Keywords

Measurement Invariance; Delta Fit Indexes; Non-normal Data; Monte Carlo Simulation; Cutoff Criteria; Satorra-Bentler Adjustments

Abstract

The concept of measurement invariance is essential in ensuring psychological and educational tests are interpreted consistently across diverse groups. This dissertation investigated the practical challenges associated with measurement invariance, specifically on how measurement invariance delta fit indexes are affected by non-normal data. Non-normal data distributions are common in real-world scenarios, yet many statistical methods and measurement invariance delta fit indexes are based on the assumption of normally distributed data. This raises concerns about the accuracy and reliability of conclusions drawn from such analyses. The primary objective of this research is to examine how commonly used delta fit indexes of measurement invariance respond under conditions of non-normality. The present research was built upon Cao and Liang (2022a)’s study to test the sensitivities of a series of delta fit indexes, and further scrutinizes the role of non-normal data distributions. A series of simulation studies was conducted, where data sets with varying degrees of skewness and kurtosis were generated. These data sets were then examined by multi-group confirmatory factor analysis (MGCFA) using the Satorra-Bentler scaled chi-square difference test, a method specifically designed to adjust for non-normality. The performance of delta fit indexes such as the Delta Comparative Fit Index (∆CFI), Delta Standardized Root Mean Square residual (∆SRMR) and Delta Root Mean Square Error of Approximation (∆RMSEA) were assessed. These findings have significant implications for professionals and scholars in psychology and education. They provide constructive information related to key aspects of research and practice in these fields related to measurement, contributing to the broader discussion on measurement invariance by highlighting challenges and offering solutions for assessing model fit in non-normal data scenarios.

Completion Date

2024

Semester

Summer

Committee Chair

Sivo, Stephen

Degree

Doctor of Philosophy (Ph.D.)

College

College of Community Innovation and Education

Department

Department of Learning Science and Education Research

Degree Program

Education; Methodology, Measurement and Analysis

Format

application/pdf

Identifier

DP0028561

URL

https://purls.library.ucf.edu/go/DP0028561

Language

English

Release Date

8-15-2029

Length of Campus-only Access

5 years

Access Status

Doctoral Dissertation (Campus-only Access)

Campus Location

Orlando (Main) Campus

Accessibility Status

Meets minimum standards for ETDs/HUTs

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Restricted to the UCF community until 8-15-2029; it will then be open access.

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