R: Estimate Variance Components in Three-Level Univariate...
reml3
R Documentation
Estimate Variance Components in Three-Level Univariate
Meta-Analysis with Restricted (Residual) Maximum
Likelihood Estimation
Description
It estimates the variance components of random-effects in three-level
univariate meta-analysis with restricted (residual) maximum likelihood (REML) estimation method.
A vector of k characters or numbers indicating the
clusters.
x
A predictor or a k x m matrix of level-2
and level-3 predictors where m is the number of predictors.
data
An optional data frame containing the variables in the model.
RE2.startvalue
Starting value for the level-2 variance.
RE2.lbound
Lower bound for the level-2 variance.
RE3.startvalue
Starting value for the level-3 variance.
RE3.lbound
Lower bound for the level-3 variance.
RE.equal
Logical. Whether the variance components at level-2
and level-3 are constrained equally.
intervals.type
Either z (default if missing) or
LB. If it is z, it calculates the 95% Wald confidence
intervals (CIs) based on the z statistic. If it is LB, it
calculates the 95% likelihood-based CIs on the
parameter estimates. Note that the z values and their
associated p values are based on the z statistic. They are not
related to the likelihood-based CIs.
model.name
A string for the model name in mxModel.
suppressWarnings
Logical. If TRUE, warnings are
suppressed. Argument to be passed to mxRun.
silent
Logical. Argument to be passed to mxRun
run
Logical. If FALSE, only return the mx model without running the analysis.
...
Futher arguments to be passed to mxRun
Details
Restricted (residual) maximum likelihood obtains the parameter estimates on the transformed data that do not include the fixed-effects parameters. A transformation matrix M=I-X(X'X)^{-1}X' is created based on the design matrix X which is just a column vector when there is no predictor in x. The last N redundant rows of M is removed where N is the rank of X. After pre-multiplying by M on y, the parameters of fixed-effects are removed from the model. Thus, only the parameters of random-effects are estimated.
An alternative but equivalent approach is to minimize the
-2*log-likelihood function:
where V is the known conditional sampling covariance matrix
of y, T^2 is the variance component combining
level-2 and level-3 random effects, and hat{α}=(t(X)(V+T^2)^{-1}X)^{-1}t(X)(V+T^2)^{-1}y. reml()
minimizes the above likelihood function to obtain the parameter estimates.
Value
An object of class reml with a list of
call
Object returned by match.call
data
A data matrix of y, v and x
mx.fit
A fitted object returned from mxRun
Note
reml is more computional intensive than meta. Moreover, reml is more
likely to encounter errors during optimization. Since
a likelihood function is directly employed to obtain the parameter
estimates, there is no number of studies and number of observed statistics
returned by mxRun. Ad-hoc steps are used
to modify mx.fit@runstate$objectives[[1]]@numObs and mx.fit@runstate$objectives[[1]]@numStats.
Author(s)
Mike W.-L. Cheung <mikewlcheung@nus.edu.sg>
References
Cheung, M. W.-L. (2013). Implementing restricted maximum likelihood estimation in structural equation models. Structural Equation Modeling, 20(1), 157-167.
Cheung, M. W.-L. (2014). Modeling dependent effect sizes with three-level meta-analyses: A structural equation modeling approach. Psychological Methods, 19, 211-229.
Mehta, P. D., & Neale, M. C. (2005). People Are Variables Too: Multilevel Structural Equations Modeling. Psychological
Methods, 10(3), 259-284.
Searle, S. R., Casella, G., & McCulloch, C. E. (1992). Variance components. New York: Wiley.