ABSTRACT

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.

摘要

本教程介绍了数值加权序数变量的单变量和双变量矩的分析推导，由它们的潜在响应的协方差矩阵和阈值暗示。当离散数据被视为连续数据时，将 SEM 拟合到这些时刻会产生总体级别的 SEM 参数，这比蒙特卡罗模拟计算转换（离散化）误差的计算强度要​​低。一个真实数据示例展示了该方法如何帮助告知研究人员如何最好地处理他们的离散数据，并且模拟复制展示了该方法为蒙特卡洛研究增加价值的潜力，该研究比较了对离散数据做出不同假设的估计器。