Chapter 13 Exploratory Factor Analysis
LEARNING OUTCOMES
- Identify and compare the key features of formative and reflective models.
- Evaluate the differences between Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA).
- Apply R to tidy and organize the data set before estimating the scale's correlation matrix and generating data visualizations.
- Apply factor extraction and rotation techniques to generate the scale's simplest factorial structure.
- Appraise the outputs of the EFA model, interpret the results, and generate plots showing the factorial structure of a scale.
Multivariate statistics are a set of statistical techniques aimed at analyzing data when we have many independent variables and/or many dependent variables correlated with one another to varying degrees (Tabachnick & Fidell, 2013). The variables included in our research design might be related via dependence or interdependence models (Hair et al., 2006).
Dependence methods attempt to predict the outcome (i.e., dependent variable) using one or several predictors (i.e., independent variables). Thus, some variables will be retained in the final model allowing us to explain, to a certain degree, the outcome. Dependence methods are usually classified as a function of the number of dependent variables being measured (i.e., one dependent variable versus two or more) and the nature of the measurement scales and predictors (i.e., nominal, ordinal, or quantitative data).
For instance, to estimate a predictive model when the outcome is one quantitative variable and the explanatory variables are quantitative as well, we use a multiple regression analysis technique (General Linear Model).
\[\begin{aligned} Y = \beta_{0} \ + \beta_{1}X_{1} \ + \beta_{2}X_{2} \ + \beta_{3}X_{1}X_{2} + \epsilon \\ \end{aligned}\]
On the other hand, to estimate a predictive model when we have several quantitative outcomes (i.e., several dependent variables) and the explanatory variables are quantitative as well, we will use a Structural Equation Modeling (SEM) approach.
Interdependence methods are aimed at finding the underlying structure of a set of variables, cases, or objects that are analyzed simultaneously. As Table 13.1 shows, these multivariate techniques are usually classified by the nature of the correlated variables (variables, cases, or objects) and by the type of data that we use (quantitative versus categorical data).
| Relationships among | Data | Statistical technique |
|---|---|---|
| Variables | Quantitative | Principal components |
| Factor analysis | ||
| Cluster analysis | ||
| Cases | Quantitative | Cluster analysis |
| Objects | Quantitative | Multidimensional scaling |
| Categorical | Correspondence analysis |
Interdependence methods could be used for three main purposes related to specific multivariate techniques:
Data reduction: We are interested in the relationship among variables by simplifying the structure of the phenomenon that we study (e.g., job burnout). To do so, we use Principal Components Analysis (PCA) and Factor Analysis (FA).
Grouping cases and variables: We are interested in clustering objects and variables by similarity. To accomplish this goal, we use Cluster Analysis.
Structure of objects: We are interested in exploring the underlying structure of objects. We use Multidimensional Scaling for quantitative data and Correspondence Analysis for categorical data.