Order Effect and Time Varying Categories

Order Effect and Time Varying Categories Lee-Xieng Yang (lxyang@nccu.edu.tw) Department of Psychology, Researcher Center for Mind, Brain and Learning National Chengchi University, No.64, Sec.2, ZhiNan Rd., Taipei City 11605, Taiwan (R.O.C) Hao-Ting Wang (htwangtw@gmail.com) Department of Psychology, National Chengchi Univserity No.64, Sec.2, ZhiNan Rd., Taipei City 11605, Taiwan (R.O.C) Abstract The main purpose of this study is to examine how people learn time-varying categories as well as whether order effect exists in such learning. To this end, we design three types of category structures, in which the stimuli vary along trials in an ascend- ing, descending, and quadratic trend. Also, tendency to repeat preceding category label as current response is regarded as ev- idence for order effect. The results show a clear order effect in these experiments. The modeling results reveal that GCM, which is modified to be sensitive to trial order and SDGCM, which relies on the similarity and dissimilarity to the exem- plars for categorization, provide a good fit for all experiments. However, the rule-based model used by Navarro, Perfors, and Vong (2013), which changes the boundary trial by trial has dif- ficulty accommodating the learning pattern in quadratic trend. Keywords: Order Effect; Time-Varying Category; Category Learning Time-Varying Categories Many natural categories are characterized by their features varying in magnitude with time. For instance, the leaves of the deciduous plant are green in summer and gradually turn to yellow or red in autumn. This type of categories we call time- varying categories. Recently, Navarro and colleagues used artificial time-varying categories to examine how people learn on them. They found that although the task was not easy, people could not only get a satisfactory learning accuracy, but also predict the forthcoming valid items based on their understanding of the category structure (Navarro & Perfors, 2009, 2012; Navarro, Perfors, & Vong, 2013). Also, these authors showed that their results can be ac- commodated by the models, which either give the recently seen items a larger weight in the framework of the exemplar or the prototype model (Navarro & Perfors, 2012) or shift the boundary trial by trial in the framework of a rule model (Navarro et al., 2013). Whichever way it goes, the key to making a model capable of accounting for the learning of time-varying categories is the sensitivity to time, specifically the sensitivity to trial order. Order effect The request for the sensitivity to trial order for modeling learning pattern of time-varying categories implies that some sort of order effect should be expected in learning of time- varying categories. Order effect can be broadly defined as any influence on current item brought by preceding item dur- ing learning. Herein, order effect is referred to as tendency of repeating category label of preceding item as response for current item. The simulation work of Stewart, Brown, and Chater (2002) following their MAC (Memory and Comparison) strategy is a good demonstration for order effect. In their simulation ex- periment, 10 items were divided into two categories, 5 taking lower values and the other 5 taking higher values on the stim- ulus dimension. Suppose item X n−1 is from the low category, when item X n takes a value even lower than X n−1 , it must come from the low category and vice versa when item X n−1 is from the high category. That is, the probability to repeat the category label of X n−1 is 1.00. However, when the change on stimulus value from preced- ing item to current one cannot guarantee what the current cat- egory label is, that is when item X n−1 is from the low category and X n > X n−1 or when item X n−1 is from the high category and X n < X n−1 , the probability to repeat the category label of item X n−1 depends on the similarity between items X n−1 and X n . These authors showed that MAC strategy, thought very simple, can get about 80% accuracy on predicting partic- ipants’ performance, hence highlighting that the exemplar temporarily retained in STM is sufficient to provide reliable information for categorization. In this study, we would like to extend the studies of Navarro and Perfors (2012) and Navarro et al. (2013) and attempt to reveal the potential order effect in learning of time-varying categories. To this end, we conduct three experiments with different category structures and compare three computa- tional models on fit to the collected data. Before we introduce the experiments, we first introduce the models we would like to test in this study. GCM GCM (Generalized Context Model) (Nosofsky, 1986, 1987) is a classic exemplar-based model, positing that the inter-item similarity is the basis of categorization and any item would be classified as the category to which it is more similar. The similarity between each item I and exemplar J, S I,J , is the negative exponential function of distance between them on