How to derive expected values of structural equation model parameters when treating discrete data as continuous

This tutorial presents an analytical derivation of univariate and bivariate moments of numerically weighted ordinal variables, implied by their latent responses’ covariance matrix and thresholds. Fitting a SEM to those moments yields population-level SEM parameters when discrete data are treated as continuous, which is less computationally intensive than Monte Carlo simulation to calculate transformation (discretization) error. A real-data example demonstrates how this method could help inform researchers how best to treat their discrete data, and a simulation replication demonstrates the potential of this method to add value to a Monte Carlo study comparing estimators that make different assumptions about discrete data.