Article Nonlinear Appraisal Modeling: An Application of Machine Learning to the Study of Emotion Production MEULEMAN, Ben, SCHERER, Klaus R. Abstract Appraisal theory of emotion claims that emotions are not caused by "raw" stimuli, as such, but by the subjective evaluation (appraisal) of those stimuli. Studies that analyzed this relation have been dominated by linear models of analysis. These methods are not ideally suited to examine a basic assumption of many appraisal theories, which is that appraisal criteria interact to differentiate emotions, and hence show nonlinear effects. Studies that did model interactions were either limited in scope or exclusively theory-driven simulation attempts. In the present study, we improve on these approaches using data-driven methods from the field of machine learning. We modeled a categorical emotion response as a function of 25 appraisal predictors, using a large dataset on recalled emotion experiences (5901 cases). A systematic comparison of machine learning models on these data supported the interactive nature of the appraisal–emotion relationship, with the best nonlinear model significantly outperforming the best linear model. The interaction structure was found to be moderately hierarchical. Strong main [...] Reference MEULEMAN, Ben, SCHERER, Klaus R. Nonlinear Appraisal Modeling: An Application of Machine Learning to the Study of Emotion Production. IEEE Transactions on Affective Computing, 2013, vol. 4, no. 4, p. 398-411 DOI : 10.1109/T-AFFC.2013.25 Available at: http://archive-ouverte.unige.ch/unige:97855 Disclaimer: layout of this document may differ from the published version. 1 / 1 398 IEEE TRANSACTIONS ON AFFECTIVE COMPUTING, VOL. 4, NO. 4, OCTOBER-DECEMBER 2013 Nonlinear Appraisal Modeling: An Application of Machine Learning to the Study of Emotion Production Ben Meuleman and Klaus R. Scherer Abstract—Appraisal theory of emotion claims that emotions are not caused by “raw” stimuli, as such, but by the subjective evaluation (appraisal) of those stimuli. Studies that analyzed this relation have been dominated by linear models of analysis. These methods are not ideally suited to examine a basic assumption of many appraisal theories, which is that appraisal criteria interact to differentiate emotions, and hence show nonlinear effects. Studies that did model interactions were either limited in scope or exclusively theory- driven simulation attempts. In the present study, we improve on these approaches using data-driven methods from the field of machine learning. We modeled a categorical emotion response as a function of 25 appraisal predictors, using a large data set on recalled emotion experiences (5,901 cases). A systematic comparison of machine learning models on these data supported the interactive nature of the appraisal-emotion relationship, with the best nonlinear model significantly outperforming the best linear model. The interaction structure was found to be moderately hierarchical. Strong main effects of intrinsic valence and goal compatibility appraisal differentiated positive from negative emotions, while more specific emotions (e.g., pride, irritation, despair) were differentiated by interactions involving agency appraisal and norm appraisal. Index Terms—Emotion, appraisal theory, machine learning, interactions, modeling Ç 1INTRODUCTION has generated much theoretical development, empirical 1.1 Emotion Production research, and applications in affective computing [3]. By HE question of what causes an emotion has been now, there are numerous studies that support the influence Taddressed by numerous theories in psychology. Promi- of appraisal on feeling, expression, physiology, and moti- nent among these is appraisal theory, which claims that vation [4]. emotions are not caused by “raw” stimuli, as such, but by Studying the influence of appraisal on emotion calls the subjective evaluation (appraisal) of those stimuli. For for explicit assumptions about the nature of that relation. example, depending on whether you have the winning lot- Even a simple analysis requires a model that specifies tery number, the number drawn on television may either what is input and output, and what kind of mapping cause joy or disappointment. The number itself has no algorithmconnectsinputtooutput.Sofar,researchhas intrinsic emotional meaning, but has to be appraised with been mostly concerned with the former, investigating respect to its personal relevance and implications. which appraisal variables differentiate a small number of Appraisal theory subscribes to the view that emotions basic emotions. Far less attention has been devoted to the are multi-componential phenomena (Fig. 1), consisting