**ERIC Number:**ED395039

**Record Type:**RIE

**Publication Date:**1996-Jan-27

**Pages:**22

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

Mathematical Models Underlying Common Factor Analysis: An Introductory Primer.

Hester, Yvette

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique yields an accurate analysis, an examination of the mathematical models underlying the procedure is necessary. Execution of factor analysis by the Statistical Analysis System and the Statistical Package for the Social Sciences will then not be a "black box." Mathematical models underlying true factor analysis and principal components analysis are presented and discussed. An explanation of the terms and basic differences is given in terms of the mathematical models. A small, heuristic example is included to illustrate the concepts and matrix algebra procedures involved in the factor analysis data reduction technique. An appendix presents commands for the MAPLE computer algebra system. (Contains 2 tables, 2 figures, and 10 references.) (Author/SLD)

Descriptors: Factor Analysis, Factor Structure, Heuristics, Mathematical Models, Matrices, Research Methodology

**Publication Type:**Reports - Evaluative; Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**Data Reduction Methods; Statistical Analysis System; Statistical Package for the Social Sciences

**Note:**Paper presented at the Annual Meeting of the Southwest Educational Research Association (New Orleans, LA, January 25-27, 1996).