Latent variable models that account for atypical responses

type="main" xml:id="rssc12032-abs-0001"> <title type="main">Summary</title> <p>Responses to a set of indicators, or items, or variables are often used in social sciences for measuring unobserved constructs as attitudes. Latent variable models, which are 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 response strategy that is driven by the latent variable of interest and a secondary response strategy 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 pseudoitem. We allow for the secondary response strategy that is 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.