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Fit Multivariate Meta-Analysis

Source: R/metaVAR-meta.R
Meta.Rd

This function estimates fixed-, random-, or mixed-effects meta-analysis parameters using the estimated coefficients and sampling variance-covariance matrix from each individual.

Usage

Meta(
  y,
  v,
  x = NULL,
  z = NULL,
  random = TRUE,
  alpha_free = NULL,
  alpha_values = NULL,
  alpha_lbound = NULL,
  alpha_ubound = NULL,
  tau_sqr_diag = FALSE,
  tau_sqr_d_free = NULL,
  tau_sqr_d_values = NULL,
  tau_sqr_d_lbound = NULL,
  tau_sqr_d_ubound = NULL,
  tau_sqr_l_free = NULL,
  tau_sqr_l_values = NULL,
  tau_sqr_l_lbound = NULL,
  tau_sqr_l_ubound = NULL,
  i_sqr_univariate = FALSE,
  gamma_free = NULL,
  gamma_values = NULL,
  gamma_lbound = NULL,
  gamma_ubound = NULL,
  kappa_free = NULL,
  kappa_values = NULL,
  kappa_lbound = NULL,
  kappa_ubound = NULL,
  phi_values = NULL,
  phi_free = NULL,
  phi_lbound = NULL,
  phi_ubound = NULL,
  omega_values = NULL,
  omega_free = NULL,
  omega_lbound = NULL,
  omega_ubound = NULL,
  psi_diag = TRUE,
  psi_d_free = NULL,
  psi_d_values = NULL,
  psi_d_lbound = NULL,
  psi_d_ubound = NULL,
  psi_l_free = NULL,
  psi_l_values = NULL,
  psi_l_lbound = NULL,
  psi_l_ubound = NULL,
  check_estimates = TRUE,
  robust = FALSE,
  tries_explore = 100,
  tries_local = 100,
  max_attempts = 10,
  grad_tol = 0.01,
  hess_tol = 1e-08,
  eps = 1e-06,
  factor = 10,
  abs_bnd_tol = 1e-06,
  rel_bnd_tol = 1e-04,
  silent = FALSE,
  seed = NULL,
  ncores = NULL
)

Arguments

y

A list. Each element of the list is a numeric vector of estimated coefficients.

v

A list. Each element of the list is a sampling variance-covariance matrix of y.

x

An optional list. Each element of the list is a numeric vector of covariates.

z

An optional list. Each element of the list is a numeric vector of distal outcomes.

random

Logical. If random = TRUE, estimates random effects. If random = FALSE, tau_sqr is a null matrix.

alpha_free

Logical vector. Optional vector of free (TRUE) parameters for alpha.

alpha_values

Numeric vector. Optional vector of starting values for alpha.

alpha_lbound

Numeric vector. Optional vector of lower bound values for alpha.

alpha_ubound

Numeric vector. Optional vector of upper bound values for alpha.

tau_sqr_diag

Logical. If tau_sqr_diag = TRUE, tau_sqr is a diagonal matrix. If tau_sqr_diag = FALSE, tau_sqr is a symmetric matrix.

tau_sqr_d_free

Logical vector indicating free/fixed status of the elements of tau_sqr_d. If NULL, all element of tau_sqr_d are free.

tau_sqr_d_values

Numeric vector with starting values for tau_sqr_d. If NULL, defaults to a vector of ones.

tau_sqr_d_lbound

Numeric vector with lower bounds for tau_sqr_d. If NULL, no lower bounds are set.

tau_sqr_d_ubound

Numeric vector with upper bounds for tau_sqr_d. If NULL, no upper bounds are set.

tau_sqr_l_free

Logical matrix indicating which strictly-lower-triangular elements of tau_sqr_l are free. Ignored if tau_sqr_diag = TRUE.

tau_sqr_l_values

Numeric matrix of starting values for the strictly-lower-triangular elements of tau_sqr_l. If NULL, defaults to a null matrix.

tau_sqr_l_lbound

Numeric matrix with lower bounds for tau_sqr_l. If NULL, no lower bounds are set.

tau_sqr_l_ubound

Numeric matrix with upper bounds for tau_sqr_l. If NULL, no upper bounds are set.

i_sqr_univariate

Logical. If i_sqr_univariate = TRUE, use the univariate formula for \(I^2\). If i_sqr_univariate = FALSE, use the multivariate formula for \(I^2\).

gamma_free

Logical matrix. Optional matrix of free (TRUE) parameters for gamma.

