HGDISPLAY procedure

Displays results from a hierarchical or double hierarchical generalized linear model analysis (R.W. Payne, Y. Lee, J.A. Nelder & M. Noh).

Options

PRINT = string tokens Controls printed output (model, fixedestimates, randomestimates, dispersionestimates, likelihoodstatistics, deviance, waldtests, fittedvalues); default *
SEMETHOD = string token Method to use to calculate the se’s for the dispersion estimates (approximate, profilelikelihood); default appr
DMETHOD = string token Method to use for the adjusted profile likelihood when calculating the likelihood statistics (choleski, lrv); default chol
DISPERSIONTERM = formula Model term for output from a dispersion analysis
SAVE = pointer Save structure (from HGANALYSE) to provide details of the analysis; if omitted, output is from the most recent analysis

No parameters

Description

HGDISPLAY is one of several procedures with the prefix HG, which provide tools for fitting the hierarchical and double hierarchical generalized linear models (HGLMs and DHGLMs) defined by Lee & Nelder (1996, 2001, 2006) and described by Lee, Nelder & Pawitan (2006). The models are defined by the HGFIXEDMODEL, HGRANDOMMODEL and HGDRANDOMMODEL procedures, and fitted by the HGANALYSE procedure. HGDISPLAY lets you display further output from the analysis.

The PRINT option specifies what output is required, with settings:

    model details of the model that has been fitted;
    fixedestimates estimates of the fixed effects in the HGLM;
    randomestimates estimates of the random effects in the HGLM;
    dispersionestimates estimates of the parameters in the dispersion models;
    likelihoodstatistics likelihood statistics for assessing the models;
    deviance scaled deviances for assessing goodness of fit;
    waldtests Wald tests of the terms that can be dropped from the fixed model (see HGWALD);
    fittedvalues table with unit number, response variable, fitted values, residuals and leverages.

The SEMETHOD option specifies which method to use to calculate standard errors for the estimated parameters of the dispersion models. The default, approximate, method is efficient to compute, but it may show downwards bias. However, the alternative profilelikelihood method can be very time-consuming. The DMETHOD option controls the method used to calculate the adjusted profile likelihood during the calculation of the likelihood statistics. The default Choleski method is fastest. The lrv method provides a more robust alternative to use if Cholesky fails.

By default the output is from the analysis of the mean model, but you can set the DISPERSIONTERM option to a formula defining one of the random terms to obtain information from the analysis to model its dispersion parameter.

Options: PRINT, SEMETHOD, DMETHOD, DISPERSIONTERM, SAVE.

Parameters: none.

Method

The output is mainly produced using RDISPLAY, RWALD and HGWALD.

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. (2001). 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. (2006). Double hierarchical generalized linear models (with discussion). Appl. Statist., 55, 139-185.

Lee, Y., Nelder, J.A. & Pawitan, Y. (2006). Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood. Chapman and Hall, Boca Raton.

See also

Procedures: HGANALYSE, HGDRANDOMMODEL, HGFIXEDMODEL, HGFTEST, HGGRAPH, HGKEEP, HGNONLINEAR, HGPLOT, HGPREDICT, HGRANDOMMODEL, HGRTEST, HGSTATUS, HGWALD.

Commands for: Regression analysis.

Example

CAPTION  'HGDISPLAY example',\
         !t('Number of faults in rolls of fabric of various lengths',\
         '(data from Bissell (1972) Biometrika, 59, 435-441).'),\
         'Fit negative binomial: var(y) = mu + alpha * mu * mu',\
         '(equivalent to Poisson-gamma HGLM with saturated random effect).';\
         STYLE=meta,3(plain)
VARIATE  [NVALUES=32] length,faults
READ     length,faults
551  6  651  4  832 17  375  9  715 14  868  8  271  5  630  7
491  7  372  7  645  6  441  8  895 28  458  4  642 10  492  4
543  8  842  9  905 23  542  9  522  6  122  1  657  9  170  4
738  9  371 14  735 17  749 10  495  7  716  3  952  9  417  2  :
CALCULATE     loglength = log(length)
&             loglength = loglength - mean(loglength)
FACTOR        [LEVELS=32; VALUES=1...32] saturated
HGFIXEDMODEL  [DISTRIBUTION=poisson; LINK=log] loglength
HGRANDOMMODEL [DISTRIBUTION=normal; LINK=identity] saturated
HGANALYSE     faults
HGDISPLAY     [PRINT=deviance,fitted]
HGDISPLAY     [PRINT=dispersionestimates; SEMETHOD=profile]
Updated on March 7, 2019

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