Fit Bayesian SEMs with minor factors assumed

The major function to fit models assuming the influence of minor factors (Uanhoro 2023) .

Usage

minorbsem(
  model = NULL,
  data = NULL,
  sample_cov = NULL,
  sample_nobs = NULL,
  data_list = NULL,
  method = "normal",
  orthogonal = FALSE,
  simple_struc = TRUE,
  correlation = FALSE,
  centered = TRUE,
  seed = 12345,
  warmup = 1000,
  sampling = 1000,
  refresh = (warmup + sampling)/10,
  adapt_delta = 0.9,
  max_treedepth = 10,
  chains = 3,
  ncores = max(parallel::detectCores() - 2, 1),
  priors = new_mbsempriors(),
  show = TRUE,
  show_messages = TRUE,
  compute_ll = FALSE,
  acov_mat = NULL,
  ret_data_list = FALSE
)

Arguments

model: A description of the user-specified model, lavaan syntax.
data: An optional data frame containing the observed variables used in the model.
sample_cov: (matrix) sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names.
sample_nobs: (positive integer) Number of observations if the full data frame is missing and only sample covariance matrix is given.
data_list: (list) A modified version of the data_list returned by minorbsem. Can be used to modify specific priors, see example below.
method: (character) One of "normal", "lasso", "logistic", "GDP", "WB", "WB-cond", "WW", or "none". See details below.
orthogonal: (logical) constrain factors orthogonal, must be TRUE to fit bifactor models.
simple_struc: (LOGICAL) Only relevant for CFAs. If TRUE: assume simple structure; If FALSE: estimate all cross-loadings using generalized double Pareto priors.
correlation: (LOGICAL) If TRUE: perform correlation structure analysis based on logarithm of a matrix transformation (Archakov and Hansen 2021) ; If FALSE (default): perform covariance structure analysis.
centered: (LOGICAL) Only relevant for WB-cond and WW methods when correlation = TRUE. If TRUE (default): Use a centered parameterization; If FALSE: Use a non-centered parameterization.
seed: (positive integer) seed, set to obtain replicable results.
warmup: (positive integer) The number of warmup iterations to run per chain.
sampling: (positive integer) The number of post-warmup iterations to run per chain, retained for inference.
refresh: (positive integer) How often to print the status of the sampler.
adapt_delta: (real in (0, 1)) Increase to resolve divergent transitions.
max_treedepth: (positive integer) Increase to resolve problems with maximum tree depth.
chains: (positive integer) The number of Markov chains to run.
ncores: (positive integer) The number of chains to run in parallel.
priors: An object of mbsempriors-class. See new_mbsempriors for more information.
show: (Logical) If TRUE, show table of results, if FALSE, do not show table of results. As an example, use FALSE for simulation studies.
show_messages: (Logical) If TRUE, show messages from Stan sampler, if FALSE, hide messages.
compute_ll: (Logical) If TRUE, compute log-likelihood, if FALSE, do not. This may be useful for cross-validation. This argument is ignored when: (i) the full dataset is not provided; (ii) the method is WB, use WB-cond instead.
acov_mat: (Optional) Asymptotic variance matrix of lower triangular half (column-order) of the correlation matrix to be used for correlation structure analysis. This parameter is useful if importing polychoric or meta-analytic SEM pooled correlation matrix.
ret_data_list: (LOGICAL) If TRUE, returns the data_list and prior objects, see example. If FALSE (default), fits the model given user inputs.

Value

An object of mbsem-class

Details

CFAs assume standardized factors. Latent variable regression models print results with standardized loadings.

There are different methods for estimating models in this package:

normal: under belief that minor factor influences are on average zero with continuous deviations away from zero (Uanhoro 2023) .
lasso: under belief that minor factor influences are largely zero with a small number of non-zero residual covariances.
logistic: for similar belief as normal but more readily accomodates extreme outliers.
GDP: to mimic a global-local approach, i.e. attempt to shrink near 0 residual covariances to 0 with minimal shrinking for larger residual covariances (Armagan et al. 2013) .
WB: to model the covariance matrix hierarchically under assumptions of adventitiuous error (Wu and Browne 2015) ; does NOT allow for computation of casewise log-likelihoods and LOO-CV.
WB-cond: same as WB but estimates the "population covariance matrix", allowing for computation of casewise log-likelihoods and LOO-CV.
WW: A variation on WB-cond, but assumes the population covariance matrix is Wishart as opposed to inverse-Wishart;
none: if intending to ignore the influence of minor factors.

WB-cond and WW are equivalent for correlation structure analysis.

References

Archakov I, Hansen PR (2021). “A New Parametrization of Correlation Matrices.” Econometrica, 89(4), 1699--1715. ISSN 1468-0262, doi:10.3982/ECTA16910 , https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA16910.

Armagan A, Dunson DB, Lee J (2013). “Generalized double Pareto shrinkage.” Statistica Sinica, 23(1), 119--143. ISSN 1017-0405, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3903426/.

Uanhoro JO (2023). “Modeling Misspecification as a Parameter in Bayesian Structural Equation Models.” Educational and Psychological Measurement, 0(0), 00131644231165306. ISSN 0013-1644, doi:10.1177/00131644231165306 , https://journals.sagepub.com/doi/abs/10.1177/00131644231165306.

Wu H, Browne MW (2015). “Quantifying Adventitious Error in a Covariance Structure as a Random Effect.” Psychometrika, 80(3), 571--600. ISSN 1860-0980, doi:10.1007/s11336-015-9451-3 .

Examples

if (FALSE) {
mod_cfa <- minorbsem(
  "# latent variable definitions
  F1 =~ x1 + x2 + x3
  F2 =~ x4 + x5 + x6
  F3 =~ x7 + x8 + x9", HS
)
new_pd <- PD
apply(PD, 2, sd) # first 8 variables have relatively large SDs
new_pd[, 1:8] <- new_pd[, 1:8] / 3 # move SDs closer to 1
mod_sem <- minorbsem(
  "# latent variable definitions
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # latent regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60", new_pd
)
mod_dl <- minorbsem(
  "# latent variable definitions
  F1 =~ x1 + x2 + x3
  F2 =~ x4 + x5 + x6
  F3 =~ x7 + x8 + x9", HS,
  ret_data_list = TRUE
)
mod_dl$load_est # prior mean for loadings
mod_dl$load_se # prior sd for loadings
mod_dl$load_se[9, 3] <- .75 # set prior SD for F3 =~ x9 to .75
# fit model with updated prior
mod <- minorbsem(data_list = mod_dl)
}