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

Calculates REML estimate of location, with standard error, assuming a random-effects model

1 2 3 4 5 |

`x` |
numeric vector of mean values for groups, or (if |

`s` |
numeric vector of length |

`n` |
integer giving the number of observations in each group. May be a vector
of length |

`groups` |
factor, or vetor which can be coerced to factor, of groups. If
present, |

`na.rm` |
logical: if |

`tol` |
numeric tolerance for convergence, used by |

`REML` |
logical: if |

`...` |
Further parameters passed to |

`reml.loc`

finds an excess variance *tau^2* and location *mu* that maximise the
restricted maximum likelihood criterion.

The estimator assumes a model of the form

*x[i]=mu+b[i]+e[i]*

in which *b[i]* is drawn from *N(0, tau^2)* and
*e[i]* is drawn from *N(0, sigma[i]^2)*.

By default the function maximises the data-dependent part of the negative log restricted likelihood:

*\frac{1}{2} ≤ft( ∑_{i=1}^{k}\frac{(x_i-mu)^2}{u_i^2} + ∑_{i=1}^{k}log(u_i^2) +
log≤ft(∑_{i=1}^{k}(1/u_i^2)\right) \right)*

where *u[i]=s[i]^2 + tau^2* and *k* is the number of mean values.
If `REML=FALSE`

, the final term is omitted to give the maximum likelihood criterion.

This implementation permits input in the form of:

means

`x`

and standard errors`s`

, in which case neither`n`

nor`groups`

are supplied;means

`x`

, standard deviations`s`

and group size(s)`n`

, standard errors then being calculated as`s/sqrt(n)`

individual observations

`x`

with a groupinf factor`groups`

, in which case standard errors are calculated from the groups using`tapply`

.

A loc.est object; see loc.est for details. In the returned object, individual
values `xi`

are always input means (calculated from groups and `n`

as
necessary); `method.details`

is returned as a list containing:

- mu
The estimated location.

- s
The standard error in the location.

- tau
The excess variance (as a standard deviation).

- REML
Logical, giving the value of REML used.

S L R Ellison s.ellison@lgc.co.uk

None, but see documentation for the metafor package for a more general implementation of REML.

1 2 3 4 5 6 | ```
#PCB measurements in a sediment from Key Comparison CCQM-K25
#s are reported standard uncertainties
pcb105 <- data.frame(x=c(10.21, 10.9, 10.94, 10.58, 10.81, 9.62, 10.8),
s=c(0.381, 0.250, 0.130, 0.410, 0.445, 0.196, 0.093))
with( pcb105, reml.loc(x, s) )
``` |

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