurrence of mixed errors.
724However, another possible explanation may be the underlying structure of the model itself where
725lexemes essentially function as the “hidden layer” between semantic and phonological layers,
726and when combined with the 2-step spreading activation process, might not be sufficient for MULTIPLEX LEXICAL NETWORK 37
727semantic and phonological information to be truly interactive within the system. The alternative
728that we have outlined above has interactivity directly built into the structure of the multiplex
729lexical network, and when combined with a spreading activation process that can occur in
730parallel across layers, could be one way of naturally introducing more opportunities for mixed
731errors to occur.
732 Critically, our proposed implementation of spreading activation in the multiplex lexical
733network emphasizes the importance of network structure in influencing where activation spreads
734and accumulates, which in turn influences the likelihood of correct picture naming and the type
735of errors made on incorrect trials. Given this process of spreading activation, we propose that
736word retrieval first results in a very broad search of the mental lexicon as activation spreads
737within and between layers of the multiplex lexical network. As activation continues to spread in
738the network, the structure constrains where activation spreads and accumulates, resulting in a
739pool of possible lemma candidates that emerge (i.e., have increasingly greater activation levels)
740until a single word is selected for production. Our results considering accuracy and errors
741indicate that the global multiplex network measure of closeness centrality may be particularly
742important for the initial search of the network, whereas the local multiplex network measure of
743degree may be particularly important for narrowing the pool of lemma candidates at a later stage.
744 First, consider the role of multiplex closeness centrality in the word retrieval process.
745Recall that closeness centrality captures how central a word is in the network relative to all other
746words. Thus, words high in multiplex closeness centrality are close to and easily accessible from
747many other words, taking into consideration simultaneously semantic and phonological
748connectivity, due to their location on short-cut paths across multiple layers. Given our finding
749that high multiplex closeness centrality words were more likely to be named accurately than low MULTIPLEX LEXICAL NETWORK 38
750multiplex closeness centrality words (Section 3), we propose that centrality in the multiplex
751lexical network is an important component in guiding the initial search process to the general
752vicinity of the correct lexical representation within the network. Consider the following analogy:
753high multiplex closeness centrality words are like lighthouses. A lighthouse “pops out” on the
754horizon, drawing the attention of ships. In the same way, a word with high multiplex closeness
755centrality also “pops out” in the landscape of the network, drawing activation toward it to allow
756for greater accumulation of activation that is necessary for successful word retrieval.
757 However, the presence of multiple network paths passing through targets with high
758multiplex closeness centrality could act as a double-edged sword. Our results considering the
759error type of incorrect trials (Section 4) indicated that when errors do occur, they were less likely
760to be mixed errors (as compared to semantic and formal errors) when the target words had high
761multiplex closeness centrality than low multiplex closeness centrality. While a target word
762residing along many short-cut paths would accumulate more activation, the presence of many
763short-cut paths could also increase the likelihood that people with aphasia inadvertently wind up
764on an incorrect path while searching for the correct representation, thus leading to the production
765of either a semantic or formal error.
766 Now consider the role of multidegree on the word retrieval process. Recall that degree
767captures the number of immediate “neighbors", with multidegree considering simultaneously
768semantic and phonological connectivity in the network. Our results on picture naming accuracy
769(Section 3) indicated that words with high multidegree were more likely to be named accurately
770than words with low multidegree. This result suggests that not only does an increasing number of
771neighbors provide more paths for activation to accumulate, but also speaks to the convergence of
772information across multiple linguistic relations that boosts the likelihood of selecting the correct MULTIPLEX LEXICAL NETWORK 39
773target word over other related “error” words. In other words, the consideration of both semantic
774and phonological layers simultaneously helps to more efficiently narrow down the pool of
775candidates available for lexical selection, leading to greater naming accuracy for high
776multidegree words than low multidegree words. Furthermore, this result aligns with interactive
777activation models that indicate that activation in the phonological system can have an “upward”
778facilitative influence on word retrieval, in combination with activation in the semantic system.
