Modeling Incomplete Scaled Questionnaire Data with a Partial Credit Hierarchical Measurement Model

The partial credit hierarchical measurement model (HMM) results when a partial credit IRT model and a hierarchical linear model are combined (Bryk & Raudenbush, 1992; Masters, 1982). This combined model enables the standard errors of parameters to be estimated accurately. The partial credit HMM is illustrated using a subset of data from the Sloan Study of Youth and Social Development, a five-year longitudinal project studying the career aspirations of adolescents. The data used for this study consisted of a subset of students’ responses to multiple administrations of an attitudinal questionnaire, as well as student-level covariates. Using student responses to seven seven-point semantic differential items tapping student mood, the partial credit HMM was used to explore the effects of gender and classroom activity upon student mood as students were engaged in a mathematics classroom. Gibbs sampling and the Metropolis-Hastings algorithm were used to impute values for the missing data and to estimate the parameters of the model. The results of the data analysis indicated that female students had lower mood than male students did for all classroom activities.