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# HGPREDICT procedure

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

### Options

`PRINT` = string token What to print (`description`, `predictions`, `se`, `sed`, `vcovariance`); default `desc`, `pred`, `se` Which combinations of factors in the current model to include (`full`, `present`, `estimable`); default `esti` Type of adjustment (`marginal`, `equal`); default `marg` Weights classified by some or all of the factors in the model; default `*` Value of offset on which to base predictions; default mean of offset variate Method of forming margin (`mean`, `total`); default `mean` How to deal with aliased parameters (`fault`, `ignore`); default `faul` What back-transformation to apply to the values on the linear scale, before calculating the predicted means (`link`, `none`); default `none` Which warning messages to suppress (`dispersion`, `nonlinear`); default `*` Supplies the total number of trials to be used for prediction with a binomial distribution (providing a value n greater than one allows predictions to be made of the number of “successes” out of n, whereas the value 1 predicts the proportion of successes); default 1 To save the predictions; default `*` To save standard errors of predictions; default `*` To save matrices of standard errors of differences between predictions; default `*` To save variance-covariance matrices of predictions; default `*` Specifies the save structure (from `HGANALYSE`) of the analysis from which to predict; default uses the most recent analysis

### Parameters

`CLASSIFY` = vectors Variates and/or factors to classify table of predictions To specify values of variates, levels of factors Identifiers for new factors that are defined when `LEVELS` are specified

### Description

`HGPREDICT` 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. `HGPREDICT` allows you to form predictions.

`HGPREDICT` uses the `PREDICT` directive internally. Its options and parameters are a subset of those of `PREDICT`, and are used in the same way except that back-transformations are possible only with conjugate models. Consequently, the default for option `BACKTRANSFORM` is `none`.

The `CLASSIFY` list can contain factors from either the fixed or random models but you may specify only one level for each random factor. If all the factors in a particular random term are in the `CLASSIFY` list, the prediction will use the BLUP (best linear unbiased predictor) for the random effect of the term corresponding to the levels that are specified for its factors. Otherwise, provided that random term was not used as a group term in the analysis (see the `GROUPTERM` option of `HGANALYSE`), the predictions will be at the mean value of the random distribution of the term. Alternatively, if that random term was used as a group term, `HGPREDICT` will make the predictions using the smallest BLUP of the term.

Options: `PRINT`, `COMBINATIONS`, `ADJUSTMENT`, `WEIGHTS`, `OFFSET`, `METHOD`, `ALIASING`, `BACKTRANSFORM`, `NOMESSAGE`, `NBINOMIAL`, `PREDICTIONS`, `SE`, `SED`, `VCOVARIANCE`, `SAVE`.

Parameters: `CLASSIFY`, `LEVELS`, `NEWFACTOR`.

### Method

`HGPREDICT` forms the predictions using the `PREDICT` directive.

### 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.

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

Commands for: Regression analysis.

### Example

```CAPTION  'HGPREDICT example',!t(\
'Breaking angles of cake baked from 3 recipes at 10 temperatures',\
'(Cochran & Cox, 1957, Experimental Designs, page 300).',\
'Data values are assumed to follow a GLM with a gamma distribution',\
'random variables, with inverse gamma distributions and reciprocal',\
'link, for replicates and batches of cake mixture.');\
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
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