779 Considering semantic and phonological neighbors simultaneously can also impact the
780type of errors likely to be made on incorrect trials. Specifically, our results (Section 4) indicated
781that when errors do occur, they were more likely to be mixed errors (as compared to semantic
782and formal errors) when the target word had high multidegree than low multidegree. This could
783be accounted for within the same framework outlined above. Although multidegree captures the
784fact that many semantic and phonological neighbors will be partially activated, the activation of
785phonological neighbors at the same time as semantic neighbors can help narrow down the pool
786of possible candidates (e.g., lead to the exclusion of semantic competitors that do not sound like
787the correct word). This process, however, also leads to the closest-competitor being a word that
788is both a semantic and phonological neighbor of the target (i.e., a mixed error). A word with high
789multidegree will have potentially more opportunities for these mixed errors (i.e., more neighbors
790that are both semantically and phonologically related) than a word with low multidegree. Thus,
791the structural overlap of the semantic and phonological layers of the mental lexicon in these
792instances could reinforce the activation of the incorrect word and lead to the production of a
793mixed error.
794 In sum, our results indicate that both the micro-level and macro-level structure of the
795mental lexicon, quantified by network measures of multidegree and multiplex closeness MULTIPLEX LEXICAL NETWORK 40
796centrality respectively, influence word retrieval. We have outlined a framework that provides a
797tentative account, but acknowledge that analysis of chronometric data and conducting
798computational simulations will be essential in testing our framework.
7996.2. Network distance as a new metric to quantify structure between two words
800 Although Sections 3 and 4 demonstrated that the inclusion of network measures derived
801from the multiplex lexical network were important for predicting picture naming accuracy and
802error types, it is important to note that these analyses focused on the structural properties of the
803target word only. However, other structural aspects of the lexicon might play a role in word
804retrieval processes, particularly in determining the type of errors produced on incorrect trials.
805Therefore, in light of recent work showing that network distance, a metric that quantifies the
806shortest path between two nodes in a network, was a significant predictor of performance on a
807semantic judgment task (Kenett et al., 2017), we examined if network distance might be
808important for predicting error types in picture naming.
809 As described earlier in the paper, network distance offers an intuitive way to measure the
810structure between specific pairs of words in a multiplex lexical network. Importantly, in a
811multiplex lexical network, it is possible for the shortest path between two nodes to traverse
812multiple layers of the network. The most striking result from the final set of multinomial
813regression models (Section 5) was that as multiplex network distance increased, the proportion of
814formal errors decreased relative to semantic and mixed errors. In other words, formal errors were
815most likely when the target and produced error were far apart on the multiplex network. This
816necessarily implies that there were no paths of short length to connect the two words, and a long,
817inefficient path through the multiplex lexical network must have ensued for the error to be
818produced. MULTIPLEX LEXICAL NETWORK 41
819 To understand this result, we must consider the structure of the multiplex lexical network
820and its individual layers, and how one would traverse the network given this structure. Previous
821work has shown that the global structure of semantic and phonological layers in the multiplex
822lexical network differs (Stella et al., 2018). Specifically, semantic layers tend to be more
823decentralized and are almost fully connected, whereas the phonological layer has a fragmented
824structure with several connected components (i.e., lexical islands) and disconnected "hermit"
825words (i.e., isolates). Therefore, spreading activation processes may be more efficient within
826semantic layers than on the phonological layer. For example, if one is navigating within a
827semantic layer, the structure of that layer might allow for better exploitation of the rest of the
828multiplex lexical network structure to find the correct representation, averting the production of a
829potential semantic error. In contrast, if one is navigating within the phonological layer, there is a
830higher likelihood of being trapped within a lexical island, leading to an inability to exploit the
831structure of the entire multiplex network and a higher probability of producing a formal error.
