Academic journal article Psychonomic Bulletin & Review

Fitting the Ratcliff Diffusion Model to Experimental Data

Academic journal article Psychonomic Bulletin & Review

Fitting the Ratcliff Diffusion Model to Experimental Data

Article excerpt

Many experiments in psychology yield both reaction time and accuracy data. However, no off-the-shelf methods yet exist for the statistical analysis of such data. One particularly successful model has been the diffusion process, but using it is difficult in practice because of numerical, statistical, and software problems. We present a general method for performing diffusion model analyses on experimental data. By implementing design matrices, a wide range of across-condition restrictions can be imposed on model parameters, in a flexible way. It becomes possible to fit models with parameters regressed onto predictors. Moreover, data analytical tools are discussed that can be used to handle various types of outliers and contaminants. We briefly present an easy-touse software tool that helps perform diffusion model analyses.

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Mental chronometry, the study of psychological processes through observed response times (RTs), is one of the most prevalent approaches in cognitive psychology. As early as 1868, Donders( 1868/1969) used RT measurements in order to investigate differences between mental processes. Since then, RT studies have been used in perhaps all fields of cognitive science. Such is the importance of RTdata to cognitive psychology that methods for analyzing them have become an object of study in their own right (e.g., Luce, 1986).

Continuing tins trend, considerable attention has been lent to the combination of RT and accuracy data (a ubiquitous combination often referred to as two-choice response time data). For the analysis of tins type of data, several nonlinear statistical models have been developed, often with substantive interpretations attached to the parameters and underlying processes (e.g., the discrete random walk model: Laming, 1968; Link & Heath, 1975). A more advanced model, and the one that is at the heart of the present article, is the Ratcliff diffusion model (RDM; Ratcliff, 1978; Ratcliff, Van Zandt, & McKoon, 1999). The latter model, which will be described in detail in the next section, has performed remarkabfy well in the analysis of two-choice RT data. It has successfully been applied to experiments in many different fields, such as memory (Ratcliff, 1978,1988), letter matching (Ratcliff, 1981), lexical decision (Ratcliff, Gomez, & McKoon, 2004; Wagenmakers, Ratcliff, Gomez, & McKoon, in press), signal detection (Ratcliff & Rouder, 1998; Ratcliff, Thapar, & McKoon, 2004; Ratcliff et al., 1999), visual search (Strayer & Kramer, 1994), and perceptual judgment (Ratcliff, 2002; Ratcliff & Rouder, 2000; Thapar, Ratcliff, & McKoon, 2003; Voss, Rothermund, & Voss, 2004). In particular, the RDM succeeds in explaining characteristic aspects of two-choice RT data such as the occurrence of both fast and slow errors. With the RDM, it is possible to make statements about entire distributions of correct and error latencies, and the parameter estimates allow for much more detailed inferences than those provided by classical models such as ANOVA or curve fitting. In particular, the RDM's parameters, which will be described in detail in the next section, can provide insight into the relative contributions of different factors, such as quality of the input stimulus, conservativeness of the participant, and time spent on processes other than deciding.

In spite of its advantages, the RDM has not yet become a popular or widely used method to analyze two-choice RT data. The reasons for tins lack of dispersion have to do with numerical, statistical, and software issues (see also W. Schwarz, 2001). The first set of reasons concerns the fact that the model is prohibitively difficult to implement for applied researchers because of numerical difficulties. One has to deal with an infinite oscillating series in the expression for the cumulative distribution function (CDF) or probability density function (PDF; see Ratcliff & Tuerlinckx, 2002). …

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