Open Access Dissertation
Date of Award
Education Evaluation and Research
ESTIMATING EFFECTS OF NON-NORMALITY IN ASSESSING
STRUCTURAL EQUATION MODEL FIT FOR USE OF PHYSICAL SCIENCE DATA
SARAH ALTA ROSE
Advisor: Dr. Barry Markman
Major: Education (Evaluation and Research)
Degree: Doctor of Philosophy
The purpose of this study was to evaluate the sensitivity of selected fit index statistics in determining model fit when the distribution varied from normality, as is typically true of data research for the physical sciences. SEM is a popular statistical method and is used in many physical and social behavioral science research projects; however, the sensitivity of the model fit indices when normality is violated had never been estimated.
The original intent for performing the research was to analyze the legitimacy of the model fit indices’ results against three different types of distributions. One data distribution contained five variables (Torque at Transmission, Engine Speed, Vehicle Speed, Accelerator Pedal Position, and Fuel Used). The variables were assessed using an SEM, and a Monte Carlo simulation of 10,000 iterations for varying sample sizes of n = 10, 20, 30, 50, 100, and 250. It was determined that an indication of poor model fit occurred with greater consistency as the sample size of the data set increased. It was also determined that the magnitude of the correlation decreased as sample size decreased, and as the correlation approached zero the model fit resulted in illogical results.
Additional Monte Carlo simulations were therefore conducted, with 1,000 repetitions, and varying magnitudes of correlation matrix values randomly selected from a range of a base value plus or minus 0.015. Twenty four Monte Carlo simulations were performed, with the base value increasing from 0.04 to 0.27. As the correlation matrix values were increased in magnitude, the results of the model fit indices became first illogical and then finally logical, with an increasing indication of a poor model fit. At a certain specified magnitude, the results of the model fit indices were an indication of a poor model fit for the model fit index studied for all Monte Carlo repetitions.
These results were forwarded to a subject matter expert. This expert, in citing Kline (2011), opined the most likely explanation for the study results was the default method of Maximum Likelihood that assumes variables are unstandardized. When variables are standardized, the results could be incorrect. The subject matter expert concluded that no systematic Monte Carlo study could be conducted by inputting an incrementally increasing correlation matrix, such as was attempted in this study.
Rose, Sarah, "Estimating Effects Of Non-Normality In Assessing Structural Equation Model Fit For Use Of Physical Science Data" (2016). Wayne State University Dissertations. 1480.