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 (`automatic` `choleski` , `lrv` ); default `auto` |

`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`

allows you to 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 `choleski`

method is fastest, while the `lrv`

method provides a more robust alternative to use if `choleski`

fails. The default setting, `automatic`

, tries `choleski`

first and then, if that fails, uses `lrv`

instead.

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`

, `HGTOBITPOISSON`

, `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]