Regression dependence in latent variable models

Three new notions of positive dependence (positive regression dependence, positive left-tail regression dependence, and positive right-tail regression dependence) are studied in this article. Consider a latent variable model where the manifest random variables T-1, T-2,..., T-n given latent random variable/vector (Theta(1),...,Theta(m)) are conditional independent. Conditions are identified under which T-1,..., T-n possesses the new dependence notions for different types of latent variable model. Applications of the results are also provided.