Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious

Three methods for fitting the diffusion model (Ratcliff, 1978) to experimental data are examined. Sets of simulated data were generated with known parameter values, and from fits of the model, we found that the maximum likelihood method was better than the chi-square and weighted least squares methods by criteria of bias in the parameters relative to the parameter values used to generate the data and standard deviations in the parameter estimates. The standard deviations in the parameter values can be used as measures of the variability in parameter estimates from fits to experimental data. We introduced contaminant reaction times and variability into the other components of processing besides the decision process and found that the maximum likelihood and chi-square methods failed, sometimes dramatically. But the weighted least squares method was robust to these two factors. We then present results from modifications of the maximum likelihood and chi-square methods, in which these factors are explicitly modeled, and show that the parameter values of the diffusion model are recovered well. We argue that explicit modeling is an important method for addressing contaminants and variability in nondecision processes and that it can be applied in any theoretical approach to modeling reaction time.

Stochastic diffusion models ( Ratcliff, 1978 ) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.

The authors bring together approaches from cognitive and individual differences psychology to model characteristics of reaction time distributions beyond measures of central tendency. Ex-Gaussian distributions and a diffusion model approach are used to describe individuals' reaction time data. The authors identified common latent factors for each of the 3 ex-Gaussian parameters and for 3 parameters central to the diffusion model using structural equation modeling for a battery of choice reaction tasks. These factors had differential relations to criterion constructs. Parameters reflecting the tail of the distribution (i.e., tau in the ex-Gaussian and drift rate in the diffusion model) were the strongest unique predictors of working memory, reasoning, and psychometric speed. Theories of controlled attention and binding are discussed as potential theoretical explanations.