Latent Variable Models that Account for Atypical Responses

Responses to a set of indicators/items/variables are often used in the social sciences for measuring unobserved constructs such as attitudes. Latent variable models, also known as factor analysis models, are used for linking the observed responses to the latent constructs. Often, some respondents provide random responses to the items. We distinguish between two response strategies: a primary one that is driven by the latent variable of interest and a secondary one that can be characterized as random. We propose an extended latent variable model for binary responses that models the secondary response mechanism through a latent class model implemented as an unobserved pseudo-item. We allow for the secondary response strategy employed by some respondents to be a function of the latent variable of interest and covariates. Not taking into account the proportion of responses generated by secondary strategies in the data can affect parameter estimates and the goodness-of-fit. Covariates are used to identify the demographic characteristics of those who choose a secondary response strategy and increase the precision of model estimation. We fit our proposed model to two data sets, one from a section of the 1990 Workplace Industrial Relations Survey and one from a section of the 2007 British Social Attitudes survey.