What is a single score from an individual representing their performance on a latent variable, computed by weighting variable scores by their factor loadings and summing?

What is a single score from an individual representing their performance on a latent variable, computed by weighting variable scores by their factor loadings and summing?

• A. Factor loading
• B. Factor transformation matrix, ∧
• C. Factor score
• D. Factorial ANOVA

Answer: (C)

A factor score is a single numeric estimate of a person’s position on a latent variable, derived from multiple observed measures by weighting each observed score by its relationship to the latent factor and then summing those weighted scores. In factor analysis, each observed variable has a factor loading that indicates how strongly it relates to the latent construct. To get the factor score for an individual, you multiply each observed score by its loading (or by the corresponding scoring weights) and add them up, yielding one overall score that represents that person’s level on the latent variable. Understanding the other terms helps place this in context: a factor loading is the weight linking one observed variable to the factor, not the single overall score. The factor transformation matrix is the collection of weights used to compute scores from all variables, not the single score itself. Factorial ANOVA is a different analysis that deals with categorical factors and their interactions, not latent variables.

A factor score is a single numeric estimate of a person’s position on a latent variable, derived from multiple observed measures by weighting each observed score by its relationship to the latent factor and then summing those weighted scores. In factor analysis, each observed variable has a factor loading that indicates how strongly it relates to the latent construct. To get the factor score for an individual, you multiply each observed score by its loading (or by the corresponding scoring weights) and add them up, yielding one overall score that represents that person’s level on the latent variable.

Understanding the other terms helps place this in context: a factor loading is the weight linking one observed variable to the factor, not the single overall score. The factor transformation matrix is the collection of weights used to compute scores from all variables, not the single score itself. Factorial ANOVA is a different analysis that deals with categorical factors and their interactions, not latent variables.