Conduct and Interpret a Factor AnalysisWhat is the Factor Analysis?The Factor Analysis is an explorative analysis. Much like the cluster analysis grouping similar cases, the factor analysis groups similar variables into dimensions. This process is also called identifying latent variables. Since factor analysis is an explorative analysis it does not distinguish between independent and dependent variables.
Factor Analysis reduces the information in a model by reducing the dimensions of the observations. This procedure has multiple purposes. It can be used to simplify the data, for example reducing the number of variables in predictive regression models. If factor analysis is used for these purposes, most often factors are rotated after extraction. Factor analysis has several different rotation methods—some of them ensure that the factors are orthogonal. Then the correlation coefficient between two factors is zero, which eliminates problems of multicollinearity in regression analysis.
Factor analysis is also used in theory testing to verify scale construction and operationalizations. In such a case, the scale is specified upfront and we know that a certain subset of the scale represents an independent dimension within this scale. This form of factor analysis is most often used in structural equation modeling and is referred to as Confirmatory Factor Analysis. For example, we know that the questions pertaining to the big five personality traits cover all five dimensions N, A, O, and I. If we want to build a regression model that predicts the influence of the personality dimensions on an outcome variable, for example anxiety in public places, we would start to model a confirmatory factor analysis of the twenty questionnaire items that load onto five factors and then regress onto an outcome variable.
Factor analysis can also be used to construct indices. The most common way to construct an index is to simply sum up the items in an index. In some contexts, however, some variables might have a greater explanatory power than others. Also sometimes similar questions correlate so much that we can justify dropping one of the questions completely to shorten questionnaires. In such a case, we can use factor analysis to identify the weight each variable should have in the index.
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