832 Furthermore, the process of traversing a multiplex lexical network may be especially
833problematic for a person with aphasia given that aphasia could lead to faster decay of spreading
834activation (i.e., impairment in maintenance) than expected of a typical adult (Dell et al., 1997;
835Martin & Dell, 2019). In other words, the number of edges that could be traversed in the network
836by a person with aphasia may be significantly less than a typical adult. Taken together with the
837unique structure of the multiplex lexical network, one could hypothesize that if a typical adult
838were “trapped” within the phonological layer, they could potentially re-trace their path back to
839the semantic layers and continue the search process. On the other hand, a person with aphasia
840might be unable to re-trace their path due to a lack of activation remaining in the system, leading
841to an early termination of the search process itself and production of the formal error. MULTIPLEX LEXICAL NETWORK 42
8426.3. Addressing long-standing research questions in cognitive science
843 Cognitive scientists have long been interested in the representation and processes of the
844human mind, including how we represent words in the mental lexicon and the processes we use
845to retrieve those words from the lexicon. Notable theories that describe how the mental lexicon is
846represented include a single mental lexicon representation (Fay & Cutler, 1977) that can account
847for both fixed and fuzzy meanings of words (Aitchison, 2012), a representation that includes
848both semantic and phonological levels/layers (Collins & Loftus, 1975; Dell et al., 1997; Levelt et
849al., 1999; Rapp & Goldrick, 2000), and the ability for processing to occur in semantics and
850phonology simultaneously (Collins & Loftus, 1975; Nadeau, 2012). Somewhat surprisingly,
851many models of semantic memory and the mental lexicon employ network-like structures, if not
852the explicit use of a network representation (e.g., Collins & Loftus, 1975; De Deyne, Navarro,
853Perfors, Brysbaert, & Storms, 2018; Landauer & Dumais, 1997; Miller, 1995; Quillian, 1967;
854Smith, Shoben, & Rips, 1974), suggesting that these types of representations are intuitive for
855capturing the structure of word-word similarity relationships. However, to date there is little
856consensus on the exact nature of the underlying representation of the mental lexicon (e.g., what
857linguistic relations to include) in part because the ability to quantify such a large, complex
858system (i.e., tens of thousands of words) has remained somewhat elusive (Jones, Willits, et al.,
8592015; Sousa & Gabriel, 2015; Steyvers & Tenenbaum, 2005).
860 In the present paper, we demonstrate that emerging techniques from network science
861provide a means to explicitly quantify the large-scale, complex structure of the mental lexicon,
862which includes consideration of semantic and phonological similarity among words, and allows
863us to begin explicitly testing the role of mental lexicon structure on language processes. One key
864advantage of the network science framework lies in the computational and mathematical power MULTIPLEX LEXICAL NETWORK 43
865of network science tools to formally represent the structure of the mental lexicon at multiple
866levels of analysis (e.g., the local and global levels) across language. Our findings pose significant
867challenges to existing models of lexical access, which, when taken to their limit, do not explicitly
868predict that a global structural measure, such as closeness centrality, would influence lexical
869processes. Furthermore, it is unclear how such a measure would even be inferred or derived from
870current models. Although one might naturally presume that a straightforward fix would be to
871simply “scale up” existing models by including more nodes at the lemma level, it remains to be
872explicitly implemented and tested if global network structure effects would naturally emerge
873from such a modification.
874 It is important to acknowledge previous work that has attempted to capture the influence
875of “distance” between two words in semantic memory, or the relative amount of similarity (low
876distance) or dissimilarity (high distance) between words. Distributional semantic space models,
877such as Latent Semantic Analysis (Landauer, Foltz, & Laham, 1998) and Hyperspace Analogue
878to Language (HAL; Lund & Burgess, 1996), are commonly used methods for defining semantic
879distance, where the distance between two words involves computing a spatial distance (e.g.,
880cosine distance) between two semantic vectors. For instance, work by Mirman and colleagues
881(e.g., Chen & Mirman, 2012; Mirman, Kittredge, & Dell, 2010; Mirman & Magnuson, 2008)
882showed that whether a related neighbor to a target word has a facilitatory or inhibitory effect on
883processing depends on the distance of that related neighbor (i.e., a “near” neighbor versus a “far”
884neighbor) in distributional semantic space. In contrast, the network science approach defines
885distance by computing the shortest path between two nodes in the network. Indeed, recent
886evidence indicates that the network approach better captures behavioral data than the
887distributional semantic approach (De Deyne, Perfors, & Navarro, 2016; De Deyne, Verheyen, & MULTIPLEX LEXICAL NETWORK 44
888Storms, 2016), including the work by Kenett et al. (2017) who used semantic network distance to
889predict semantic similarity judgments of human participants. These findings, as well as those of
890the present paper, suggest that in addition to semantic distributional models, the network
891approach represents a viable method to quantify the similarity structure of words in the mental
892lexicon.
