reml_loc: Restricted maximum likelihood estimate of location
In metRology: Support for Metrological Applications

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

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

	reml.loc(x, ..., na.rm = FALSE)

	## Default S3 method:
reml.loc(x, s, n = NULL, groups = NULL, na.rm = FALSE,
	          tol=.Machine$double.eps^0.5, REML=TRUE, ...)

`x`	numeric vector of mean values for groups, or (if `groups` is given) of individual observations
`s`	numeric vector of length `length(x)` of standard deviations or standard uncertainties associated with the values `x`.
`n`	integer giving the number of observations in each group. May be a vector of length `length(x)`. If `n` is `NULL`, `s` is interpreted as a vector of standard uncertainties or standard errors. `n` is recycled to `length(x)`
`groups`	factor, or vetor which can be coerced to factor, of groups. If present, `x` is interpreted as a vector of individual observations and `s` and `n` ignored, if present, with a warning.
`na.rm`	logical: if `TRUE`, `NA` values are removed before processing.
`tol`	numeric tolerance for convergence, used by `optimize()`.
`REML`	logical: if `TRUE` (the default), the function optimises the REML criterion (see Details). If FALSE, the maximum likelihood criterion is used.
`...`	Further parameters passed to `optimize()`.

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.

loc.est-class

  #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) )