Evaluating random choice models using multivariate correlation analysis

Abstract

Researchers often use specific models to predict the vector of selection probabilities , for some population of decision makers. We assume that the i-th decision maker's vector of selection probabilities follows some prior cross-sectional distribution ,. (v being the parameter vector of F.) To assess the predictive power of random choice models we use two data sets: , the model-based estimates, and r i, the sample-based relative frequency vectors. We suggest the use of the correlation coefficient between . Estimates of the latter are given for an arbitrary F(π,v) and when F is the Dirichlet distribution. In the latter case we show that . We use a distribution free estimation method, the method of moments and the maximum likelihood estimation method to estimate . These estimation methods are tested and evaluated in a Monte Carlo study that simulates a six-brand product class. The third method is found superior to the other two.