The General Latent Variable Model with Discrete Data

Abstract

This chapter is devoted to the presentation of an estimation technique when all variables arranged in meaningful relations are ordinal. The model that we consider may be stated in a very compact way as follows. Let ɳ’ = (ɳ₁, ɳ₂, …, ɳ_m) be a random vector of latent variables, ζ’ = (ζ₁, ζ_2, …, ζ_p) a random vector of residuals (errors-in-equations, random disturbances terms), B a m by m non-singular matrix of regression coefficients with zeros on the main diagonal. Rather than observing ɳ directly, we assume for the moment that we have information on y^*’ = (y ^*₁ , y ^*₂ , y ^*_p ), a column vector of m variables which are linear functions of the m variables in ɳ. Let Γ be a p by m coefficient matrix of the regressions for the unobserved variables in ɳ. Then we consider:

• (3.1) ɳ = B ɳ + ζ

• (3.2) y^* = Γ ɳ

• (3.3) y = g(y^*)