fitz: Fitzmaurice
In hyperdirichlet: A Generalization of the Dirichlet Distribution

Description Usage Arguments Details Value Note Author(s) References Examples

Hyperdirichlet distribution corresponding to a dataset of Fitzmaurice et al

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

`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)

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

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

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.

Robin K. S. Hankin

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.

  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)