Calculates likelihood tests to assess the random terms in a generalized linear mixed model (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`tests` ); default `test` |

`SELECTION` = string tokens |
Specifies information to print with the tests (`aic` , `sic` , `bi` c, `critical` ); default `crit` |

`CRITICAL` = variate |
Saves the index number that follows the prefix in the filename |

`GLSAVE` = pointer |
Save structure of the original analysis from `GLMM` ; default `*` uses the save structure from the most recent GLMM analysis |

### Parameters

`TERMS` = formula |
Random terms to be tested; default is to test them all |

`TESTSTATISTIC` = scalar or pointer to scalars |
Test statistics for each term |

`DF` = = scalar or pointer to scalars |
Degrees of freedom of the test statistics |

`AIC` = = scalar or pointer to scalars |
Akaike information coefficients for each term |

`sIC` = = scalar or pointer to scalars |
Schwarz (Bayesian) information coefficients for each term |

### Description

`GLRTEST`

can be used after a `GLMM`

analysis to assess the effect of dropping random terms from the model. It uses the `REML`

deviances to do this. In the `GLMM`

algorithm, `REML`

is used to analyse the adjusted dependent variate *z*, with the variate of iterative weights, defined by the generalized linear model. These depend on the current fitted values, and change at each iteration until convergence. (See the *Method* section of the `GLMM`

procedure for more details.) The `REML`

deviance is taken from the analysis of the final adjusted z-variate with the final iterative weights.

`GLRTEST`

saves the deviance from the original analysis using `VKEEP`

, and the final adjusted z-variate and variate of iterative weights using `GLKEEP`

. It then does `REML`

analyses with these variates, omitting each random term, saving their deviances, and calculating their differences from the original deviance. Akaike and Schwarz (Bayesian) information coefficients are obtained using the `VAIC`

procedure.

Note that, for compatibility, it is important to use the same adjusted z-variate and the same iterative weights as in the original analysis. With the alternative, of doing `GLMM`

analyses removing each random term, we would be taking deviances from `REML`

analyses with their own adjusted z-variates and weights, which could be very different from those in the original analysis. So we would be comparing `REML`

analyses with different models, different response variates and different weights, which would not provide a valid comparison. Of course this does mean that the results pertain to the `REML`

analysis rather than to the `GLMM`

analysis itself. So they should be used as guidance rather than as a definitive test. Often, however, the random terms will have been defined by the design of the investigation. The tests will then be used more as an indication of the effectiveness of the design than to decide whether to omit terms from the analysis.

By default, `GLRTEST`

produces tests for every random term. However, you can use the `TERMS`

parameter to request tests for a specific set of terms.

The default is to print the tests, but you can set option `PRINT=*`

to suppress this. The additional information to be printed with the tests is controlled by the `SELECTION`

option, with settings:

`aic `

Akaike information coefficients;`sic`

Schwarz (Bayesian) information coefficients;`bic`

synonym for sic, and`critical`

critical values (default).If the variance components are unconstrained, the critical values are from a chi-square distribution with one degree of freedom. Alternatively, if they are constrained to be positive, the asymptotic distribution of test is a 50:50 mixture of chi-square distributions with zero and one degree of freedom. Essentially this means that the critical values are from a chi-square distribution with one degree of freedom but at double the probability level. See, for example, Lee, Nelder & Pawitan 2006, Section 6.5. The `CRITICAL`

option can save three critical values, in a variate with units for probabilities of 0.05, 0.001 and 0.001.

The `TESTSTATISTIC`

parameter can save the statistics. the DF parameter can save their numbers of degrees of freedom. (These will always be equal to one, but the parameter is included for compatibility with the `HGFTEST`

and `HGRTEST`

procedures.) The `AIC`

and `SIC`

parameters can save the Akaike and Schwarz (Bayesian) information coefficients, respectively. If you are making a test for a single term, you can supply a scalar for each of these parameters. However, if you have several terms, you must supply a pointer which will then be set up to contain as many scalars as there are terms.

Options: `PRINT`

, `SELECTION`

, `CRITICAL`

, `GLSAVE`

.

Parameters: `TERMS`

, `TESTSTATISTIC`

, `DF`

, `AIC`

, `SIC`

.

### See also

Procedures: `GLDISPLAY`

, `GLKEEP`

, `GLMM`

, `GLPLOT`

, `GLPERMTEST`

, `GLPREDICT`

, `GLTOBITPOISSON`

.

Commands for: Regression analysis.

### Example

CAPTION 'GLRTEST example',\ !t('Data from an experiment on Great Knott, Rothamsted;',\ 'see West, J.S., Fitt, B.D.L., Leech, P.K., Biddulph, J.E.,',\ 'Huang, Y.-J. &, Balesdent, M.-H. (2002).',\ 'Effects of timing of ~italic{Leptosphaeria maculans}',\ 'ascospore release and fungicide regime on phoma leaf spot',\ 'and phoma stem canker development on winter oilseed rape',\ '(~italic{Brassica napus}) in southern England.',\ 'Plant Pathology, 51, 454–463.'); STYLE=meta,plain SPLOAD '%data%/GtKnott2000.gsh' GLMM [PRINT=model,components,wald,deviance; DISTRIBUTION=binomial;\ LINK=logit; DISPERSION=*; FIXED=Cultivar*Fungicide;\ RANDOM=Block/Wholeplot] LMplants; NBINOMIAL=Nplants GLRTEST [SELECTION=aic,sic,critical]