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Factor analysis, a statistical technique introduced by British psychologist Charles Spearman, belongs to the general linear model (GLM) set of procedures, hence requiring many of the same assumptions as multiple regressions. The two types of factor analysis are exploratory factor analysis (EFA) that is most commonly used and confrmatory factor analysis (CFA).
Often, direct measurement of underlying concepts (or latent variables) such as ”women’s empowerment,” “IQ_,” or ”leadership” is difficult. Instead, they are best approximated through other intercorrelated and quantifiable variables using factor analysis. In this approach, a large set of variables that tap into a latent concept are condensed into a smaller coherent array of variables that, even if correlated with the original variables, are orthogonal (or non-overlapping) with each other. To do so, factor analysis uses only the variance that a variable shares with the other variables, and divides it into factors that focus on what is common to all variables, with minimum loss of information. Thus, highly correlated variables (whether positively or negatively) are influenced by the same factor and thus, have high factor loading, while relatively un-correlated ones may be influenced by other factors.
Factor analysis generates a table where rows consist of the original set of variables, columns are the factors, and table cells consist of factor loadings or the correlation coefficients between the variables and factors. Analogous to Pearson’s r, the squared factor loading is the percentage of variance in the variable explained by a factor and is the basis for imputing a label. Because computers do not automatically label underlying factors, they must be tagged by a statistician, often making the process vulnerable to researcher subjectivity. Factor loadings may also be rotated to obtain a new factor structure. Finally, a factor’s eigenvalue is the sum of its squared factor loadings for all the variables, with a low eigenvalue indicating little contribution to the explanation of variances in the variables by the factor.
- Thompson, B. (2004) Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications. American Psychological Association, Washington, DC.