# Inferences of associated latent variables by the observable test scores

## TL;DR

This paper explores how test scores can be used to infer hidden variables in a general class of models.

## Contribution

Generalizes conditions for using test scores to infer latent variables in monotone models.

## Key findings

- Sum scores can be used for inferences under weaker stochastic ordering conditions.
- The approach applies to any monotone latent variable model with associated variables.
- Test scores are shown to have broader theoretical significance beyond classical test theory.

## Abstract

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.