Memory & Cognition 1993, 21 (2), 168-175 A multinomial processing tree model for degradation and redintegration in immediate recall RICHARD SCHWEICKERT Purdue University. West Lafayette. Indiana When items are presented for immediate recall, a verbal trace is formed and degrades quickly, becoming useless after about 2 sec. The span for items such as digits equals the number of items that can be pronounced in the available time. The length of the items affects span by affecting pronunciation rate. Other properties, such as phonological similarity and lexicality, can affect span without affecting pronunciation rate. These properties change the trace's useful lifetime by affecting redintegration. An analogy is drawn between trace reconstruction and repair of er­ rors in speech. When a trace is degraded, one process attempts to form a phoneme string, and another process attempts to form a word. The two processes are autonomous and can be selec­ tively influenced by lexicality and phonological similarity. The resulting processing tree models make simple predictions that depend on whether or not the influenced processes are sequential. The results are illustrated with data from experiments by Besner and Davelaar (1982). It has been known since at least the time of Oliver Wen­ correct if it is completed before the trace degrades to an dell Holmes (1871, p. 101) that a person cannot repeat unusable state. The trace can be refreshed by rehearsing verbatim a list of unrelated items immediately after pre­ the material, provided the time required to pronounce the sentation, unless the list is short. To this day, we do not items internally is less than the trace degradation time. know what determines how long the list can be. The num­ Memory span is often defined as the number of items ber of items in the list is not limited per se, because mem­ in a list that, half of the time, can be recalled in order ory span differs for different materials such as shape immediately after presentation. Then, the time to pro­ names and color names (Brener, 1940). Furthermore, the nounce a list of span length equals the time at which the span for a single material (e.g., digits) can differ when trace has become unusable. Ordinarily, this time is about the same individual uses different languages (e.g., Ellis 2 sec. & HenneUey, 1980). These facts challenge Miller's (1956) A particular version of this hypothesis is given in the idea that the span is limited to a certain number ofchunks model of Schweickert and Boruff (1986). It accounts for or meaningful units (according to this hypothesis, why differences in memory span for different materials in should the number of chunks in a list of digits change when terms of a race between recall and degradation of the the language is changed?). trace. According to the model, a list will be recalled cor­ A leading hypothesis is that short-term memory is not rectly if the time T, required to emit the list is less than limited to a number of items or chunks but is limited by the duration Tv of the verbal trace. Then, the probability the time for which a trace endures (Baddeley, Thomson, of correct recall is P = P[T, :5 Tvl. & Buchanan, 1975; Brown, 1958; Mackworth, 1963; The model leads to an equation originally proposed by Muter, 1980; Peterson & Peterson, 1959; Schweickert Baddeley et al. (1975) relating memory span, s, and pro­ & Boruff, 1986). According to this hypothesis, when nunciation rate, r, items are presented, a trace is formed and begins to de­ (1) grade, perhaps by decaying over time or by becoming s = rt + c, noisy because of interference. The useful lifetime of the in which t is the time required to pronounce a list of span trace will depend on what it is used for. Recall will be length. The intercept c is sometimes interpreted as the number of items recalled with the assistance of long-term knowledge (e.g., Hulme, Maughan, & Brown, 1991), al­ I thank William H. Batchelder, Gordon Brown, Richard Chechile, though Schweickert, Guentert, and Hersberger (1990) ar­ Nelson Cowan, Xiangen Hu, Randi Martin, and Mary C. Potter for gue that nonzero intercept values may be caused by an their helpful comments. Portions of this work were supported by NSF artifact. Grant DBS-9123865. Data in Tables I and 2 are copyrighted 1982 by Because one way to define the pronunciation rate r is the Canadian Psychological Association and are reprinted with permis­ with this equation, the fact that it holds is not surprising, sion. Correspondence should be addressed to the author at the Depart­ ment of Psychological Sciences, Purdue University, West Lafayette, nor is the fact that word length changes the pronuncia­ IN 47907. tion rate. What is surprising is that under a wide variety Copyright 1993 Psychonomic Society, Inc. 168 DEGRADATION AND REDINTEGRATION 169 of