Date of Award

5-2004

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Daniel C. Coster

Abstract

Objective: To access the robustness of factor analyses when the data does not conform to standard parametric requirements.

Methods: Data were simulated in package R. Maximum likelihood was used to fit and assess the factor models. Chi-square statistics were obtained to test hypotheses about the correct number of factors in simulated settings where the true number of factors was known. The number of true factors varied between 1 and 3; the number of observed variables was either 6 (for 1 factor) or 3 per factor for 2 or more factors.

Results: With standard normal factor populations, and normal errors added to each observed variable, the standard MLE statistics and chi-squared tests gave expected results, in terms of false rejection (Type I Error) rates, with sample size set at 100, and either 3 or 6 observed variables per factor. For normal factors, but non-normal noise added to observed variables, the robustness of the chi-square statistics varied from excellent to modest, depending on the extent to which the noise distribution varied from normal.

Conclusions: When the sample size n=100, the robustness of the chi-square statistics for the normal data added with gamma or Poisson noise and the discrete uniform data added with discrete uniform noise are excellent, and those for the normal data with exponential or lognormal noise are pretty remarkable, too. However, when the sample size decreased to 25, the robustness for all the data become very modest; Among them, the robustness for the normal data added with gamma and Poisson are better than the others, and that for the discrete uniform data with discrete uniform case is next to them, the chi-square statistics for the normal data added with exponential and lognormal have the modest robustness.

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