A Regression Model for Questionnaires: When a Regressor is the Within-Subject Variance

Educational psychology research often deals with psychological constructs that cannot be directly measured. Reseachers usually evaluate the value of the construct for each person by a factor score or in terms of mean scores on a questionnaire that is thought to measure the construct. Although it is often the case that not only each person's mean score but also the intra-person variability will have important information, no method has been developed for utilizing within-subject variance. In the present research, by introducing random effects for each person into a weakly congeneric measurement model in classical test theory, we developed a model in which not only the mean but also the within-subject variance are regressors for other variables or scales. The proposed method is also applicable to repeated measurement. A simulation study demonstrated the validity of the estimation method of the proposed model. We also showed that within-subject variance on emotionality (in the Five-Factor Model) can be one of the regressors of STAI.