893 In addition to theoretical questions related to the representation of the mental lexicon
894structure, there remains a long-standing debate in the cognitive sciences with regard to the
895challenges in dissociating the influence of cognitive processes and the structure of the cognitive
896systems on behavior. For example, understanding how semantic search operates in memory
897among a clinical population (frequently studied using a semantic fluency task where people list
898as many members of a given category as possible) requires a close consideration of how the type
899of representation that the modeler specifies (Abbott, Austerweil, & Griffiths, 2015; Jones, Hills,
900& Todd, 2015) interacts with disruptions to the process or damage to that structure (Gotts &
901Plaut, 2002). Furthermore, although many models of speech production consider how semantic
902and phonological information interact to influence the process of lexical selection (Dell et al.,
9031997; Rapp & Goldrick, 2000), they do not explicitly consider how the structure of semantic and
904phonological relationships among words influences that interactivity during lexical retrieval.
905 This theoretical debate of disentangling the influences of structure and process is
906particularly relevant in the present context if we are to advance our understanding of the nature
907of language impairment among clinical populations. The network science framework allows us
908to explicitly and systematically test whether language impairment in aphasia is largely due to
909deficits in the structure of the mental lexicon, deficits in the processes operating on the mental
910lexicon, or some combination of both. First, one could conduct simulations of a spreading MULTIPLEX LEXICAL NETWORK 45
911activation process on the multiplex lexical network in accordance with recent work by Siew
912(2019) who demonstrated how the implementation of spreading activation in a network
913representation could account for a variety of different lexical tasks, including spoken word
914recognition, false memory, and semantic priming. To simulate a deviant process, extra noise
915could be added to the spreading activation process by allowing activation to decay more rapidly
916(as done by Dell and colleagues; e.g., Dell et al., 1997; Foygel & Dell, 2000; Martin & Dell,
9172019), or by increasing the probability of jumps between layers of the multiplex network.
918Second, given that the underlying structure of the mental lexicon changes as a result of the
919aphasia through the weakening of connections between nodes (Dell et al., 1997; Foygel & Dell,
9202000), one could model “damaged” multiplex lexical networks with different structures based on
921aphasia type by deleting nodes from the representation and/or adjusting edge weights between
922and within layers to simulate a deficient structure. These simulations could systematically vary
923the network structure and the processes operating on that structure to examine which
924combinations of structure and process accounts for the overall pattern of picture naming
925performance by persons with aphasia.
926 In, sum, we argue that the application of network science will prove fruitful in addressing
927long-standing questions in the cognitive sciences by providing the means to explicitly quantify
928the vast and massively complex mental lexicon, and carefully incorporating the influence of
929structure on process. Although our proposed tentative framework remains to be formally tested
930and compared against existing models of word retrieval, this framework aligns with neural
931network models of word retrieval and naturally allows for incorporation of chronometric and
932error analyses to assess the dynamics of word retrieval—critical issues that have remained in the
933study of word retrieval (Levelt, 1999). MULTIPLEX LEXICAL NETWORK 46
9347. Conclusion
935 To recapitulate, we found that multiplex lexical network measures of degree, closeness
936centrality, and network distance influence picture naming accuracy and errors by people with
937aphasia. Our results add to the growing body of evidence showing the importance of adopting a
938multiplex approach to study the influence of mental lexicon representation on language
939processes. Specifically, we proposed a novel framework for the role of local and global multiplex
940lexical network measures on word retrieval based on the present pattern of results of picture
941naming accuracy and errors on incorrect naming trials: multiplex closeness centrality influences
942the initial search of the mental lexicon, whereas multidegree influences the narrowing of lemma
943candidates until lexical selection. In conclusion, this work shows how the application of network
944science can address long-standing questions in cognitive science, namely the quantification of
945mental lexicon representation and the ability to capture the influence of mental lexicon
946representation on language processes.
947
948
949
950 MULTIPLEX LEXICAL NETWORK 47
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1131 MULTIPLEX LEXICAL NETWORK 55
1132 Supplementary Materials 1133 1134S1. The 139 Philadelphia Naming Test items analyzed. anchor apple baby ball balloon banana basket bat beard bed bell belt bench bone book boot bottle bowl bread bridge broom bus butterfly cake camera can candle cane cannon carrot cat celery chair chimney church clock closet clown comb corn cow cowboy cross crown dive dog door dragon drum duck ear eye fan fireman fireplace fish flower foot football fork frog garage ghost glass glove goat hair hammer hand harp hat heart helicopter horse hose house iron key king knife leaf letter lion man map monkey mountain nail nose nurse octopus owl pear pen piano pig pillow pineapple pipe pirate plant queen rake ring rope ruler saddle sailor saw scale scarf scissors seal shoe snail snake sock spider spoon star suit sun table tent toilet top train tree turkey van vest volcano wagon waterfall well whistle wig window zipper 1135 1136 MULTIPLEX LEXICAL NETWORK 56
1137S2. Correlation Matrix of Psycholinguistic Variables, Degree, and Closeness Centrality. 1138Correlations that were not statistically significant using a Kendall Tau test at a 0.01 confidence 1139level were grayed out. Red indicates strongly positive correlation while blue indicates strongly 1140negative correlation. 1141
1142
1143 MULTIPLEX LEXICAL NETWORK 57
1144Appendix 1. Regression Model Building Procedures for Sections 3-5.
