Urbano Lorenzo-Seva, 2024
Mild-restricted factor analysis is a method for computing confirmatory factor analysis (CFA). The aim in CFA is to assess if a hypothesized factor model can be expected to be true at the population level.
In CFA, it is usual that each variable in the model is expected to be a pure indicator of a factor at the population level: a variable that shows a single salient loading value related to the factor, and any other loading value of the variable is exactly zero. Frequently, even if a variable is strongly related to a single factor (i.e., the variable has only a large loading value associated with a factor in the model), it cannot be considered a pure indicator because the other loading values of the variable are not exactly zero, but close to zero. A variable that meets this situation can be said to be a close indicator of a factor.
From a practical point of view, researchers tend to interpret close indicators as if they were pure indicators (i.e., secondary loadings close to zero are not given a substantive interpretation). It means that when applied researchers propose a factor model based on pure indicators, they would also accept a factor model based on close indicators. However, a CFA based on restricted factor model will reject a factor model based on pure indicators if the condition related to the secondary loadings values equal to zero is not meet.
The same reasoning can be applied to other model parameters usually expected be zero at the population level: inter-factor correlations and correlated errors. A CFA based on mild-restricted factor analysis helps to assess if a factor model can be expected to exists at population level even if the variables are close indicators, or none the inter-factor correlations or the correlated errors are not exactly zero.
Mild-restricted factor analysis is a three-step method:
- First, all the parameters of the model are estimated using unrestricted factor analysis based on Morgana.
- Second, parameters are restricted to the proposed values in the hypothetical model.
- And, third, the goodness-of-fit of the model is computed using the chi-square test statistic scaled with LOSEFER.
We implemented Mild-Restricted Factor Analysis method in R code:
Download MildRectrictedFactorAnalysis.zip
Here you have the manual to use our R code: