Ingmar Visser

Fitting hidden Markov models to psychological data

Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.

Testing overall and moderator effects in random effects meta-regression

Random effects meta-regression is a technique to synthesize results of multiple studies. It allows for a test of an overall effect, as well as for tests of effects of study characteristics, that is, (discrete or continuous) moderator effects. We describe various procedures to test moderator effects: the z, t, likelihood ratio (LR), Bartlett-corrected LR (BcLR), and resampling tests. We compare the Type I error of these tests, and conclude that the common z test, and to a lesser extent the LR test, do not perform well since they may yield Type I error rates appreciably larger than the chosen alpha. The error rate of the resampling test is accurate, closely followed by the BcLR test. The error rate of the t test is less accurate but arguably tolerable. With respect to statistical power, the BcLR and t tests slightly outperform the resampling test. Therefore, our recommendation is to use either the resampling or the BcLR test. If these statistics are unavailable, then the t test should be used since it is certainly superior to the z test.

Multiple learning modes in the development of performance on a rule-based category-learning task

Behavioral and neuropsychological data suggest that multiple systems are involved in category-learning. In this paper, the existence and the development of multiple modes of learning of a rule-based category structure was examined, and features of different learning processes were identified. Data were obtained in a cross-sectional study by Raijmakers et al. [Raijmakers, M. E. J., Dolan, C. V., & Molenaar, P. C. M. (2001). Finite mixture distribution models of simple discrimination learning. Memory and Cognition, 29, 659-677], in which subjects aged 4-20 years carried out a rule-based category-learning task. Learning models were employed to investigate the development of the learning processes in the sample. The results support the hypothesis of two distinct learning modes, rather than a single general mode of learning with a continuum of appearances. One mode represents sudden rational learning by means of hypothesis testing. In the second, slow learning mode, learning also occurs suddenly as opposed to incrementally. The probability of rational learning increases with age, and seems to be related to dimension preference in the younger age groups. However, the finding of distinct learning modes does not necessarily imply that distinct learning systems are involved. Implications for the interpretation and clinical use of tasks with a category-learning component, such as the Wisconsin Card Sorting Test (WCST [Heaton, R. K., Chelune, G. J., Talley, J. L., Kay, G. G., & Curtis, G. (Eds.). (1993). Wisconsin card sorting test manual: Revised and expanded. Odessa, FL: Psychological Assessment Resources]), are discussed.

A phase transition model for the speed-accuracy trade-off in response time experiments

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction--hysteresis in the transitions between guessing and stimulus-controlled behavior--was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction--bimodal RT distributions--was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding.

Hidden Markov models for individual time series

This chapter introduces hidden Markov models to study and characterize (individual) time series such as observed in psychological experiments of learning, repeated panel data, repeated observations comprising a developmental trajectory etc. Markov models form a broad and flexible class of models with many possible extensions, while at the same time allowing for relatively easy analysis and straightforward interpretation. Here we focus on hidden Markov models with a discrete underlying state space, and observations at discrete times; however, hidden Markov models are not limited to these situations and some pointers are provided to literature on possible extensions.

The dynamics of development on the Dimensional Change Card Sorting task

A widely used paradigm to study cognitive flexibility in preschoolers is the Dimensional Change Card Sorting (DCCS) task. The developmental dynamics of DCCS performance was studied in a cross-sectional design (N = 93, 3 to 5 years of age) using a computerized version of the standard DCCS task. A model-based analysis of the data showed that development on the DCCS task is best described as a discontinuous change in performance on the post-switch phase of the task. In addition to a perseveration group and a switch group, a transitional group that showed shifts between perseverating and switching during the post-switch trials could be distinguished. Computational models of performance and development on the DCCS task cannot, in their current forms, explain these results. We discuss how a catastrophe model of the developmental changes in task performance could be used to generate specific hypotheses about the variables that control development of DCCS performance.

Characterizing sequence knowledge using online measures and hidden Markov models.

What knowledge do subjects acquire in sequence-learning experiments? How can they express that knowledge? In two sequence-learning experiments, we studied the acquisition of knowledge of complex probabilistic sequences. Using a novel experimental paradigm, we were able to compare reaction time and generation measures of sequence knowledge online. Hidden Markov models were introduced as a novel way of analyzing generation data that allowed for a characterization of sequence knowledge in terms of the grammar that was used to generate the stimulus material. The results indicated a strong correlation between the decrease in reaction times and an increase in generation performance. This pattern of results is consistent with a common knowledge base for improvement on both measures. On a more detailed level, the results indicate that at the start of training, generation performance and reaction times are uncorrelated and that this correlation increases with training.

Different Executive Functions Support Different Kinds of Cognitive Flexibility: Evidence From 2-, 3-, and 4-Year-Olds.

Improvements in cognitive flexibility during the preschool years have been linked to developments in both working memory and inhibitory control, though the precise contribution of each remains unclear. In the current study, one hundred and twenty 2‐, 3‐, and 4‐year‐olds completed two rule‐switching tasks. In one version, children switched rules in the presence of conflicting information, and in the other version, children switched rules in the presence of distracting information. Switching in the presence of conflict improved rapidly between the ages of 3 and 3.5 years, and was associated with better working memory. Conversely, switching in the presence of distraction developed significantly between the ages of 2 and 3 years, and was associated with better inhibitory control.

Developing representations of compound stimuli.

Classification based on multiple dimensions of stimuli is usually associated with similarity-based representations, whereas uni-dimensional classifications are associated with rule-based representations. This paper studies classification of stimuli and category representations in school-aged children and adults when learning to categorize compound, multi-dimensional stimuli. Stimuli were such that both similarity-based and rule-based representations would lead to correct classification. This allows testing whether children have a bias for formation of similarity-based representations. The results are at odds with this expectation. Children use both uni-dimensional and multi-dimensional classification, and the use of both strategies increases with age. Multi-dimensional classification is best characterized as resulting from an analytic strategy rather than from procedural processing of overall-similarity. The conclusion is that children are capable of using complex rule-based categorization strategies that involve the use of multiple features of the stimuli. The main developmental change concerns the efficiency and consistency of the explicit learning system.

The role of reversal frequency in learning noisy second order conditional sequences.

The hallmark of implicit learning is that complex knowledge can be acquired unconsciously. The second order conditionals (SOCs) of Reed and Johnson (1994) were developed to be complex, and they are popular materials for implicit learning research. Recently, it was demonstrated that in a sequence made noisy (by combining two SOCs), shared features of the SOCs may be learned explicitly (Fu, Fu, & Dienes, 2008). What are these shared features? We hypothesized that low reversal frequency may play a significant role. We have varied reversal frequency, and discovered that reversal frequency affected response times, inclusion exclusion behavior, and recognition ratings. Not only does it appear to be important to distinguish implicit and explicit knowledge, but also to distinguish what the knowledge is of.