metRology (version 0.9-28-1)

REML location estimate: Restricted maximum likelihood estimate of location

Description

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

Usage

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

Arguments

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().

Value

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.

Details

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:

$$\frac{1}{2} \left( \sum_{i=1}^{k}\frac{(x_i-mu)^2}{u_i^2} + \sum_{i=1}^{k}log(u_i^2) + log\left(\sum_{i=1}^{k}(1/u_i^2)\right) \right)$$

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.

References

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

See Also

loc.est-class

Examples

# NOT RUN {
  #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) )

# }