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
T1,T2,…,Tn
given latent random variable/vector
(Θ1,…,Θm) are conditional
independent. Conditions are identified under which
T1,…,Tn possesses
the new dependence notions for different types of latent variable model.
Applications of the results are also provided.