Structural Equation Modeling with Ordinal Variables: Performance of Robust Estimators Under Conditions of Misspecification, Missing Data, and Nonnormality
Restricted (Penn State Only)
- Author:
- Shiverdecker, Levi Keith
- Graduate Program:
- Psychology (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 05, 2021
- Committee Members:
- Rustin Meyer, Major Field Member
Pui-Wa Lei, Outside Unit & Field Member
James Lebreton, Chair & Dissertation Advisor
Kristin Buss (She/Her), Program Head/Chair
Jean Phillips, Major Field Member - Keywords:
- Structural equation modeling
SEM
Simulation
Estimators
maximum likelihood
weighted least squares
ordinal
missing data
nonormal - Abstract:
- Applied psychologists are often faced with many challenges when testing hypotheses using structural equation modeling. For instance, the real-world data used by researchers and practitioners can often violate the assumptions underlying the estimators used to derive model parameters. The use of ordinal variables to indicate our latent constructs (e.g., Likert-type scales), nonnormal distributions, small sample sizes, missing data, and model misspecification can all impact the accuracy of parameter estimates, standard errors, and model fit statistics if these assumption violations occur. Fortunately, robust estimation methods have been developed to help mitigate the impact that these unfavorable data conditions have on estimation. Robust maximum likelihood (MLR), robust maximum likelihood using polychoric correlations to estimate covariances between ordinal variables (MLR-CAT), and robust weighted least squares (WLSMV) are all alternative estimation methods when the assumptions of normal-theory based maximum likelihood (ML) are violated or sample sizes needed for full weighted least squares (WLS) are unrealistic. Although these methods have been independently investigated in many of these unfavorable data conditions, there has not been a direct comparison of all three estimation methods across a such a broad range of conditions using a full SEM framework. Of particular interest is the relative performance of the full-information methods (MLR and MLR-CAT) and limited-information method (WLSMV) when missing data are present across different types of model misspecification. A large-scale Monte Carlo simulation will be used to help determine and develop recommendations for what robust estimation methods are best suited to handle the messy data often used in applied psychology.