Analyzing multiple-item measures of crime and deviance I: Item response theory scaling

Abstract

Multiple-item measures of self-reported offending typically provide the principal outcome measures for individual level research on the causes of crime and deviance. This article directs attention to the substantial problems presented by the task of forming composite scores for these measures, and it presents a possible solution to those problems. We consider scaling by means of the graded response model from item response theory (IRT) as a potential means of overcoming the shortcomings of traditional summative scaling and of obtaining valuable information about the strengths and weaknesses of our measures. We illustrate this strategy through a scale analysis of a fourteen-item, self-report measure of delinquency, using three years of data from the Monitoring the Future study, an annual national survey of high school seniors. The graded response model proves to be consistent with the data, and it provides results that address important substantive questions about self-report measures. The findings are informative about the strengths and weaknesses of alternative strategies for developing self-report instruments, indicating that there is little to be gained by making fine distinctions in the frequency of individual delinquent acts.