A Multivariate, Multilevel Rasch Model with Application to Self-Reported Criminal Behavior

In studying correlates of social behavior, attitudes, and beliefs, a measurement model is required to combine information across a large number of item responses. Multiple constructs are often of interest, and covariates are often multilevel (e.g., measured at the person and neighborhood level). Some item-level missing data can be expected. This paper proposes a multivariate, multilevel Rasch model with random effects for these purposes and illustrates its application to self-reports of criminal behavior. Under assumptions of conditional independence and additivity, the approach enables the investigator to calibrate the items and persons on an interval scale, assess reliability at the person and neighborhood levels, study the correlations among crime types at each level, assess the proportion of variation in each crime type that lies at each level, incorporate covariates at each level, and accommodate data missing at random. Using data on 20 item responses from 2842 adolescents ages 9 to 18 nested within 196 census tracts in Chicago, we illustrate how to test key assumptions, how to adjust the model in light of diagnostic analyses, and how to interpret parameter estimates.