Description Usage Arguments Details Value Note Author(s) References See Also

It estimates the variance components of random-effects in univariate and multivariate meta-analysis with restricted (residual) maximum likelihood (REML) estimation method.

1 2 3 4 |

`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. 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-Xα)'(V+T^2)^{-1}(y-X*α)*

where *V* is the known conditional sampling covariance matrix
of *y*, *T^2* is the variance component of the 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.

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 computational 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 `[email protected]$objectives[[1]]@numObs`

and `[email protected]$objectives[[1]]@numStats`

.

Mike W.-L. Cheung <[email protected]>

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.

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