(Exploratory) Factor Analysis in Personality Psychology
© 2005
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There are countless numbers of words and phrases to describe people's personality. If a personality psychologist wanted to understand a particular person's personality, it would be an overwhelming task to figure out how much each of these countless numbers of words and phrases was characteristic of that person. To make life easier, personality psychologists commonly use a statistical tool to simplify vast amounts of information by lumping similar information into clusters. This tool is a procedure known as (exploratory) factor analysis.
The basic idea behind factor analysis is quite simple. If two or more characteristics correlate, they may reflect a shared underlying trait. We could say then that, patterns of correlations reveal the trait dimensions that lie beneath the measured qualities (Tabachnik & Fidell, 2005). Factor analysis is a more complex version of a correlation. Instead of looking at the correlation between just two variables, factor analysis uses a large number of correlations among a large number of variables (Kline, 1994).
In order to conduct factor analysis, we first collect data on many variables, across large numbers of people. The data can be collected in a myriad of ways. They can be derived from paper and pencil questionnaires rating ourselves on various personality characteristics. They can also be derived from behavior ratings made by objective observers. We can also obtain data about people from their family members, asking them about what they think about that those people. As long as the same data is collected from everybody participating, we can use that data for factor analysis.
Once we collect the data, we can calculate the correlations between every possible pair of variables. The researcher then examines the eigenvalues, among other things, to decide on the number of factors the data should be reduced to. Eigenvalues are values corresponding to how much accuracy we would lose if we simplified the data by lumping it to a specific number of factors. Although the point of this analysis is to simplify the data, there is a cost to simplifying data. By simplifying data, we lose the details and therefore we lose accuracy. The smaller number of factors we reduce the data to, the more we simplify the data, but the more accuracy we lose. Eigenvalues, among other things, allow us to conduct a cost-benefit analysis regarding how much we should simplify the data. After determining the number of factors the data should be reduced to, the set of correlations is then put through a procedure called factor extraction. This procedure allows us to reduce the large number of variables to a smaller set of higher-order variables that we call "factors" (Kline, 1994).
Once the factors are extracted, we end up with a factor structure. The factor structure consists of numerical figures known as factor loadings. It may be useful to think of factor loadings as numbers representing how much each variable correlates with particular "factors" (Gorsuch, 1983). Variables that correlate highly with the factor are said to "load on" that factor. Variables that do not correlate with the factor are said not to load on it. The variables that load on the factor allow us to figure out the underlying meaning of the factor (i.e., what do all of the variables loading on that factor have in common?).
The final step in this process involves labeling the factors. Because a factor is defined by variables that load on it, we must decide on a label to characterize this factor as closely as possible to the content of those variables (especially to the variables with the highest factor loadings). When we use factor analysis in personality research, the factor is typically viewed as a reflection of a personality trait. The label for the factor is the name of the personality trait. Choosing representative labels for the factors is extremely important. Many researchers in Psychology use factor analysis to construct and refine personality tests. Because we often forget that the label of a factor is merely something we have inferred from a cluster of correlating variables, we assume that personality test scores directly reflect the person's personality traits with little to no error. Therefore, carelessness in labeling a factor may lead to misunderstandings of test scores for thousands of people who take that personality test.
To sum up, factor analysis is a very useful statistical tool in the trait approach to personality psychology. Perhaps we could say that it has three very important functions in the study of personality. It simplifies the multiple ways we can understand a person by reducing the information to a smaller set of personality traits. Second, it provides a basis for thinking that perhaps some traits (those that form large highly correlating clusters) are more important than others. Third, factor analysis is extremely useful in creating personality measures. We keep test items (i.e., variables) that load highly and discard items that don't load highly on specific factors. As researchers continue to create new test items, the items that do not load highly on certain factors are replaced by better ones.
Factor analysis is a very useful tool. However, please keep in mind that it is only a tool. Factor analysis can only tell us about the variables we put into it. Thus, the factors that emerge depend largely on the kind of data collected or the variables that were included in the analysis to begin with (Kline, 1994).
References
Gorsuch, R. L. (1983). Factor analysis (2nd ed.). Hillsdale, NJ: Erlbaum.
Kline, P. (1994). An easy guide to factor analysis. New York: Routledge.
Tabachnik, B. G., & Fidell, L. S. (2005). Using multivariate statistics (5th ed.). Needham Heights, MA: Allyn and Bacon.