Model Specification Searches in Structural Equation Modeling with R

“How Well Does Your Structural Equation Model Fit Your Data?”: Is Marcoulides and Yuan’s Equivalence Test the Answer?

“…Such specification searches have long been known to produce results that subsequent research typically fails to replicate (see MacCallum, 1986;MacCallum et al, 1992). A recent increase in dedicated software programs that automate specification searches (e.g., Brandmaier et al, 2016;Marcoulides and Falk, 2018;Gates et al, 2019) for the purpose of recommending additional model specification changes that would enhance fit exacerbates the concern that researchers are engaging in "HARKing" (hypothesizing after results are known), theoretically 6 Specifically, for the misspecified model shown in Figure 1, both Mplus and AMOS define a null model's df as the differences in df between the alternative (H A :) and null (H 0 :) baseline models as follows. In Mplus, the H A : baseline model has df values that are the sum of: 1) four variances, four means, and six covariances (14 total) among the response variables (i.e., Video Viewing, MLQ Self-Efficacy Posttest, MLQ Task Value Posttest, and Lab Report: Discussion), plus 2) all possible covariances between MLQ Self-Efficacy Posttest, MLQ Task Value Posttest, and Lab Report: Discussion with Video Viewing (six) plus all possible covariances between MLQ Self-Efficacy pretest, MLQ Task Value pretest, and Lawson's test of Scientific Reasoning with Video Viewing (six; 12 total) for an H A : baseline model total of df = (14 + 12) = 26.…”

Causality on cross-sectional data: Stable specification search in constrained structural equation modeling

“…An alternative approach is exploratory search in which no prior hypothesis is specified. Typical approaches in the literature for addressing the exponential search space include tabu search [18], genetic algorithms [19], [20], ant colony optimization [21], and others [22], [23], [24].…”

Regularized Structural Equation Modeling

“…Model modification with the use of modification indexes might work well if the number of misspecifications is small, but when there is a higher degree of uncertainty regarding the model structure, global search strategies are needed. This has led to the proposal of heuristic search algorithms such as ant colony optimization (Leite, Huang, & Marcoulides, 2008; Marcoulides & Drezner, 2003), genetic algorithm (Marcoulides & Drezner, 2001), and tabu search (Marcoulides, Drezner, & Schumacker, 1998; for overview, see Marcoulides & Ing, 2012). …”