Inferences of associated latent variables by the observable test scores

Test scores, like the sum score, can be useful for making inferences about the latent variables. The conditions under which such test scores allow for inferences of the latent variables based on a "weaker" stochastic ordering are generalized to any monotone latent variable model for which the latent variables are associated. The generality of these conditions places the sum score, or indeed any test score, well beyond a mere intuitive measure or a relic from classical test theory.