of choice of mapping algorithm. In the next section, we will changes in appraisal, physiology (e.g., heart rate, blushing), argue step by step why this choice cannot be glossed expression (e.g., smiling, shouting), motivation (e.g., fight, over. First, we will discuss appraisal theories, highlight- flight), and subjective feeling [1], [2]. Each of these compo- ing interactional hypotheses which imply (potentially) nents contributes to the overall phenomenology of emotion complex mapping algorithms. Following this, we review (like symptoms of a syndrome), but the appraisal compo- how traditional approaches to appraisal-emotion model- nent takes central stage due to its presumed causal role in ing have handled the interaction assumption. These the emotion production process. Appraisal theorists believe approachescanbebrokendownintotwoareas:theory- that changes in the other four components are (largely) a driven modeling and data-drive modeling. Theory-driven consequence of changes in appraisal [1]. This causal modeling is typically found in pure appraisal theory and hypothesis makes the appraisal-emotion relationship of thefieldofaffectivecomputing,wheretheexpresspur- special interest for the study of emotion production, and pose is to create a computational model of emotion pro- duction. Data-driven modeling is typically found in psychological studies that collect data, and then apply a The authors are with the Swiss Center for Affective Sciences, University of Geneva, 7 rue des Battoirs, CH-1205 Geneva, Switzerland. model to estimate relations between appraisal and emo- E-mail: {ben.meuleman, klaus.scherer}@unige.ch. tion (e.g., linear regression). We will identify problems Manuscript received 30 July 2012; revised 26 Sept. 2013; accepted 4 Oct. with the current practice in both of these approaches. 2013; date of publication 22 Oct. 2013; date of current version 13 Mar. 2014. Finally, we propose an improved data-driven strategy Recommended for acceptance by G. Jonathan. basedonmethodsfromthefieldofstatisticalmachine For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference the Digital Object Identifier below. learning, and show how this strategy can aid our under- Digital Object Identifier no. 10.1109/T-AFFC.2013.25 standing of emotion production. 1949-3045 ß 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. MEULEMAN AND SCHERER: NONLINEAR APPRAISAL MODELING: AN APPLICATION OF MACHINE LEARNING TO THE STUDY OF... 399 What are the main effects and interactions predicted by specific appraisal theories? In Roseman’s model [7], appraisal of unexpectedness is assumed to separate sur- prise from all other emotions. Within the other emotions, appraisal of goal compatibility (consistent or inconsistent with one’s goals) is assumed to separate positive from negative emotions. Finally, specific differentiation is made by further appraisals of agency, coping potential and cer- tainty. Thus, for a group of positive and negative emo- tions—as we have in our data—Roseman’s model predicts goal compatibility as the main effect, and agency, coping potential, and certainty as interactions. Lazarus also con- sidered the interactive role of coping potential, distin- guishing primary from secondary appraisal [6]. Primary Fig. 1. Emotions as componential phenomena, consisting of changes in appraisal refers to an evaluation of personal implication, appraisal, motivation, physiology, expression, and feeling. Adapted from [11, Fig. 1]. and asks whether “something is at stake” for the person (relevance, novelty, and goal-compatibility). Conditional on this primary appraisal, a secondary appraisal concerns 1.2 Modeling the Appraisal—Emotion Relation how the subject can cope with these implications, espe- 1.2.1 Theory-Driven Modeling cially if goal obstructive [6]. The OCC model of Ortony The oldest appraisal models are not computational models et al. [12] proposes an explicit tree-structured chain of but theoretical tables proposed by appraisal theorists. Such appraisals to differentiate emotions, with appraisal of tables specify which combinations of appraisal criteria pro- agency as the main effect (circumstance, agent, or object), duce a limited number of discrete emotions. Different followed by interaction effects of goal compatibility, rele- appraisal theories include different appraisal criteria, but vance, and even more agency (other versus self) to differ- most have representations of relevance, intrinsic valence, entiate specific emotions. A hierarchical appraisal goal compatibility, agency, coping potential, and normative structure such as the OCC model implies that the main significance [4]. Thus, a particular configuration of