RMGLM procedure

Fits a model where different units follow different generalized linear models (R.W. Payne).


Options

PRINT = strings
Controls printed output (model, deviance, summary, estimates, correlations, fittedvalues, accumulated, monitoring, loglikelihood); default mode, summ, esti

Y = variate
Response variate

TERMS = formula
Terms in the model

NBINOMIAL = variate
Binomial totals

DISPERSION = scalar
Dispersion parameter; default * for DIST=norm, gamm, inve or calc, and 1 for DIST=pois, bino, mult, nega, geom, expo or bern

WEIGHTS = variate
Prior weights; default 1

OFFSET = variate
Offset variate to be included in model; default * i.e. none

CONSTANT = string
How to treat the constant (estimate, omit, ignore); default esti

FACTORIAL = scalar
Limit for expansion of model terms; default 3

FULL = string
Whether to assign all possible parameters to factors and interactions (no, yes); default no

DATASET = factor
Indicates which generalized linear model to apply to each unit; default defined from NVALUES

LINEARPREDICTOR = variate
Initial values for linear predictor

MAXCYCLE = scalar
Maximum number of iterations; default 30

MVINCLUDE = string
Whether to include units with missing values in the explanatory factors and variates (explanatory); default * i.e. omit these

SAVE = identifier
To name the regression save structure; default *


Parameters

NVALUES = scalars
Number of units for each generalized linear model

DISTRIBUTION = strings
Error distributions (normal, poisson, binomial, gamma, inversenormal, multinomial, calculated, negativebinomial, geometric, exponential, bernoulli); default norm

LINK = strings
Link functions (canonical, identity, logarithm, logit, reciprocal, power, squareroot, probit, complementaryloglog, calculated, logratio); default cano (i.e. iden for DIST=norm or calc; loga for DIST=pois; logi for DIST=bino, bern or mult; reci for DIST=gamm or expo; powe for DIST=inve; logr for DIST=nega or geom)

EXPONENT = scalars
Exponent for power links


Description

RMGLM is useful if you want to fit a model where there are several generalized linear models, each one applying to a different set of data units. This is required, for example, in the fitting of hierarchical generalized linear models (see HGANALYSE), and would also allow the fitting of multivariate generalized linear models.

   The NVALUES parameter can specify a list of scalars defining the number of units following each generalized linear model. If NUNITS is used, the units are assumed to be ordered so that all the units with the first generalized linear model come first, then those with the second one, and so on. The DATASET option can then save a factor to indicate which generalized linear model applies to each unit. Alternatively, you can specify a list of null settings (*) for NVALUES, and supply a pre-defined factor using the DATASET option. The DISTRIBUTION parameter specifies the error distributions, the LINK parameter specifies the link function, and the EXPONENT exponent parameter specifies the exponent where there is a power link.

   The Y option specifies response variate, and the NBINOMIAL option specifies the totals for binomial data. Prior weights can be supplied using the WEIGHTS option. The TERMS option specifies the terms to be fitted, and the FULL option controls the parameterization, as in the TERMS directive. The MVINCLUDE option allows units with missing values with missing values in factors or variates in the model to be included (by default these are excluded). Where this occurs, the factor or variate is taken to make no contribution to the fitted value for the unit concerned (see TERMS for more details).

   The CONSTANT option indicates whether or not to fit a constant, and the FACTORIAL option specifies a limit (default 3) on the number of variates and factors in each term, as in the FIT directive. An offset can be supplied using the OFFSET option. The LINEARPREDICTOR option can supply initial values for linear predictor, and the MAXCYCLE option can set a limit (default 30) on the number of iterations. Printed output is controlled by the PRINT option, with the same settings as in the FIT directive.

   After the fit, the RDISPLAY directive can be used to generate additional output, and the RKEEP directive can be used to save information, in the usual way.

 

Options: PRINT, Y, TERMS, NBINOMIAL, DISPERSION, WEIGHTS, OFFSET, CONSTANT, FACTORIAL, FULL, DATASET, LINEARPREDICTOR, MAXCYCLE, MVINCLUDE, SAVE.

Parameter: NVALUES, DISTRIBUTION, LINK, EXPONENT.


Method

RMGLM uses the calculated settings of the DISTRIBUTION and LINK options

of MODEL.


Action with RESTRICT

You can restrict the units that GenStat will use for the fit by putting a restriction on the response variates, weight variate, offset variate, binomial totals, or any explanatory variate or factor. However, you must then supply the initial values for linear predictor (using the LINEARPREDICTOR option), as the default calculation requires use of RESTRICT.