How can you identify latent variables in customer satisfaction data using factor analysis?

1 What is factor analysis?

Factor analysis is a method of data reduction that can help you find patterns and structure in a large set of variables. It can help you answer questions such as: What are the main factors that affect customer satisfaction? How are these factors related to each other? How much variance in customer satisfaction can be explained by these factors? Factor analysis can also help you simplify your data by creating new variables, called factors, that represent the common variance among a group of original variables.

2 How to prepare your data for factor analysis?

Before you can perform factor analysis, you need to prepare your data and check some assumptions. First, you need to have a dataset that contains multiple variables that measure different aspects of customer satisfaction, such as service quality, product quality, price, loyalty, etc. Second, you need to check if your data is suitable for factor analysis by testing the correlation among the variables, the sample size, and the normality of the distribution. You can use tools such as the correlation matrix, the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy, and the Bartlett's test of sphericity to assess these criteria.

3 How to choose the number of factors?

One of the most important decisions in factor analysis is how many factors to extract from your data. There are different methods to determine the optimal number of factors, such as the eigenvalue criterion, the scree plot, and the parallel analysis. The eigenvalue criterion suggests that you should retain only the factors that have an eigenvalue greater than 1, which means that they explain more variance than a single variable. The scree plot is a graph that shows the eigenvalues of each factor in descending order, and you should look for a point where the curve flattens out, indicating the point of diminishing returns. The parallel analysis is a more rigorous method that compares the eigenvalues of your data with those of a random dataset, and you should retain only the factors that have larger eigenvalues than the random ones.

4 How to rotate and interpret the factors?

After you have extracted the factors, you need to rotate them to make them more meaningful and easier to interpret. Rotation is a process that changes the orientation of the factors without altering their statistical properties. There are two main types of rotation: orthogonal and oblique. Orthogonal rotation assumes that the factors are independent of each other, while oblique rotation allows for some correlation among the factors. The most common orthogonal rotation method is varimax, which maximizes the variance of each factor. The most common oblique rotation method is promax, which produces a simpler factor structure. To interpret the factors, you need to look at the factor loadings, which are the correlations between the variables and the factors. You can assign a label or a name to each factor based on the variables that have high loadings on it.

5 How to validate and use the factors?

The final step in factor analysis is to validate and use the factors for your analysis. To validate the factors, you need to assess their reliability and validity. Reliability refers to the consistency and stability of the factors, and you can measure it using the Cronbach's alpha coefficient, which should be above 0.7 for each factor. Validity refers to the accuracy and relevance of the factors, and you can measure it using different methods, such as convergent validity, discriminant validity, and criterion validity. To use the factors, you can create factor scores, which are the weighted averages of the variables that belong to each factor. You can use these factor scores as new variables for further analysis, such as regression, clustering, or classification.

6 Here’s what else to consider

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