What multivariate technique identifies whether the correlations among a set of observed variables arise from one or more latent variables?

What multivariate technique identifies whether the correlations among a set of observed variables arise from one or more latent variables?

• A. Factor analysis
• B. Regression
• C. Cluster analysis
• D. Discriminant analysis

Answer: (A)

The idea being tested is how to uncover underlying, unobserved constructs that explain the pattern of correlations among observed measures. Factor analysis is the method that models these correlations with a smaller number of latent variables (factors). By looking at how strongly each observed variable loads on the latent factors, you can determine whether a single latent variable accounts for most of the shared variance or whether several latent variables are needed. This approach directly addresses whether one or more latent variables give rise to the observed relationships, and it’s also used to reduce dimensionality and reveal underlying structure. The other techniques don’t focus on hidden causes of correlations: regression aims to predict one variable from others, cluster analysis groups observations by similarity, and discriminant analysis classifies cases into predefined groups.

The idea being tested is how to uncover underlying, unobserved constructs that explain the pattern of correlations among observed measures. Factor analysis is the method that models these correlations with a smaller number of latent variables (factors). By looking at how strongly each observed variable loads on the latent factors, you can determine whether a single latent variable accounts for most of the shared variance or whether several latent variables are needed. This approach directly addresses whether one or more latent variables give rise to the observed relationships, and it’s also used to reduce dimensionality and reveal underlying structure. The other techniques don’t focus on hidden causes of correlations: regression aims to predict one variable from others, cluster analysis groups observations by similarity, and discriminant analysis classifies cases into predefined groups.