Abstract
We consider Bayesian inference on an extented conjeneric test model (Jöreskog, 1971) xij=αj+βjθi+eij; i=1, 2, …, n and j=1, 2, …, p. The errors for each subject are assumed to distribute p-variates normal N(o, Σ), where Σ is nonsingular matrix. Several different types of multivariate linear test models are classified by means of the joint posterior distribution of β and Σ with reference prior. The marginal posterior distribution of Σ, θ and the approximated marginal posterior distribution of α are derived. The Gibbs sampler is applied to the practical test data to estimate the marginal posterior distribution of scalar parameters.
