Path Model Function — path

Fit path or latent-variable models to a synthesized correlation matrix and optionally propagate uncertainty from the meta-analytic synthesis into the path coefficients.

Usage

path_model(
  mars_object,
  model,
  num_obs = NULL,
  adjust_se = TRUE,
  se_method = c("delta", "simulation", "bootstrap"),
  se_draws = 1000,
  se_seed = NULL,
  method_null = "sem",
  synthesis_method = c("model", "average", "weighted"),
  synthesis_transform = c("none", "fisher_z"),
  missing_corr = c("available", "pairwise", "em"),
  attenuation = c("none", "correct"),
  reliability = NULL,
  reliability_missing = c("error", "skip", "impute_mean", "assume_1"),
  pd_adjust = c("none", "eigen_clip", "nearpd"),
  pd_tol = 1e-08,
  ...
)

Arguments

mars_object: The mars fitted object, or an object returned by mixed_corr_meta.
model: Model syntax in a lavaan-like format. Regression paths use ~, latent measurement paths use =~, and residual variances or covariances use ~~.
num_obs: Number of observations. For objects returned by mixed_corr_meta, supply this explicitly if you want chi-square/RMSEA-style fit statistics; otherwise those statistics are reported as unavailable because the mixed-correlation workflow does not imply a defensible SEM sample size by default.
adjust_se: Logical; if TRUE, compute standard errors that reflect uncertainty in the synthesized correlation matrix when supported by se_method.
se_method: Method used for standard errors. "delta" uses the current delta-method approximation, "simulation" uses parametric draws from the pooled correlation vector, and "bootstrap" uses available bootstrap correlation draws when present.
se_draws: Number of draws/resamples used when se_method = "simulation" or "bootstrap".
se_seed: Optional random seed for se_method.
method_null: Null-model method for observed-variable path models. Currently "sem" uses the SEM-style independence model implemented by model_fit. Latent-variable models use their internal independence-model calculation and ignore this argument.
synthesis_method: Correlation synthesis method used to build the matrix supplied to latent/path modeling. One of "model" (default, use the fitted MARS coefficients), "average", or "weighted".
synthesis_transform: Optional transform applied for "average"/"weighted" pooling. One of "none" or "fisher_z".
missing_corr: Missing-correlation handling for synthesized matrices. One of "available" (fallback to model-estimated pair), "pairwise" (pairwise pooling with simple fill for absent pairs), or "em" (EM-style matrix completion).
attenuation: Attenuation-correction mode for synthesized correlations. One of "none" or "correct".
reliability: Reliability input used when attenuation = "correct". Accepts either a named numeric vector by variable or a data frame with variable/reliability columns (optionally with a study column).
reliability_missing: Strategy for missing reliability values. One of "error", "skip", "impute_mean", or "assume_1".
pd_adjust: Positive-definite repair applied to the synthesized correlation matrix prior to model fitting. One of "none", "eigen_clip", or "nearpd".
pd_tol: Minimum eigenvalue tolerance used by pd_adjust = "eigen_clip".
...: Reserved for future extensions.

Value

List output with class path; The output is the parameter estimates from the fitted path model.

Details

path_model() first extracts or constructs a pooled correlation matrix from mars_object. With the default synthesis_method = "model", this matrix is assembled from the fitted MARS coefficients; alternatively, the matrix can be formed by average or weighted pooling with optional Fisher-z transformation, missing-correlation handling, attenuation correction, and positive-definite adjustment.

The fitted path model is then delegated to model_fit. For observed-variable regression syntax, path coefficients are computed directly from the relevant submatrices of the synthesized correlation matrix. For latent-variable or covariance syntax, model_fit() minimizes the normal theory SEM discrepancy function for the observed correlation matrix using optim with the BFGS method. Variance parameters are optimized on the log scale, fixed parameters supplied with value * variable are held fixed, and unscaled latent factors receive a marker loading of one.

Model fit statistics are calculated from the fitted implied correlation matrix. Observed-variable models use the package's GLS-style discrepancy and SEM-style null model; latent-variable models use the maximum-likelihood discrepancy \(\log|\Sigma(\theta)| + \mathrm{tr}(R\Sigma(\theta)^{-1}) - \log|R| - p\). In both cases, CFI, TLI, RMSEA, and SRMR are reported with raw values retained when bounded display values are clipped.

Examples

if (FALSE) { # \dontrun{
fit <- mars(
  data = becker09,
  studyID = "ID",
  effectID = "numID",
  sample_size = "N",
  effectsize_type = "cor",
  varcov_type = "weighted",
  variable_names = c(
    "Cognitive_Performance",
    "Somatic_Performance",
    "Selfconfidence_Performance",
    "Somatic_Cognitive",
    "Selfconfidence_Cognitive",
    "Selfconfidence_Somatic"
  )
)
path_model(fit, "Performance ~ Cognitive + Somatic + Selfconfidence")
} # }