Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors or dimensions that explain the patterns of correlations among a set of observed variables. It is often used in social sciences and psychology to study complex relationships among variables and to reduce the number of variables in a dataset.

Factor analysis assumes that the observed variables are related to one or more latent (unobserved) factors that can account for the observed correlations among the variables. The goal of factor analysis is to identify these underlying factors and to estimate the strength of their influence on each observed variable.

There are two main types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA is used to identify the underlying factors that explain the patterns of correlations among observed variables, while CFA is used to confirm a pre-specified factor structure.

To perform factor analysis in SPSS, you can use the Factor Analysis procedure. This procedure allows you to specify the variables to be analyzed, the method of factor extraction, and the number of factors to be extracted. The output of the Factor Analysis procedure includes factor loadings (i.e., estimates of the strength of the relationship between each observed variable and each underlying factor), communalities (i.e., estimates of the proportion of variance in each observed variable that is accounted for by the underlying factors), and other statistics.

Factor analysis can be useful in a variety of applications, such as identifying the underlying dimensions of a psychological test, reducing the number of variables in a dataset, and understanding the relationships among variables in a complex system. It is a powerful statistical tool that can help researchers to better understand the structure of their data and to test hypotheses about the underlying factors that explain patterns of correlation.

Factor Analysis steps

The steps involved in conducting a factor analysis using SPSS are as follows:

1. Determine the research question: Before beginning a factor analysis, it is important to determine the research question and the specific variables that will be analyzed.
2. Choose the appropriate type of factor analysis: Decide whether exploratory factor analysis (EFA) or confirmatory factor analysis (CFA) is most appropriate for the research question.
3. Select the variables: Choose the variables that will be included in the factor analysis. It is important to ensure that the variables are suitable for factor analysis, such as having a sufficient sample size and being normally distributed.
4. Determine the number of factors: Decide on the number of factors to extract. This can be done using various methods such as Kaiser’s criterion, scree plot, or parallel analysis.
5. Choose a factor extraction method: Select a factor extraction method, such as principal component analysis (PCA) or maximum likelihood (ML). The choice of method will depend on the research question and the characteristics of the data.
6. Conduct the factor analysis: Run the factor analysis in SPSS, specifying the chosen options such as the number of factors and factor extraction method.
7. Interpret the factor loadings: Review the factor loadings, which represent the strength and direction of the relationship between each variable and each factor.
8. Determine the number of factors to retain: Decide on the number of factors to retain, based on the factor loadings and the chosen method for determining the number of factors.
9. Interpret the factors: Interpret the factors, based on the variables that have high loadings on each factor. This involves naming each factor and interpreting the meaning of the factor based on the variables that contribute most strongly to it.
10. Assess the reliability and validity of the factors: Evaluate the reliability and validity of the factors, such as assessing the internal consistency of the items that load on each factor, and assessing whether the factors make theoretical sense based on prior research.