HGDRANDOMMODEL procedure

Defines the random model in a hierarchical generalized linear model for the dispersion in a double hierarchical generalized linear model (R.W. Payne, Y. Lee, J.A. Nelder & M. Noh).


Options

DISTRIBUTION = string
Distribution for the random model (beta, normal, gamma, inversegamma); default norm

LINK = string
Link for the random model (identity, logarithm, logit, reciprocal); default iden

RANDOMTERM = formula
Random term whose dispersion is being modelled; if unset, the model is assumed to be for the residual dispersion parameter (phi)

PHIMETHOD = string
Whether to fix or estimate the residual dispersion parameter in the dispersion HGLM (fix, estimate); default fix


Parameters

TERMS = formula
Random model

DFORMULA = formulae
Dispersion model for each random term; default * i.e. none

LMATRIX = matrices
Linear transformation to apply to design matrix Z of each random term, in order to define correlations between its effects; default * i.e. none


Description

HGDRANDOMMODEL allows you to extend a hierarchical generalized linear model (HGLM) to become a double hierarchical generalized linear model (DHGLM); see Lee & Nelder (1996, 2001a, 2006). This is done by adding some random terms to one of the generalized linear models that is to model the dispersion, so that this becomes an HGLM. By default the residual dispersion of this HGLM is fixed, but you can set option PHIMETHOD=estimate to estimate it. The random term whose dispersion is to be modelled by the HGLM is indicated by the RANDOMTERM option. If RANDOMTERM is omitted, the dispersion model is assumed to be for the residual dispersion parameter (phi) of the original HGLM.

   The TERMS parameter defines the additional random terms, and the LINK and DISTRIBUTION options specify their distribution and link function respectively. You can specify a generalized linear model (GLM) to model the dispersion parameter for any of these additional random terms by specifying a GenStat formula structure, containing the (fixed) terms to be fitted in the GLM, using the DFORMULA parameter (which runs in parallel with the list of random terms supplied by the TERMS parameter).

   The LMATRIX parameter allows correlation structures to be defined for random terms, using the method described by Lee & Nelder (2001b). This is done by setting LMATRIX to a matrix L that is used as a post-multiplier for the Z matrix of the random term concerned. Lee & Nelder (2001b) give examples illustrating the types of model that can be defined.

 

Options: DISTRIBUTION, LINK, RANDOMTERM, PHIMETHOD.

Parameters: TERMS, DFORMULA, LMATRIX.


Method

The information is stored in a workspace G5PL_HG (accessed using the WORKSPACE directive) for later use by HGANALYSE.


References

Lee, Y., & Nelder, J.A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society, Series B, 58, 619-678.

Lee, Y., & Nelder, J.A. (2001a). Hierarchical generalized linear models: a synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika, 88, 987-1006.

Lee, Y. & Nelder, J.A. (2001b). Modelling and analysing correlated non-normal data. Statistical Modelling, 1, 3-16.

Lee, Y. & Nelder, J.A. (2006). Double hierarchical generalized linear models (with discussion). Appl. Statist., 55, 139-185.