reml | R Documentation |
It estimates the variance components of random-effects in univariate and multivariate meta-analysis with restricted (residual) maximum likelihood (REML) estimation method.
reml(y, v, x, data, RE.constraints = NULL, RE.startvalues = 0.1,
RE.lbound = 1e-10, intervals.type = c("z", "LB"),
model.name="Variance component with REML",
suppressWarnings = TRUE, silent = TRUE, run = TRUE, ...)
y |
A vector of effect size for univariate meta-analysis or a |
v |
A vector of the sampling variance of the effect size for univariate
meta-analysis or a |
x |
A predictor or a |
data |
An optional data frame containing the variables in the model. |
RE.constraints |
A |
RE.startvalues |
A vector of |
RE.lbound |
A vector of |
intervals.type |
Either |
model.name |
A string for the model name in |
suppressWarnings |
Logical. If |
silent |
Logical. An argument to be passed to |
run |
Logical. If |
... |
Further arguments to be passed to |
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:
\log(\det|V+T^2|)+\log(\det|X'(V+T^2)^{-1}X|)+(y-X\hat{\alpha})'(V+T^2)^{-1}(y-X\hat{\alpha})
where V
is the known conditional sampling covariance matrix
of y
, T^2
is the variance component of the random
effects, and \hat{\alpha}=(X'(V+T^2)^{-1}X)^{-1}
X'(V+T^2)^{-1}y
. reml()
minimizes the above likelihood function to obtain the parameter estimates.
An object of class reml
with a list of
call |
Object returned by |
data |
A data matrix of y, v and x |
no.y |
No. of effect sizes |
no.x |
No. of predictors |
miss.vec |
A vector indicating missing data. Studies will be removed before the analysis if they are |
mx.fit |
A fitted object returned from |
reml
is more computationally 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
.
Mike W.-L. Cheung <mikewlcheung@nus.edu.sg>
Cheung, M. W.-L. (2013). Implementing restricted maximum likelihood estimation in structural equation models. Structural Equation Modeling, 20(1), 157-167.
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.
Viechtbauer, W. (2005). Bias and efficiency of meta-analytic variance estimators in the random-effects model. Journal of Educational and Behavioral Statistics, 30(3), 261-293.
meta
, reml3
, Hox02
, Berkey98
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.