Quantal Response Techniques for Random Predictor Variables

The relationship between quantitative predictors and the probability of occurrence of one or more levels of a qualitative criterion can be analyzed by quantal response techniques. This paper presents two quantal response models. The first model treats the predictors as mathematical variables used as a stratification dimension; the second model uses random variables as predictors. Model II estimation techniques are presented for dichotomous and polychotomous criteria and for single and multiple predictors. The estimation techniques are illustrated with examples of the use of MMPI scale scores to predict the diagnostic classification of psychiatric patients and to model the actual diagnostic classifications of judges. These uses of quantal response methodology are contrasted with those of multiple linear regression and discriminant analysis. Many of the dependent variables collected in school settings are qualitative, e.g., the passing or failing of an item, the mastery or non-mastery of a task, the presence or absence of a behavioral trait or skill. When the interest of the researcher is to relate these variables to quantitative variables, quantal response procedures are potentially applicable for such educational data analyses.