metRology (version 0.9-16.1)

derSimonian-Laird: derSimonian-Laird estimator

Description

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

Usage

dsl(x, ..., na.rm = FALSE)

	## S3 method for class 'default':
dsl(x, s, n = NULL, groups = NULL, \dots, na.rm = FALSE)

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

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.

...

Further parameters passed to other methods.

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: [object Object],[object Object],[object Object]

Details

dsl implements the derSimonian-Laird random-effects estimate of location, using the implementation described by Jackson (2010). 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 $N(0, \sigma_i^2)$. The estimator forms a direct calculation of $\tau$, and uses this to form revised estimates of standard error $\sqrt{s_i^2+\tau^2}$ in x, calculates weights as the inverse of these and in turn calculates a weighted mean, allowing for any calculated excess variance $\tau^2$. This implementation permits input in the form of:

• meansxand standard errorss, in which case neithernnorgroupsare supplied;
• meansx, standard deviationssand group size(s)n, standard errors then being calculated ass/sqrt(n)
• individual observationsxwith a groupinf factorgroups, in which case standard errors are calculated from the groups usingtapply.

References

Jackson et al. (2010) J Stat Plan Inf 140, 961-970

See Also

link{loc.est-class}

Examples

#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, dsl(x, s) )