1145 All regression model building used a data-driven approach to determine the constellation
1146of predictors best suited for each analysis. We tested several models over multiple stages using
1147forward and backward hierarchical model building procedures and Chi-Square tests. We outline
1148below the model building stages for each analysis.
1149 Predicting Confrontation Naming Accuracy
1150 As stated in Section 3, we used a binomial logistic crossed-effects regression model to
1151predict the probability of correct picture naming (i.e., correct vs incorrect) using the “lme4”
1152package in R (Bates, Mächler, Bolker, & Walker, 2015). Three stages of model testing ensued
1153(see Table A1). The first stage identified the appropriate random effects structure for our data to
1154account for variability among subjects and words. The second stage tested the inclusion of
1155psycholinguistic variables (word frequency, word length, and age of acquisition) as fixed effects.
1156Finally, the third stage tested the inclusion of single-layer and multiplex network measures of
1157degree and closeness centrality as fixed effects, while controlling for psycholinguistic variables
1158and diagnosis.
1159 The appropriate random intercept structure for our data included the nested effect of
1160diagnosis and subject, where each subject was assigned to only one type of diagnosis, and the
1161crossed random intercept of word (as each subject responded to each word). We found that
1162random slopes did not contribute to the model without issues of convergence, and follow best
1163practices outlined by (Matuschek, Kliegl, Vasishth, Baayen, & Bates, 2017) to model the
1164simplest random effects structure possible. Stage 2 testing resulted in retaining all fixed effects
1165of psycholinguistic variables. Stage 3 testing results in retaining some of the network measures, MULTIPLEX LEXICAL NETWORK 58
1166specifically generalization degree, multidegree, phonological closeness centrality, and multiplex
1167closeness centrality.
1168
1169Table A1.
1170Model building procedure to determine the appropriate fixed and random effects to predict the 1171likelihood of correct picture naming. 1172 R2 AIC Chi-Square Test Stage 1: Random Effect Structure A. Int + (1|Subject) + (1|Word) .519 53882 B. Int + (1|Diagnosis) + (1|Word) .521 53615 A-B: Χ2 (1) = 268.98, p < .0001 C. Int + (1|Diagnosis/Subject) + (1|Word) .514 53565 A-C: Χ2 (1) = 319.24, p < .0001 B-C: Χ2 (0) = 50.26, p < .0001 Stage 2: Fixed Effects of Psycholinguistic Variables D. Int + Freq + Len + AoA + (1|Diagnosis/ .513 53479 C-D: Χ2 (3) = 91.63, p < .0001 Subject) + (1|Word) Stage 3: Fixed Effects of Network Measures E. Int + Freq + Len + AoA + Gene Deg + .513 53462 D-E: Χ2 (4) = 25.12, p < .0001 Multidegree + Phon CC + Multiplex CC + (1|Diagnosis/Subject) + (1|Word) 1173Int = Intercept, Freq = Log Word Frequency, Len = Word Length, AoA = Age of Acquisition, 1174Asso = Association Layer, Syno = Synonym Later, Gene = Generalization Layer, Phon = 1175Phonological Layer, Deg = Degree, and CC = Closeness Centrality. We report the conditional 1176theoretical R2, which accounts for fixed and random effects, according to Nakagawa, et al. 1177(2017). 1178
1179 Predicting Error Type on Incorrect Confrontation Naming Trials
1180 As stated, in Sections 4 and 5, we used a multinomial regression model to predict the
1181probability of error type (semantic, formal, or mixed) on incorrect picture naming trials using
1182“mlogit” in R (Croissant, 2018). Four stages of model testing ensued (see Table A2), where
1183Section 4 focuses on stages 1-3 and Section 5 focused on stage 4. The first stage provided a null,
1184intercept-only model, since we could not test the random effects of subject and word in this
1185approach. The second stage tested the inclusion of psycholinguistic variables (word frequency,
1186word length, and age of acquisition) and diagnosis as fixed effects. The third stage tested the MULTIPLEX LEXICAL NETWORK 59
1187inclusion of single-layer and multiplex network measures of degree and closeness centrality as
1188fixed effects, while controlling for psycholinguistic variables and diagnosis. Finally, the fourth
1189stage tested the inclusion of single-layer and multiplex measures of network distance.
