Inference and Interval Estimation Methods for Indirect Effects With Latent Variable Models
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Bibliographic record
Abstract
AbstractAlthough much is known about the performance of recent methods for inference and interval estimation for indirect or mediated effects with observed variables, little is known about their performance in latent variable models. This article presents an extensive Monte Carlo study of 11 different leading or popular methods adapted to structural equation models with latent variables. Manipulated variables included sample size, number of indicators per latent variable, internal consistency per set of indicators, and 16 different path combinations between latent variables. Results indicate that some popular or previously recommended methods, such as the bias-corrected bootstrap and asymptotic standard errors had poorly calibrated Type I error and coverage rates in some conditions. Likelihood-based confidence intervals, the distribution of the product method, and the percentile bootstrap emerged as leading methods for both interval estimation and inference, whereas joint significance tests and the partial posterior method performed well for inference.Keywords: indirect effectlatent variablesmediation analysisstructural equation modeling Notes1 More general representations of all possible indirect effects among latent variables are given by Bollen (Citation1987, Citation1989): indirect effects of endogenous latent variables on other endogenous latent variables, , and indirect effects of exogenous latent variables on the endogenous latent variables, , where the unsubscripted is an identity matrix.2 The full model implied covariance matrix can be obtained from and is given in detail by Bollen (Citation1989).3 Note that previous instantiations of this method used a different equation to convert these quantiles back to the original metric. Specifically, Biesanz et al. (Citation2010) reported the distribution of the product as based on an R macro Prodclin.r for the program PRODCLIN (MacKinnon, Fritz, et al., Citation2007) formerly available from http://www.public.asu.edu/˜davidpm/ripl/Prodclin/. The formulation we report here is implemented in RMediation and matches Biesanz et al.'s (Citation2010) DPR or revised distribution of the product method.4 A normal approximation to the posterior distributions of these parameters is not unreasonable given that under noninformative priors many posterior distributions often asymptotically approach normality because the prior will have increasingly less effect on the estimate (e.g., Gelman, Carlin, Stern, & Rubin, Citation1995).5 Although we note there are no consensual standards for effect sizes in mediation analysis (Preacher & Kelley, Citation2011), we report population for all path combinations as recommended by these authors as well as (see also Fairchild, MacKinnon, Taborga, & Taylor, Citation2009): = .14, = .14, = .02, = .0004; = .14, = .39, = .06, = .003; = .14, = .59, = .10, = .007; = .39, = .14, = .05, = .003; = .39, = .39, = .15, = .02; = .39, = .59, = .24, = .05; = .59, = .14, = .07, = .004; = .59, = .39, = .19, = .04; and = .59, = .59, = .31, = .09. Both effect sizes are zero when either path is zero.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it