Faktoreerub

Faktoreerub is a hypothetical concept used in this article to describe a measure of how much of the variation in multivariate data is explained by a specified set of latent factors when estimated with robust statistical methods. The term is not part of an established literature, but is presented here to illustrate a general principle of model fit in factor-based analyses.

Definition: By definition, faktoreerub is the ratio of the variance explained by the factor reconstruction to the total variance of the observed data, after centering and standardization. Conceptually it is similar to explained variance or R-squared for a factor model, with emphasis on latent factors and robust estimation.

Calculation: To compute faktoreerub, standardize the data, fit a factor model with a chosen number of factors using a robust estimator, obtain factor scores and loadings, reconstruct X_hat = F Λ^T, and compute the variance of X_hat (usually the trace of its covariance). Faktoreerub equals trace(var(X_hat)) / trace(var(X)).

Interpretation and use: Values near 1 indicate the factors capture most of the data's variability under the model; values near 0 indicate little explanatory power. The metric depends on the number of factors, scaling, and model assumptions, and is best used with cross-validation or information criteria.

Relation and limitations: Faktoreerub relates to explained variance, R-squared, and goodness of fit in factor models, but differs from principal components analysis by focusing on latent factors and robust estimation. It is sensitive to misspecification and sample size, so results should be interpreted cautiously.