1190 Stage 2 testing resulted in retaining all psycholinguistic variables and diagnosis. Stage 3
1191testing resulted in retaining association degree, synonym degree, phonological degree,
1192multidegree, association closeness centrality, synonym closeness centrality, generalization
1193closeness centrality, and multiplex closeness centrality. Stage 4 testing resulted in retaining all
1194variables of Stage 3, plus all network distance variables.
1195
1196Table 2A.
1197Model building procedure to determine the appropriate model to predict the error type on 1198incorrect picture naming trials. 1199 R2 LogLik Chi-Square Test Stage 1: Intercept Only Null Model A. Int < .01 -4990.9 Stage 2: Psycholinguistic Variables and Diagnosis B. Int + Freq + Len + AoA + Diagnosis .060 -4687.2 A-B: Χ2 (12) = 567.72, p < .0001 Stage 3: Degree and Closeness Centrality C. Int + Freq + Len + AoA + Diagnosis + .094 -4520.8 B-C: Χ2 (16) = 314.74, p Asso Deg + Syno Deg + Phon Deg + < .0001 Multidegree + Asso CC + Syno CC + Gene CC + Multiplex CC Stage 4: Network Distance D. Model C + Asso Dist + Syno Dist + 0.329 -3347.9 C-D: Χ2 (10) = 1167.1, p Gene Dist + Phon Dist + Multiplex Dist < .0001 1200 1201Int = Intercept, Freq = Log Word Frequency, Len = Word Length, AoA = Age of Acquisition, 1202Asso = Association Layer, Syno = Synonym Later, Gene = Generalization Layer, Phon = 1203Phonological Layer, Deg = Degree, CC = Closeness Centrality, and Dist = Network Distance. 1204We report McFadden’s pseudo-R2. 1205 Appendix 2. Null model testing the viability of network distance used in Section 5. MULTIPLEX LEXICAL NETWORK 60
1206 In order to assess whether network distance between a target word and a produced error
1207is important for predicting error type, we first aimed to determine the dependency of error types
1208over network distance. In other words, we asked whether there was a quantifiable relationship
1209between empirical target-error word pairs that was not random. Here, we examined the network
1210distance between a target word and produced error, and compared these target word-error pairs
1211to a random expectation baseline (i.e., randomly selected errors). If meaningful differences were
1212obtained, this would motivate the inclusion of network distance as a new predictor to be included
1213in the multinomial regression model tested in Section 4 predicting error types on incorrect
1214picture naming trials. On the other hand, if network distance between empirical target-error pairs
1215is not different from network distance between random target-error pairs, then this would suggest
1216that network distance might not be a viable metric to consider for predicting error types.
1217 To assess a null model for network distance between empirical target words and
1218produced errors, we first needed to obtain a set of random errors. We conducted random error
1219sampling for every empirical target-error pair in our dataset. Specifically, for a given empirical
1220target-error pair (e.g., CAT-DOG), we sampled 50 random “errors,” or words from the multiplex
1221lexical network (e.g., SNOW). We connected each of the obtained random errors to the given
1222target word (CAT-SNOW), resulting in 50 random target-error pairs to compare to that given
1223empirical target-error pair (CAT-DOG). Choosing to do the randomization for every empirical
1224target-error pairs allowed us to maintain the distribution of error types across aphasia sub-types
1225(e.g., Foygel & Dell, 2000). To illustrate, there were a total of 1,165 empirical target-error pairs
1226produced by the Anomic aphasia group, with 573 coded as semantic errors, 299 coded as formal
1227errors, and 293 coded as mixed errors (see Table 5). Given our random sampling procedure, for
1228the Anomic aphasia group, we had 28,650 random target-error pairs to compare to the empirical MULTIPLEX LEXICAL NETWORK 61
1229target-(semantic) error pairs, 14,950 random target error pairs to compare to the empirical target-
1230(formal) error pairs, and 14,650 random target-error pairs to compare to the empirical target-
1231(mixed) error pairs.
