Fitzmaurice

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Description

Hyperdirichlet distribution corresponding to a dataset of Fitzmaurice et al

Usage

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fitz(dat , include.missing=TRUE , validated=NULL)

Arguments

dat

A vector corresponding to either male or female data

include.missing

Boolean, with default TRUE meaning to return the likelihood function for the data including the missing cases, and FALSE meaning to include only the data corresponding to complete cases

validated

Boolean, with TRUE meaning to omit the checks (OK if all elements of dat are non-negative) and FALSE meaning to check them all (time-consuming)

Details

Fitzmaurice considered childhood obesity. See the reference for further details.

Value

Returns a hyperdirichlet distribution (without normalizing factor) corresponding to the observations, either male or female, made by Fitzmaurice et al.

Note

Pat Altham originally spotted that this dataset could be represented using the hyperdirichlet distribution.

The functional form for replacement “[<-()” is used because it is possible to set the validated argument to TRUE: this suppresses the computationally intensive checking that the distribution is proper.

warning. Setting validated to TRUE is not recommended in general. It is OK here because the function knows that no elements of dat is negative.

Author(s)

Robin K. S. Hankin

References

G. M. Fitzmaurice, N. M. Laird, and S. R. Lipsitz 1994. “Analysing incomplete longitudinal binary responses: a likelihood-based approach”. Biometrics, volume 50, pp601-612.

Examples

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  boys  <- c(20,7,9,8, 8, 8,15,150,13,3,2,42,3,1, 6,16,11,1,3,38,14,55,4,33,7,45)
  girls <- c(21,6,6,2,19,13,14,154, 8,1,4,47,4,0,16, 3,11,1,3,25,13,39,5,23,7,47)

  male <- fitz(boys)
  maximum_likelihood(male)

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