ADDITIVE AND MULTIPLICATIVE MODELS FOR GAMMA-DISTRIBUTED RANDOM-VARIABLES, AND THEIR APPLICATION AS PSYCHOMETRIC MODELS FOR RESPONSE-TIMES

A class of models for gamma distributed random variables is presented. These models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expect ed value. In particular, both additive, multiplicative, and combined a dditive-multiplicative models can be formulated. As a special case, a class of psychometric models for reaction times is presented, together with their psychological interpretation. By means of a comparison wit h existing models, this class of models is shown to offer some possibi lities that are not available in existing methods. Parameter estimatio n by means of maximum likelihood (ML) is shown to have some attractive properties, since the models belong to the exponential family. Then, the results of a simulation study of the bias in the ML estimates are presented. Finally, the application of these models is illustrated by an analysis of the data from a mental rotation experiment. This analys is is preceded by an evaluation of the appropriateness of the gamma di stribution for these data.