Produces model-checking plots for a hierarchical or double hierarchical generalized linear model analysis (R.W. Payne, Y. Lee, J.A. Nelder & M. Noh).

### Options

`MODELTYPE` = string token |
Type of model for which plots are required (`mean` , `dispersion` ); default `mean` |
---|---|

`RANDOMTERM` = formula |
Random term whose residuals are to be plotted; default * i.e. the residuals from the full model |

`DHGRANDOMTERM` = formula |
Random model term in a DHGLM whose residuals are to be plotted; default `*` |

`RMETHOD` = string token |
Type of residual to use (`deviance` , `Pearson` , `simple` ); default `devi` |

`INDEX` = variate or factor |
X-values to use for an index plot; default `!(1,2...)` |

`GRAPHICS` = string token |
What type of graphics to use (`lineprinter` , `highresolution` ); default `high` |

`TITLE` = text |
Overall title for the plots; if unset, the identifier of the y-variate is used |

`SAVE` = pointer |
Specifies the analysis (by `HGANALYSE` ) from which the residuals and fitted values are to be taken; by default they are taken from the most recent analysis |

### Parameters

`METHOD` = string tokens |
Types of graph (up to four out of the six possible) to be plotted (`histogram` , `fittedvalues` , `absresidual` , `normal` , `halfnormal` , `index` ); default `hist` , `fitt` , `norm` , `absr` |
---|---|

`PEN` = scalars, variates or factors |
Pen(s) to use for each plot |

### Description

`HGPLOT`

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 discussed by Lee, Nelder & Pawitan (2006). The models are defined by the `HGFIXEDMODEL`

, `HGRANDOMMODEL`

and `HGDRANDOMMODEL`

procedures, and fitted by the `HGANALYSE`

procedure. `HGPLOT`

displays plots of residuals to help with model checking.

Six types of plot are available. They are selected using the `METHOD`

parameter

with settings:

`histogram` |
histogram of residuals; |
---|---|

`fittedvalues` |
residuals versus fitted values; |

`absresidual` |
absolute values of residuals versus fitted values; |

`normal` |
Normal plot; |

`halfnormal` |
half-Normal plot; and |

`index` |
plot against an “index” variable (specified by the `INDEX` option). |

Up to four can be examined in any call of the procedure. The `PEN`

parameter can be used to specify the graphics pen or pens to use for each plot. The `TITLE`

option can supply an overall title. If this is not set, the identifier of the y-variate is used.

The `MODELTYPE`

option indicates the type of model for which the plots are required. The default setting `mean`

requests plots from the mean model, and the alternative setting `dispersion`

obtains plots from the dispersion model. The `RANDOMTERM`

option specifies the random term whose residuals are to be plotted; if this is omitted the plot is for the residual term (phi). If a DHGLM has been fitted, you can plot residuals from the HGLM that is being used as a dispersion model by setting the `DHGRANDOMTERM`

parameter to the random term concerned. The type of residual to plot is specified by the `RMETHOD`

option; by default these are deviance residuals.

By default, high-resolution graphics are used. Line-printer graphics can be used by setting option `GRAPHICS=lineprinter`

.

Options: `MODELTYPE`

, `RANDOMTERM`

, `DHGRANDOMTERM`

, `RMETHOD`

, `INDEX`

, `GRAPHICS`

, `TITLE`

, `SAVE`

.

Parameters: `METHOD`

, `PEN`

.

### Method

`HGPLOT`

calls procedure `DRESIDUALS`

to do the plotting.

### 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`

, `HGDISPLAY`

, `HGDRANDOMMODEL`

, `HGFIXEDMODEL`

, `HGFTEST`

, `HGGRAPH`

, `HGKEEP`

, `HGNONLINEAR`

, `HGPREDICT`

, `HGRANDOMMODEL`

, `HGRTEST`

, `HGSTATUS`

, `HGWALD`

.

Commands for: Regression analysis.

### Example

CAPTION 'HGPLOT example',!t(\ 'Breaking angles of cake baked from 3 recipes at 10 temperatures',\ '(Cochran & Cox, 1957, Experimental Designs, page 300).');\ STYLE=meta,plain FACTOR [NVALUES=270; LEVELS=3] Recipe & [LEVELS=15] Replicate & [LEVELS=!(175,185...225)] Temperature GENERATE Recipe,Replicate,Temperature VARIATE [NVALUES=270] Angle READ Angle 42 46 47 39 53 42 47 29 35 47 57 45 32 32 37 43 45 45 26 32 35 24 39 26 28 30 31 37 41 47 24 22 22 29 35 26 26 23 25 27 33 35 24 33 23 32 31 34 24 27 28 33 34 23 24 33 27 31 30 33 33 39 33 28 33 30 28 31 27 39 35 43 29 28 31 29 37 33 24 40 29 40 40 31 26 28 32 25 37 33 39 46 51 49 55 42 35 46 47 39 52 61 34 30 42 35 42 35 25 26 28 46 37 37 31 30 29 35 40 36 24 29 29 29 24 35 22 25 26 26 29 36 26 23 24 31 27 37 27 26 32 28 32 33 21 24 24 27 37 30 20 27 33 31 28 33 23 28 31 34 31 29 32 35 30 27 35 30 23 25 22 19 21 35 21 21 28 26 27 20 46 44 45 46 48 63 43 43 43 46 47 58 33 24 40 37 41 38 38 41 38 30 36 35 21 25 31 35 33 23 24 33 30 30 37 35 20 21 31 24 30 33 24 23 21 24 21 35 24 18 21 26 28 28 26 28 27 27 35 35 28 25 26 25 38 28 24 30 28 35 33 28 28 29 43 28 33 37 19 22 27 25 25 35 21 28 25 25 31 25 : FACPRODUCT !p(Replicate,Recipe); Batch HGFIXEDMODEL [DISTRIBUTION=gamma; LINK=reciprocal] Recipe*Temperature HGRANDOMMODEL [DISTRIBUTION=inversegamma; LINK=reciprocal] Replicate+Batch HGANALYSE Angle HGPLOT [RANDOMTERM=Replicate] HGPLOT HGPLOT index,normal,halfnormal