New Developments in Factor Score Regression: Fit Indices and a Model Comparison Test

Abstract

Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the model. In this article, we propose fit indices for FSR that can be used to inspect the model fit. We also introduce a model comparison test based on one of these newly proposed fit indices that can be used for inference of the estimators on the regression coefficients. In a simulation study we compare FSR with Croon’s corrections and structural equation modeling in terms of bias of the regression coefficients, Type I error rate and power.

Thinking twice about sum scores

“…In previous examples in this paper, we use the maximum a posteriori method as implemented by Mplus (MAP; also known as the regression method when the items are continuous; Thomson, 1934;Thurstone, 1935). With the MAP method, the covariance matrix of the factor scores will not be identical to the covariance matrix of the latent variables (Croon, 2002), so corrections are needed to accurately estimate parameters and model fit (Devlieger & Rosseel, 2017;Devlieger, Talloen, & Rosseel, 2019). Alternatively, Skrondal and Laake (2001) show that MAP factor scores are better when the latent variable is intended as a predictor, but that the Bartlett scoring method (Bartlett, 1937;Thomson, 1938) is preferable when the latent variable is intended as an outcome and suggest that different scoring methods be used for different factors, depending on their role in the analysis in the second stage.…”

“…Multistage approaches possess the added benefit that the measurement model is estimated in a separate first stage, meaning that misspecifications do not permeate across different parts of the model (Hayes & Usami, 2020b) and that estimation is more stable with smaller sample sizes (Rosseel, 2020). The multistage approach has been recently been extended to fit measures (Devlieger et al, 2019), path analysis (Devlieger & Rosseel, 2017), and multilevel settings (Devlieger & Rosseel, 2019), giving advantages to multistage approaches broader coverage and narrowing the gap between their performance and the performance of the simultaneous approach.…”

Latent Logistic Interaction Modeling: A Simulation and Empirical Illustration of Type D Personality

“…First, they often require a large sample size, especially when the models become more complex. Furthermore, because latent variables typically estimate all the parameters in a single step, increasingly complex models can produce unstable parameter estimates (Devlieger et al, 2019). To overcome these problems, researchers may use a two-step approach, called factor score regression (Lu et al, 2011).…”

Problematika měření socio-emočních schopností u dětí: srovnatelnost faktorové struktury posuzovací škály mezi otci, matkami a pedagogy

“…Na základě výše uvedené hypotézy jsme přitom předpokládali, že vzorek otců na rozdíl od vzorku učitelů poskytne akceptovatelný fit. Analýzy jsme provedli v balíčku lavaan (Devliegerh et al, 2019) Jak jsme předpokládali, model vykazuje akceptovatelné (nikoli však dokonalé) parametry fitu na vzorku otců, a to především s přihlédnutím k intervalu spolehlivosti okolo RMSEA (0,07; 0,09). Jak je patrné z nízké hodnoty CFI, hodnoty interkorelací nejsou tak vysoké, jak bychom předpokládali.…”