*! version 1.0 10March2015

help fsdet

Title

fsdet -- Factor score determinacy coefficient

Description

fsdet computes determinacy coefficient for a factor score obtained from a common
factor model (exploratory or confirmatory factor analysis) using the following
formula to find in Beauducel's (2011) work:

mat A = Phi*Lambda'*inv(Sigma)*Lambda*Phi
(Phi, Lambda and Sigma represent their respective matrices)
sqrt(A[diag])

The value resulting from this formula represents the correlation between the factor
score estimate and its factor. According to Gorsuch (1983) this coefficient should
be >= 0.90 if the factor score is to be used as a substitute for the factor itself.

KW: factor
KW: score
KW: indeterminacy

Examples

. use http://www.ats.ucla.edu/stat/stata/output/m255, clear

. keep item13 item14 item15 item16 item27 item39

. qui factor item13 item14 item15 item16 item27 item39, factors(2) (without rotation)

. fsdet

. qui factor item13 item14 item15 item16 item27 item39, ml factors(2)

. qui rotate, equamax (orthogonal rotation)

. fsdet

. qui factor item13 item14 item15 item16 item27 item39, ipf factors(2)

. qui rotate, promax (oblique rotation)

. fsdet

. qui sem (F1->item13 item14 item15 item16) (F2->item27 item39) (rotation is not needed)

. fsdet

Author

Mehmet Mehmetoglu
Department of Psychology
Norwegian University of Science and Technology
mehmetm@svt.ntnu.no

References

Beauducel, A. (2011). Indeterminacy of Factor Score Estimates In Slightly
Misspecified Confirmatory Factor Models. Journal of Modern Applied Statistical
Methods, 10(2), 583-598.

Gorsuch, R. L. (1983). Factor analysis. Hillsdale, N.J.: L. Erlbaum Associates.