1232 We sampled random errors with replacement to allow for the repetition of empirical
1233target-error pairs naturally found in the data (e.g., the same “error” could be selected more than
1234one time for a given target word). Additionally, although it is possible for a random error to be
1235the same as the empirical error, we did not attempt to control for any similarity between random
1236errors and empirical targets and errors. Thus, this randomization results in a useful null model for
1237detecting and quantifying similarities between the empirical target-error pairs generated by
1238people with aphasia.
1239 For both empirical target-error pairs and random target-error pairs, we calculated the
1240inverse of network distance between a target word and the error using the shortest path length.
1241Network distance ranged from 0 (disconnected nodes) to 1 (adjacent nodes) and can be computed
1242using edges on a specific layer of the multiplex lexical network or all layers of the multiplex
1243lexical network.
1244 Non-parametric testing using the Kruskal-Wallis test was used to compare the relative
(α) 1245difference, Δ , between the network distance of empirical target-error pairs (eij) to the network
1246distance of random target-error pairs (rij) on a specific network layer or the entire multiplex
1247lexical network structure (α). Specifically, we used the following formula:
(α) (α) (α) E −R (2) Δ = , E(α)
1248where E(α) was the median network distance between empirical target-error pairs and R(α) was the
1249median network distance between random target-error pairs. Large, positive values indicate that
1250the network distance between the empirical target-error pairs were closer (i.e., smaller distance) MULTIPLEX LEXICAL NETWORK 62
1251than expected when compared to the random baseline (i.e., target-random error pairs), whereas
1252large, negative values indicate that the network distance between the empirical target-error pairs
1253were farther (i.e., greater distance) than expected when compared to the random baseline. Values
1254close to 0 indicate that the distance between the empirical target-error pairs were not different
1255from the random baseline. For example, a relative difference of +30% would indicate that the
1256empirical target-error pairs were on average 30% closer than the random target-error pairs.
1257 Table 6 shows the relative difference in network distance between empirical target-error
1258pairs and random target-error pairs computed to match the error type distributions of each
1259aphasia sub-type. That is, we include error type in Table 6 to capture the differences in the
1260number of trials for each error type, not to instantiate any type of similarity between random
1261errors and target words.
1262 Across all error types, empirical target-error pairs were closer than the random target-
1263error pairs on the multiplex lexical network structure, which considers all semantic and
1264phonological layers simultaneously. Note that these patterns of relative differences in network
1265distance between empirical target-error pairs and random target-error pairs were consistent
1266across all types of aphasia. The results indicate that network distance between a target and
1267produced error could be considered in order to better understand what aspects of the network
1268structure influence lexical retrieval processes in people with aphasia.
1269
1270 MULTIPLEX LEXICAL NETWORK 63
1271 1272Table 1. 1273 1274The relative distance of empirical target-error pairs as compared to random target-error pairs 1275for each diagnosis, each error type, and each network layer/structure. 1276 Aphasia Empirical Association Synonym Generalization Phonological Multiplex Sub-type Error Type Layer Layer Layer Layer Network Anomic Semantic 46% **** 28% **** 26% **** 4% 40% **** Mixed 46% **** 22% *** 28% **** 34% **** 40% **** Formal 10% * 4% 3% 50% **** 30% **** Broca’s Semantic 45% **** 29% **** 23% *** 4% 39% **** Mixed 46% **** 26% **** 27% **** 23% *** 38% **** Formal 10% * 1% 10% * 37% **** 20% *** Conduction Semantic 45% **** 21% *** 28% **** 11% * 39% **** Mixed 41% **** 23% **** 23% **** 29% **** 37% **** Formal 13% ** 2% 9% * 48% **** 25% **** Wernicke Semantic 43% **** 22% *** 23% **** 4% 37% **** Mixed 43% **** 22% *** 22% *** 26% **** 39% **** Formal 14% ** 3% 7% * 40% **** 22% *** 1277* < .05, ** < .01, *** < .001, **** < .0001 MULTIPLEX LEXICAL NETWORK 64
1278