Binomial dispersion: intra-cluster correlation parameter.

MME estimates of binomial dispersion parameter tau (intra-cluster correlation).

Usage

tauWt(
  fit,
  subset.factor = NULL,
  fit.only = TRUE,
  iter.max = 12,
  converge = 1e-06,
  trace.it = FALSE
)

Arguments

fit: A glm object.
subset.factor: Factor for estimating phi by subset. Will be converted to a factor if it is not a factor.
fit.only: Return only the final fit? If FALSE, also returns the weights and tau estimates.
iter.max: Maximum number of iterations.
converge: Convergence criterion: difference between model degrees of freedom and Pearson's chi-square. Default 1e-6.
trace.it: Display print statements indicating progress

Value

A list with the following elements. fit: the new model fit, updated by the estimated weights weights: vector of weights phi: vector of phi estimates

Details

Estimates binomial dispersion parameter \(\tau\) by the method of moments. Iteratively refits the model by the Williams procedure, weighting the observations by \(1 / \phi_{ij}\), where \(\phi_{ij} = 1 + \tau_j(n_{ij} - 1)\), \(j\) indexes the subsets, and \(i\) indexes the observations.

References

Williams DA, 1982. Extra-binomial variation in logistic linear models. Applied Statistics 31:144-148.

Wedderburn RWM, 1974. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61:439-447.

Author

PF-package

Examples

birdm.fit <- glm(cbind(y, n - y) ~ tx - 1, binomial, birdm)
RRor(tauWt(birdm.fit))
#> 
#> 95% t intervals on 4 df
#> 
#> PF 
#>     PF     LL     UL 
#>  0.489 -0.578  0.835 
#> 
#>       mu.hat    LL    UL
#> txcon  0.737 0.944 0.320
#> txvac  0.376 0.758 0.104

# 95% t intervals on 4 df
#
# PF
#     PF     LL     UL
#  0.489 -0.578  0.835
#
#       mu.hat    LL    UL
# txcon  0.737 0.944 0.320
# txvac  0.376 0.758 0.104
#
# binomial family only
# any link