Measurement That Matches Theory: Theory-Driven Identification in Item Response Theory Models

Measurement is the weak link between theory and empirical test. Complex concepts such as ideology, identity, and legitimacy are difficult to measure; yet, without measurement that matches theoretical constructs, careful empirical studies may not be testing that which they had intended. Item response theory (IRT) models offer promise by producing transparent and improvable measures of latent factors thought to underlie behavior. Unfortunately, those factors have no intrinsic substantive interpretations. Prior solutions to the substantive interpretation problem require exogenous information about the units, such as legislators or survey respondents, which make up the data; limit analysis to one latent factor; and/or are difficult to generalize. We propose and validate a solution, IRT-M, that produces multiple, potentially correlated, generalizable, latent dimensions, each with substantive meaning that the analyst specifies before analysis to match theoretical concepts. We offer an R package and step-by-step instructions in its use, via an application to survey data.