Latent variable models for mixed manifest variables
Latent variable models are widely used in social sciences in which interest is centred on entities such as attitudes, beliefs or abilities for which there e)dst no direct measuring instruments. Latent modelling tries to extract these entities, here described as latent (unobserved) variables, from measurements on related manifest (observed) variables. Methodology already exists for fitting a latent variable model to manifest data that is either categorical (latent trait and latent class analysis) or continuous (factor analysis and latent profile analysis). In this thesis a latent trait and a latent class model are presented for analysing the relationships among a set of mixed manifest variables using one or more latent variables. The set of manifest variables contains metric (continuous or discrete) and binary items. The latent dimension is continuous for the latent trait model and discrete for the latent class model. Scoring methods for allocating individuals on the identified latent dimen-sions based on their responses to the mixed manifest variables are discussed. ' Item nonresponse is also discussed in attitude scales with a mixture of binary and metric variables using the latent trait model. The estimation and the scoring methods for the latent trait model have been generalized for conditional distributions of the observed variables given the vector of latent variables other than the normal and the Bernoulli in the exponential family. To illustrate the use of the naixed model four data sets have been analyzed. Two of the data sets contain five memory questions, the first on Thatcher's resignation and the second on the Hillsborough football disaster; these five questions were included in BMRBI's August 1993 face to face omnibus survey. The third and the fourth data sets are from the 1990 and 1991 British Social Attitudes surveys; the questions which have been analyzed are from the sexual attitudes sections and the environment section respectively.