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Fit Multivariate Meta-Analysis (metaVAR via OpenMx)

Source: R/metaDyn-meta-var-mx.R
MetaVARMx.Rd

This function estimates fixed-, random-, or mixed-effects meta-analytic parameters using per-individual coefficient estimates and their sampling variance-covariance matrices. Optionally, it fits distal-outcome models in which between-person outcomes are regressed on between-person covariates and the meta-analyzed parameters/effect sizes. This function uses the estimated coefficients and sampling variance-covariance matrix from each individual fitted using the fitVARMxID::FitVARMxID() function.

Usage

MetaVARMx(
  object,
  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_free = NULL,
  phi_values = NULL,
  phi_lbound = NULL,
  phi_ubound = NULL,
  omega_free = NULL,
  omega_values = NULL,
  omega_lbound = NULL,
  omega_ubound = NULL,
  psi_diag = FALSE,
  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,
  effects = TRUE,
  set_point = TRUE,
  int_meas = TRUE,
  int_dyn = TRUE,
  cov_meas = TRUE,
  cov_dyn = TRUE,
  robust_v = FALSE,
  robust = FALSE,
  alpha = 0.05,
  seed = NULL,
  tries_explore = 100,
  tries_local = 100,
  max_attempts = 10,
  silent = FALSE,
  ncores = NULL
)

Arguments

object

Output of the fitVARMxID::FitVARMxID() function.

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_free

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

phi_values

Numeric matrix. Optional matrix of starting values 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_free

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

omega_values

Numeric matrix. Optional matrix of starting values 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().

effects

Logical. If effects = TRUE, include estimates of the dynamic effects matrix, if available. If effects = FALSE, exclude estimates of the dynamic effects matrix.

set_point

Logical. If set_point = TRUE, include estimates of the set-point vector, if available. If set_point = FALSE, exclude estimates of the set-point vector.

int_meas

Logical. If int_meas = TRUE, include estimates of the measurement intercept vector, if available. If int_meas = FALSE, exclude estimates of the measurement intercept vector.

int_dyn

Logical. If int_dyn = TRUE, include estimates of the dynamic process intercept vector, if available. If int_dyn = FALSE, exclude estimates of the dynamic process intercept vector.

cov_meas

Logical. If cov_meas = TRUE, include estimates of the measurement error covariance matrix, if available. If cov_meas = FALSE, exclude estimates of the measurement error covariance matrix.

cov_dyn

Logical. If cov_dyn = TRUE, include estimates of the process noise covariance matrix, if available. If cov_dyn = FALSE, exclude estimates of the process noise covariance matrix.

robust_v

Logical. If TRUE, use robust (sandwich) sampling variance-covariance matrix in stage 1. If FALSE, use normal theory sampling variance-covariance matrix in stage 1.

robust

Logical. If TRUE, calculate robust (sandwich) sampling variance-covariance matrix in stage 2.

alpha

NUmeric. Alpha for test of significance and confidence intervals.

seed

Random seed for reproducibility.

tries_explore

Integer. Number of extra tries for the wide exploration phase.

tries_local

Integer. Number of extra tries for local polishing.

max_attempts

Integer. Maximum number of remediation attempts after the first Hessian computation fails the criteria.

silent

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

ncores

Positive integer. Number of cores to use.

Value

Returns an object of class metadynmeta which is a list with the following elements:

call

Function call.

args

List of function arguments.

fun

Function used ("Meta").

output

A fitted OpenMx model.

robust

Output from OpenMx::imxRobustSE() with argument details = TRUE if robust = TRUE.

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: Meta()

Author

Ivan Jacob Agaloos Pesigan

Examples

if (requireNamespace("simStateSpace")) {
  # Generate data using the simStateSpace package-------------------------
  library(simStateSpace)
  set.seed(42)
  n <- 5
  time <- 100
  p <- 2
  alpha <- rep(x = 0, times = p)
  beta <- 0.50 * diag(p)
  psi <- 0.001 * diag(p)
  psi_l <- t(chol(psi))
  mu0 <- SSMMeanEta(
    beta = beta,
    alpha = alpha
  )
  sigma0 <- SSMCovEta(
    beta = beta,
    psi = psi
  )
  sigma0_l <- t(chol(sigma0))
  sim <- SimSSMVARFixed(
    n = n,
    time = time,
    mu0 = mu0,
    sigma0_l = sigma0_l,
    alpha = alpha,
    beta = beta,
    psi_l = psi_l
  )
  data <- as.data.frame(sim)

