Date of Award


Degree Name

Doctor of Philosophy


Educational Leadership, Research and Technology

First Advisor

Dr. Brooks Applegate

Second Advisor

Dr. Fernando Andrade

Third Advisor

Dr. Jianping Shen


Experimental design, Sampling Design (SD), precision and stability of data model, Monte Carlo simulation, orthogonal solution, Confirmatory Factor Analysis


Factor analysis (FA) is the study of variance within a group. Within-subject variance (WSV) is affected by multiple features in a study context, such as: the study experimental design (ED) and sampling design (SD), thus anything that influences or changes variance may affect the conclusions related to FA.

The aim of this study was to provide empirical evaluation of the influence of different aspects of ED and SD on WSV in the context of FA in terms of model precision and model estimate stability. Four Monte Carlo population correlation matrices were hypothesized based on different communality magnitudes (high, moderate, low, and mixed). Within each population matrix this study investigated: (a) variable-to-factor ratio (VTF) (4:1, 7:1, and 10:1) that were randomly sampled from a population of 100 indicator variables, and (b) subjects-to-variables ratio (STV) (2:1, 4:1, 8:1, 16:1, and 32:1).

Overall model precision (RQ1) of factor solutions was evaluated by the examination of chi-square value (χ2) and overall model fit indices (OMF) after aggregating 1000 simulation replications in separate three-way ANOVAs. The procedure for measurement and structural mean invariance were conducted to compare the impact of ED and SD on WSV among groups (RQ2 & 3) by examination of model stability and precision.

Study results showed that the precisions of the overall model fit indices TLI, CFI, and RMR were varying as a function of VTF, STV, h2, and their interaction. Whereas, the precisions of the overall model fit indices GFI, AGFI, and RMSEA were varying as a function of VTF, STV, and their interactions. Factorial invariance result revealed that stability and precision of the models were varying over increasingly levels of measurement and structural mean invariance as a function of VTF, STV, and their interactions. The researcher must determine the number of indicator variables that represent each latent trait and adequate sample size. This is a necessary consideration to obtain a precise and stable model.

Several restrictions were imposed on the study design: (a) Use of the normal distribution, and (b) complexity of the factor model. Future research should examine manipulating one or more of these design restrictions.

Access Setting

Dissertation-Open Access