Abstract
Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.
Highlights
One of the most commonly used measure in scientific psychology is reaction time (RT) ([25]; [26]), i.e., the time taken by a human being to make a response to a stimulus
Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method
We recall the quantile maximum likelihood (QML) estimation method proposed by [3], [23] and [2] to estimate the ex-Gaussian distribution and the frequentist approach based on the maximum likelihood estimation (MLE) in order to compare them later to the proposed Bayesian approach
Summary
One of the most commonly used measure in scientific psychology is reaction time (RT) ([25]; [26]), i.e., the time taken by a human being to make a response to a stimulus. Another well described aspect is the impact of this positive skewness on parameter estimates ([21]) and on hypothesis testing (i.e., t-tests, ANOVA, etc.) This issue is mostly managed in scientific psychology using strategies to normalize the RT distribution, such as data transformation using link functions ([6]) or as a procedure for right-censoring the distribution (e.g., [22]; [14]) without, ignoring all the problems that these strategies can generate (e.g., [9]).
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