  # Stage 1---------------------------------------------------------------
  library(fitVARMxID)
  stage1 <- FitVARMxID(
    data = data,
    observed = paste0("y", seq_len(p)),
    id = "id",
    center = TRUE
  )
  summary(stage1)
  # Stage 2---------------------------------------------------------------
  # Meta-analyze set point vector and matrix of lagged-effects
  library(metaDyn)
  stage2 <- MetaVARMx(
    object = stage1,
    random = FALSE,
    effects = TRUE,
    set_point = TRUE,
    int_meas = FALSE,
    int_dyn = FALSE,
    cov_meas = FALSE,
    cov_dyn = FALSE
  )
  # Methods for the output of the MetaVARMx() function
  print(stage2)
  summary(stage2)
  coef(stage2)
  vcov(stage2)
  confint(stage2)
  extract(stage2, what = "alpha")
}
#> Running DTVAR_ID1 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID1 with 9 parameters
#> 
#>  Lowest minimum so far:  -822.060942313193
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-822.06094 (started at 367.82482)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.331612745243841,-0.0197631400065759,0.0270181292624815,0.539260086092713,0.0057946951525851,0.007106199232002,0.0623713422440293,-6.91195717901486,-6.98806630902827
#> Running DTVAR_ID2 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID2 with 9 parameters
#> 
#>  Lowest minimum so far:  -834.035953636412
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-834.03595 (started at 367.84346)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.546679030340841,-0.0201020488638611,-0.0487574618599386,0.297450290600703,-0.00284153166188121,-0.0199122101192943,0.176134255014816,-7.14253861726531,-6.87719884724769
#> Running DTVAR_ID3 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID3 with 9 parameters
#> 
#>  Lowest minimum so far:  -808.550007472268
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-808.55001 (started at 367.87017)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.528105561142997,-0.332501283495961,0.0108536161301484,0.361419705300276,-0.00426229999671594,-0.00173173484843314,-0.21387789357269,-6.9657202697529,-6.80024208411447
#> Running DTVAR_ID4 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID4 with 9 parameters
#> 
#>  Lowest minimum so far:  -845.339407101868
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-845.33941 (started at 367.80199)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.160844162100514,-0.121824766994102,-0.0298919550660853,0.481815653357755,-0.0130955259827441,0.00326100822229185,0.00601848006477796,-7.23151794331632,-6.89984913049538
#> Running DTVAR_ID5 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID5 with 9 parameters
#> 
#>  Lowest minimum so far:  -832.354548096018
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-832.35455 (started at 367.7976)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.299055985152669,0.0348621727088368,-0.0801687055865619,0.465890390856868,-0.00111115045695215,0.00331563195705935,-0.166419668597626,-6.91180267781828,-7.08999323366805
#> Running Model with 6 parameters
#> 
#> Beginning initial fit attempt
#> Running Model with 6 parameters
#> 
#>  Lowest minimum so far:  -93.184957280109
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-93.184957 (started at -91.256471)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> -0.00428470046284236,-0.00406757081116166,0.386594914967842,-0.0851794164286438,-0.0234341474339058,0.444138933642437
#> Call:
#> MetaVARMx(object = stage1, random = FALSE, effects = TRUE, set_point = TRUE, 
#>     int_meas = FALSE, int_dyn = FALSE, cov_meas = FALSE, cov_dyn = FALSE)
#> 
#> Status code:
#> 0
#> 
#> CI type:
#> "normal"
#> 
#>                est     se       z      p    2.5%   97.5%
#> alpha[1,1] -0.0043 0.0020 -2.1572 0.0310 -0.0082 -0.0004
#> alpha[2,1] -0.0041 0.0025 -1.6581 0.0973 -0.0089  0.0007
#> alpha[3,1]  0.3866 0.0404  9.5726 0.0000  0.3074  0.4657
#> alpha[4,1] -0.0852 0.0426 -2.0016 0.0453 -0.1686 -0.0018
#> alpha[5,1] -0.0234 0.0366 -0.6403 0.5220 -0.0952  0.0483
#> alpha[6,1]  0.4441 0.0389 11.4250 0.0000  0.3679  0.5203
#>           alpha
#> y1 -0.004284700
#> y2 -0.004067571
#> y3  0.386594915
#> y4 -0.085179416
#> y5 -0.023434147
#> y6  0.444138934