reml3L | R Documentation |
It estimates the variance components of random-effects in three-level univariate meta-analysis with restricted (residual) maximum likelihood (REML) estimation method.
## Depreciated in the future
reml3(y, v, cluster, x, data, RE2.startvalue=0.1, RE2.lbound=1e-10,
RE3.startvalue=RE2.startvalue, RE3.lbound=RE2.lbound, RE.equal=FALSE,
intervals.type=c("z", "LB"), model.name="Variance component with REML",
suppressWarnings=TRUE, silent=TRUE, run=TRUE, ...)
reml3L(y, v, cluster, x, data, RE2.startvalue=0.1, RE2.lbound=1e-10,
RE3.startvalue=RE2.startvalue, RE3.lbound=RE2.lbound, RE.equal=FALSE,
intervals.type=c("z", "LB"), model.name="Variance component with REML",
suppressWarnings=TRUE, silent=TRUE, run=TRUE, ...)
y |
A vector of |
v |
A vector of |
cluster |
A vector of |
x |
A predictor or a |
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 |
model.name |
A string for the model name in |
suppressWarnings |
Logical. If |
silent |
Logical. 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 the 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 combining
level-2 and level-3 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 |
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.
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.
meta3L
, reml
, Cooper03
, Bornmann07
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