Scott Brown, Denis Cousinau, and Andrew Heathcote (2004)
Technical manual for QMPE v2.18: Fortran code to fit response time distributions
Manual.
Estimating distributional parameters from empirical data is a decidedly non-trival task, especially given
the conditions which usually prevail in psychological measurement: high levels of noise and small
sample sizes. Various estimation methods have been proposed, most of which fall into two classes:
least-squares estimation based on statistics calculated from the theoretical and empirical distributions
and maximum likelihood estimation. More recently Heathcote, Brown and Mewhort (in press)
suggested the use of a new variant of maximum likelihood estimation: quantile maximum likelihood
(QMP). This method was shown to have both smaller bias and variance than Van Zandt’s (2000) best
method: continuous maximum likelihood (CML). QMP fitting was shown to perform much more
effectively in small sample sizes: for example, CML typically requires at least 100 sample data points,
but QMP seems to give good results with sample sizes as small as 40. This represents a major and very
useful advance in methodology, given that RT sample sizes are often limited to well below 100 points
by experimental considerations.
The most important disadvantages of QMP fitting are that it is more complex to implement than other
methods, and is more computationally intensive to use. To remove these problems, and to take the
burdens of calculating gradients and Hessians for the likelihood objective function from the end user,
we present an open-source-code program for fitting the ex-Gaussian distribution by QMP and CML
methods.