The latent class multitrait-multimethod model

A latent class multitrait-multimethod (MTMM) model is proposed to estimate random and systematic measurement error in categorical survey questions while making fewer assumptions than have been made so far in such evaluations, allowing for possible extreme response behavior and other nonmonotone effects. The method is a combination of the MTMM research design of Campbell and Fiske (1959), the basic response model for survey questions of Saris and Andrews (1991), and the latent class factor model of Vermunt and Magidson (2004, pp. 227-230). The latent class MTMM model thus combines an existing design, model, and method to allow for the estimation of the degree to and manner in which survey questions are affected by systematic measurement error. Starting from a general form of the response function for a survey question, we present the MTMM experimental approach to identification of the response function's parameters. A "trait-method biplot" is introduced as a means of interpreting the estimates of systematic measurement error, whereas the quality of the questions can be evaluated by item information curves and the item information function. An experiment from the European Social Survey is analyzed and the results are discussed, yielding valuable insights into the functioning of a set of example questions on the role of women in society in 2 countries.