circumstances, the time t is about the same, approxi­ The results of the experiments just described were in­ mately 2 sec, regardless of word length (Baddeley et al., terpreted by the investigators to mean that the trace du­ 1975; Hulme, Thomson, Muir, & Lawrence, 1984; Mack­ ration can be extended by the reconstruction of partially worth, 1963; Schweickert & Boruff, 1986). The time t degraded traces. Reconstruction is easier if the items are can be interpreted as the mean trace duration. The invari­ words and if they are phonologically dissimilar (Sperling ance of this time over materials initially suggested that & Speelman, 1970). the trace duration is relatively constant and that the limit Cowan (in press) gives a detailed treatment of the role on memory span could be explained in terms of a limit of trace reconstruction. He proposed that trace reactiva­ on the time available for rehearsal or recall. This hypoth­ tion takes place in the pauses between items during spoken esis is contradicted by recent experiments, described in recall and that decay of the traces of items takes place the next section, in which the time t was malleable. Recon­ during actual speaking. The model in the following sec­ sideration of Equation 1 shows that a variable affecting tion can be thought of as sketching in a few details about memory span can do so by affecting the pronunciation what goes on during the reconstruction postulated in Co­ rate r, the trace duration t, the intercept c, or some com­ wan's model. Since the following model is not necessar­ bination of these. If variables affecting memory span al­ ily tied to the model of Cowan, I use the terms degrada­ ways affected all of the parameters, the equation would tion and redintegration in lieu of his terms decay and provide no resolving power. But the studies mentioned reactivation. above have shown that word length affects the pronunci­ ation rate r, without affecting the trace duration t. This A Model for Trace Degradation and Redintegration leads to the question of whether there are variables capa­ The challenge in modeling short-term memory trace ble of affecting memory span in another way, by chang­ redintegration is that so little is known about the nature ing t or c without changing r. of degraded traces that it is premature to specify details about how missing or noisy features are reconstituted. Phonological Similarity Some knowledge about degraded traces is available; for Hulme and Tordoff(1989) and, independently, Schweick­ example, Cowan and Morse (1986) provide a detailed ert et al. (1990) carried out experiments to investigate the analysis of vowel changes in short-term memory. But until locus of the effect of phonological similarity in serial or­ more is known, modeling with a moderate level of detail dered recall. The experiments differed in several respects, seems most likely to succeed, and multinomial processing but each supported the conclusion that phonological sim­ trees are useful structures for this purpose (Batchelder & ilarity can affect memory span without changing speak­ Riefer, 1986, 1990; Chechile, 1987; Chechile & Meyer, ing rate. That is, phonologically similar items have a 1976; Hu & Batchelder, 1992; Riefer & Batchelder, smaller memory span because they have a shorter useful 1988). In a multinomial processing tree (e.g., Figure 1), trace duration. an attempt to recall an item is carried out with a sequence of cognitive processes represented by branches on a path Lexicality from the root of the tree to one of the terminal nodes. Memory span is typically greater for words than for The outcome of the recall attempt depends on which ter­ nonwords. In the experiment by Schweickert and Boruff minal node is reached. (1986), the nonwords were pronounced more slowly than The model in Figure 1 represents the act of immediate the words, suggesting that the effect of lexicality could recall of a single item in a randomly ordered list. A com­ simply be a by-product of an effect on pronunciation rate. plete account of immediate recall would model aspects However, Hulme et al. (1991) found that when words and such as serial position effects and memory for the order nonwords were selected so that speech rates were equated, of the items (see, e.g., Lee & Estes, 1977; Nairne, 1991; memory span for the words was greater than memory span Shiffrin & Cook, 1978); a complete account would also for the nonwords. They concluded that, for their data, lexicality affected the intercept c in Equation 1, but did c not affect r. Support from an independent experiment was reported by Schweickert, Ansel, and McDaniel (1991). The words and nonwords used as stimuli were closely matched in several ways. Each list of items was presented visually and rehearsed aloud once; during this rehearsal, words and nonwords were spoken at the same rate.