gamma_values

Numeric matrix. Optional matrix of starting values for gamma.

gamma_lbound

Numeric matrix. Optional matrix of lower bound values for gamma.

gamma_ubound

Numeric matrix. Optional matrix of upper bound values for gamma.

kappa_free

Logical vector. Optional vector of free (TRUE) parameters for kappa.

kappa_values

Numeric vector. Optional vector of starting values for kappa.

kappa_lbound

Numeric vector. Optional vector of lower bound values for kappa.

kappa_ubound

Numeric vector. Optional vector of upper bound values for kappa.

phi_values

Numeric matrix. Optional matrix of starting values for phi.

phi_free

Logical matrix. Optional matrix of free (TRUE) parameters for phi.

phi_lbound

Numeric matrix. Optional matrix of lower bound values for phi.

phi_ubound

Numeric matrix. Optional matrix of upper bound values for phi.

omega_values

Numeric matrix. Optional matrix of starting values for omega.

omega_free

Logical matrix. Optional matrix of free (TRUE) parameters for omega.

omega_lbound

Numeric matrix. Optional matrix of lower bound values for omega.

omega_ubound

Numeric matrix. Optional matrix of upper bound values for omega.

psi_diag

Logical. If psi_diag = TRUE, psi is a diagonal matrix. If psi_diag = FALSE, psi is a symmetric matrix.

psi_d_free

Logical vector indicating free/fixed status of the elements of psi_d. If NULL, all element of psi_d are free.

psi_d_values

Numeric vector with starting values for psi_d. If NULL, defaults to a vector of ones.

psi_d_lbound

Numeric vector with lower bounds for psi_d. If NULL, no lower bounds are set.

psi_d_ubound

Numeric vector with upper bounds for psi_d. If NULL, no upper bounds are set.

psi_l_free

Logical matrix indicating which strictly-lower-triangular elements of psi_l are free. Ignored if psi_diag = TRUE.

psi_l_values

Numeric matrix of starting values for the strictly-lower-triangular elements of psi_l. If NULL, defaults to a null matrix.

psi_l_lbound

Numeric matrix with lower bounds for psi_l. If NULL, no lower bounds are set.

psi_l_ubound

Numeric matrix with upper bounds for psi_l. If NULL, no upper bounds are set.

check_estimates

Logical. Check elements of v for positive definiteness. If the test fails, the function generates a near positive definite matrix to replace the original using Matrix::nearPD().

robust

Logical. If TRUE, use robust (sandwich) sampling variance-covariance matrix in stage 2. If FALSE, use normal theory sampling variance-covariance matrix in stage 2.

tries_explore

Integer. Number of extra tries for the wide exploration phase using OpenMx::mxTryHardWideSearch() with checkHess = FALSE.

tries_local

Integer. Number of extra tries for local polishing via OpenMx::mxTryHard() when gradients remain above tolerance.

max_attempts

Integer. Maximum number of remediation attempts after the first Hessian computation fails the criteria. Each attempt may nudge off bounds, refit locally without the Hessian, and, on the last attempt, relax bounds.

grad_tol

Numeric. Tolerance for the maximum absolute gradient. Smaller values are stricter.

hess_tol

Numeric. Minimum allowable Hessian eigenvalue. Smaller values are less strict.

eps

Numeric. Proximity threshold to detect parameters on their bounds and to nudge them inward by 10 * eps.

factor

Numeric. Multiplicative factor to relax parameter bounds on the final remediation attempt. Lower bounds are divided by factor and upper bounds are multiplied by factor.

abs_bnd_tol

Numeric scalar. Absolute tolerance used when comparing parameter values to bounds.

rel_bnd_tol

Numeric scalar. Relative tolerance multiplier.

silent

Logical. If TRUE, suppresses messages during the model fitting stage.

seed

Random seed for reproducibility.

ncores

Positive integer. Number of cores to use.

References

Cheung, M. W.-L. (2015). Meta-analysis: A structural equation modeling approach. Wiley. doi:10.1002/9781118957813

Neale, M. C., Hunter, M. D., Pritikin, J. N., Zahery, M., Brick, T. R., Kirkpatrick, R. M., Estabrook, R., Bates, T. C., Maes, H. H., & Boker, S. M. (2015). OpenMx 2.0: Extended structural equation and statistical modeling. Psychometrika, 81(2), 535–549. doi:10.1007/s11336-014-9435-8

See also

Other Meta-Analysis of VAR Functions: MetaVARMx()

Author

Ivan Jacob Agaloos Pesigan