34 Multivariate analysis with latent variables

Publisher Summary This chapter focuses on models in which both manifest and latent variables are continuous. This restriction still generates a large class of models when they are considered simultaneously in several populations and when certain variables are considered fixed rather than random. The field of multivariate analysis with continuous latent and measured random variables has made substantial progress in recent years, particularly, from mathematical and statistical points of view. Mathematically, clarity has been achieved in understanding representation systems for structured linear random variable models. Statistically, large sample theory has been developed for a variety of competing estimators, and the associated hypothesis testing procedures have been developed. The applied statistician, who is concerned with utilizing the above theory in empirical applications, will quickly find that causal modeling is a very finicky methodology having many pitfalls.

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