In memory of Dr. Dennis John McFarland, who passed away recently, our objective is to continue his efforts to compare psychometric networks and latent variable models statistically. We do so by providing a commentary on his latest work, which he encouraged us to write, shortly before his death. We first discuss the statistical procedure McFarland used, which involved structural equation modeling (SEM) in standard SEM software. Next, we evaluate the penta-factor model of intelligence. We conclude that (1) standard SEM software is not suitable for the comparison of psychometric networks with latent variable models, and (2) the penta-factor model of intelligence is only of limited value, as it is nonidentified. We conclude with a reanalysis of the Wechlser Adult Intelligence Scale data McFarland discussed and illustrate how network and latent variable models can be compared using the recently developed R package Psychonetrics. Of substantive theoretical interest, the results support a network interpretation of general intelligence. A novel empirical finding is that networks of intelligence replicate over standardization samples.

Meta-analytic structural equation modeling (MASEM) is a relatively new method in which effect sizes of different independent studies between multiple variables are typically first pooled into a matrix and next analyzed using structural equation modeling. While its popularity is increasing, there are issues still to be resolved, such as how to deal with primary studies in which variables have been artificially dichotomized. To be able to advise researchers who apply MASEM and need to deal with this issue, we performed two simulation studies using random-effects two stage structural equation modeling. We simulated data according to a full and partial mediation model and systematically varied the size of one (standardized) path coefficient (beta(MX) = .16, beta(MX) = .23, beta(MX) =.33), the percentage of dichotomization (25%, 75%, 100%), and the cut-off point of dichotomization (.5,.1). We analyzed the simulated datasets in two different ways, namely, by using (1) the pointbiserial and (2) the biserial correlation as effect size between the artificially dichotomized predictor and continuous variables. The results of these simulation studies indicate that the biserial correlation is the most appropriate effect size to use, as it provides unbiased estimates of the path coefficients in the population.

Bi-factor models of intelligence tend to outperform higher-order g factor models statistically. The literature provides the following rivalling explanations: (i) the bi-factor model represents or closely approximates the true underlying data-generating mechanism; (ii) fit indices are biased against the higher-order g factor model in favor of the bi-factor model; (iii) a network structure underlies the data. We used a Monte Carlo simulation to investigate the validity and plausibility of each of these explanations, while controlling for their rivals. To this end, we generated 1000 sample data sets according to three competing models—a bi-factor model, a (nested) higher-order factor model, and a (non-nested) network model—with 3000 data sets in total. Parameter values were based on the confirmatory analyses of the Wechsler Scale of Intelligence IV. On each simulated data set, we (1) refitted the three models, (2) obtained the fit statistics, and (3) performed a model selection procedure. We found no evidence that the fit measures themselves are biased, but conclude that biased inferences can arise when approximate or incremental fit indices are used as if they were relative fit measures. The validity of the network explanation was established while the outcomes of our network simulations were consistent with previously reported empirical findings, indicating that the network explanation is also a plausible one. The empirical findings are inconsistent with the (also validated) hypothesis that a bi-factor model is the true model. In future model selection procedures, we recommend that researchers consider network models of intelligence, especially when a higher-order g factor model is rejected in favor of a bi-factor model.

Meta-analytic structural equation modeling (MASEM) allows a researcher to simultaneously examine multiple relations among variables by fitting a structural equation model to summary statistics from multiple studies. Consider, for example, a mediation model with a predictor (X), mediator (M), and outcome variable (Y). In such a model, X can be a dichotomous variable, allowing researchers to examine the direct and indirect effects of an intervention as in randomized controlled trials (RCTs). However, the natural choice of a meta-analysis of RCTs would involve standardized mean differences as effect sizes, whereas MASEM requires correlation matrices as input. This can be solved by converting standardized mean differences (Cohen's d or Hedges' g) to point-biserial correlations (r_pb). Possible conversion formulas vary across publications and conversion tools, and it is unclear which one is most appropriate for use in MASEM. The aim of this article is to describe and evaluate several conversions of standardized mean differences to point-biserial correlations in the context of RCTs. We investigate the impact of the usage of various conversions on MASEM parameter estimation using the R package metaSEM in a simulation study, varying the ratio of group sample sizes, number of primary studies, sample sizes, and missingness. The results show that a relatively unknown d-to-r_pb conversion generally performs best. However, this conversion formula is not implemented in the mainstream conversion tools. We developed a user-friendly web application entitled Effect Size Calculator and Converter (https://hdejonge.shinyapps.io/ESCACO) that converts the user's primary study statistics into an effect size suitable for use in MASEM. (PsycInfo Database Record (c) 2025 APA, all rights reserved).