Principal Components Analysis ( Pca ) Versus Principal Axes Factors
2012 Words9 Pages
Principal Components Analysis (PCA) versus Principal Axes Factors (PAF) and Other Extraction Methods
Broadly, conducting factor analysis (FA) allows a researcher to analyze or interpret his or her data (e.g., measured variables) by reducing those variables into factors or components that underlie the structure or explain the greatest amount of variance in the data (Thompson, 2004). Thompson (2004) also tells us that FA may be used for many purposes, the most common of which is to uncover a relationship between variables, to develop “theory regarding the nature of constructs” (p. 5), or to evaluate the validity of observed scores. To accomplish this analysis, the researcher uses statistical software, such as the Statistical Package for…show more content… The present paper describes the most common factor extraction methodologies and highlights differences, similarities, and important considerations when conducting a factor analysis.
Terminology of Consequence
Before continuing, some basic terminology used in discussion of factor analysis and factor analytic methods should be clarified. Communality coefficients (h2), according to Thompson (2004), reveal “…how much of the variance of a given measured variable was useful in delineating the factors as a set” (p. 20). Alternately, communality coefficients represent the proportion of that variable’s variance that is explained by the underlying factor. Additionally, the communality coefficient can be thought of as a lower-bound estimate of a score’s reliability (Thompson, 2004).
Sources of error and their effects must be understood as well. Sampling error is error unique to each sample drawn or selected; so, the sampling error in two different samples are each different