How to create factors from factanal?

Question

When performing a factor analysis using factanal the usual result is some loadings table plus several other information. Is there a direct way to use these loadings to create a

Answer 1

A similar question was asked on Psych SE.

There, I provide a function in case you want to generate factor scores for new data.

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I wrote the following function that takes the fit object returned by factanal and new data that you provide (e.g., a data frame or matrix with identical variable names).

score_new_data <- function(fit, data) {
    z <- as.matrix(scale(data[,row.names(fit$correlation)]))
    z %*% solve(fit$correlation, fit$loadings)
}

So for example,

bfi <- na.omit(bfi)
variables <- c("A1", "A2", "A3", "A4", "C1", "C2", "C3", "C4")
data <- bfi[,variables]
fit <- factanal(data, factors = 2, scores = "regression", rotation = "varimax")

This is a typical factor analysis.

And now supply some new data along with the fit of the factor analysis:

score_new_data(fit, data[1:5, ])

And it generates the following:

> score_new_data(fit, data[1:5, ])
         Factor1    Factor2
61623  1.5022427  0.5457393
61629 -0.6817812 -0.9755466
61634 -0.2901822  0.1051234
61640  0.5429929 -0.4955180
61661 -1.0732722  0.8202019