This is a package for Bayesian meta-analytic structural equation models (MASEM, Cheung and Chan 2009), specifically meta-analysis of confirmatory factor models. The package fits fixed-, random- and dependent-samples MASEMs.
Features of bayesianmasem include:
- Uses lavaan-style syntax for model specification
- Fits fixed-effects, random-effects and dependent-samples MASEM
- Allows fixing loadings to known values or constraining loadings equal
- Estimates minor factor influences (Uanhoro 2023), i.e. full residual correlation matrix reflecting misspecification in the true shared correlation matrix
- Ability to relax simple-structure, i.e. allow for estimation of all cross-loadings using shrinkage-to-zero priors leading to more accurate estimates of interfactor correlations.
- Built atop Stan (an efficient Bayesian sampler).
bayesianmasem is hosted on GitHub, so we need the remotes package to
install it. We also need to install the cmdstanr package and CmdStan
in order to use Stan.
Instructions:
install.packages("remotes") # install remotes
# next install cmdstanr and CmdStan:
install.packages(
"cmdstanr",
repos = c("https://mc-stan.org/r-packages/", getOption("repos"))
)
cmdstanr::check_cmdstan_toolchain(fix = TRUE)
cmdstanr::install_cmdstan()
# Then finally bayesianmasem:
remotes::install_github("jamesuanhoro/bayesianmasem")We use the example in the Norton data (Norton et al. 2013). Let’s fit the Zigmond-Snaith anxiety-depression model to the HADS assuming a positive factor on select items.
model_syntax <- "
anxiety =~ x1 + x3 + x5 + x7 + x9 + x11 + x13
depression =~ x2 + x4 + x6 + x8 + x10 + x12 + x14
pos =~ a * x2 + a * x4 + a * x6 + a * x7 + a * x12 + a * x14
pos =~ 0 * x1 + 0 * x3 + 0 * x5 + 0 * x8 + 0 * x9 + 0 * x10 + 0 * x11 + 0 * x13
pos ~~ 0 * anxiety + 0 * depression
"There are 14 items. The model assumes odd-numbered items load onto anxiety, even-numbered item load on depression. Items 2, 4, 6, 7, 12, and 14 load on a positive-wording factor, i.e. a method effect. We assume the loadings on this positive factor to be equal, and this factor assumed uncorrelated to the substantive factors. We also specify that other items have a fixed loading of 0 on this positive factor – this helps when we relax simple structure, we want to ensure the positive method factor has 0 loading on other items.
We can fit a random-effects model to the input correlation matrices and
provide sample size information. The Norton13 data come from the
metaSEM package (Cheung
2015):
fit_ad <- bmasem(
model_syntax,
sample_cov = Norton13$data, sample_nobs = Norton13$n,
method = "normal", simple_struc = FALSE
)Setting method = "normal" implies the true correlation matrix
underlying the data differs from the structured correlation matrix due
to minor factors. Setting simple_struc = FALSE allows for all
cross-loadings to be estimated using priors that attempt to shrink the
cross-loadings to 0. Parameters for all functions including bmasem()
are documented: ?bmasem.
Cheung, Mike W.-L. 2015. “metaSEM: An r Package for Meta-Analysis Using Structural Equation Modeling.” Frontiers in Psychology 5 (1521). https://doi.org/10.3389/fpsyg.2014.01521.
Cheung, Mike W.-L., and Wai Chan. 2009. “A Two-Stage Approach to Synthesizing Covariance Matrices in Meta-Analytic Structural Equation Modeling.” Structural Equation Modeling: A Multidisciplinary Journal 16 (1): 28–53. https://doi.org/10.1080/10705510802561295.
Norton, Sam, Theodore Cosco, Frank Doyle, John Done, and Amanda Sacker. 2013. “The Hospital Anxiety and Depression Scale: A Meta Confirmatory Factor Analysis.” Journal of Psychosomatic Research 74 (1): 74–81. https://doi.org/10.1016/j.jpsychores.2012.10.010.
Uanhoro, James Ohisei. 2023. “Modeling Misspecification as a Parameter in Bayesian Structural Equation Models.” Educational and Psychological Measurement 0 (0): 00131644231165306. https://doi.org/10.1177/00131644231165306.