Forms predictions from a `REML`

model.

### Options

`PRINT` = string tokens |
What to print (`description` , `predictions` , `se` , `sed` , `avesed` , `vcovariance` ); default `desc` , `pred` , `se` , `aves` |
---|---|

`CHANNEL` = scalar |
Channel number for output; default `*` i.e. current output channel |

`MODEL` = formula |
Indicates which model terms (fixed and/or random) are to be used in forming the predictions; default `*` includes all the fixed terms and relevant random terms |

`OMITTERMS` = formula |
Specifies terms to be excluded from the `MODEL` ; default `*` i.e. none |

`FACTORIAL` = scalar |
Limit on the number of factors or variates in each term in the models specified by `MODEL` or `OMITTERMS` ; default 3 |

`PRESENTCOMBINATIONS` = identifiers |
Lists factors for which averages should be taken across combinations that are present |

`WEIGHTS` = tables |
One-way tables of weights classified by factors in the model; default `*` |

`PREDICTIONS` = table or scalar |
To save the predictions; default `*` |

`SE` = table or scalar |
To save standard errors of predictions; default `*` |

`SED` = symmetric matrix |
To save standard errors of differences between predictions; default `*` |

`VCOVARIANCE` = symmetric matrix |
To save variances and covariances of predictions; default `*` |

`SAVE` = REML save structure |
Specifies the save structure from which to predict; default `*` i.e. that from most recent `REML` |

### Parameters

`CLASSIFY` = vectors |
Variates and/or factors to classify table of predictions |
---|---|

`LEVELS` = variates, scalars or texts |
To specify values of variates and/or levels of factors for which predictions are calculated |

`PARALLEL` = identifiers |
For each vector in the `CLASSIFY` list, allows you to specify another vector in the `CLASSIFY` list with which the values of this vector should change in parallel (you then obtain just one dimension in the table of predictions for these vectors) |

`NEWFACTOR` = identifiers |
Identifiers for new factors that are defined when `LEVELS` are specified |

### Description

The `VPREDICT`

directive can be used after the `REML`

directive to produce predictions of the values of the response variate at particular values of the variables in the fixed or random models. By default the predictions are from the most recent `REML`

analysis, but you can use another analysis by supplying its save structure using the `SAVE`

option.

The `CLASSIFY`

parameter specifies those variates or factors to be included in the table of predictions, and the `LEVELS`

parameter supplies the values at which the predictions are to be made. For a factor, you can select some or all of the levels, while for a variate you can specify any set of values. A single level or value is represented by a scalar; several levels or values must be combined into a variate (which may of course be unnamed). Alternatively, if the factor has labels, you can use these to select the levels for prediction by setting `LEVELS`

to a text. A missing value in the `LEVELS`

parameter is taken to stand for all the levels of a factor, or the mean value of a variate.

The `PARALLEL`

parameter allows you to indicate that a factor or variate should change in parallel with another factor or variate. Both of these should have the same number of values specified for it by the `LEVELS`

parameter of `VPREDICT`

. The predictions are then formed for each set of corresponding values rather than for every combination of these values. For example, suppose we had fitted a fixed model containing a factor `Treatment`

, a variate `Time`

representing the times when measurements were made, and a variate `Timesqrd`

containing the squares of the times. We could then put

`VPREDICT Treatment,Timesqrd,Time; PARALLEL=*,Time,*;\`

` LEVELS=*,!(0,1,9,25,49,81),!(0,1,3,5,7,9)`

to produce predictions at times 0, 1, 3, 5, 7 and 9 for the treatments. The `PARALLEL`

parameter specifies that `Timesqrd`

should change in parallel to `Time`

, so that we obtain predictions only for matching values of `Time`

and `Timesqrd`

.

When you specify `LEVELS`

, `VPREDICT`

needs to define a new factor to classify that dimension of the table. By default this will be an unnamed factor, but you can use the `NEWFACTOR`

parameter to give it an identifier. The `EXTRA`

attribute of the factor is set to the name of the corresponding factor or variate in the `CLASSIFY`

list; this will then be used to label that dimension of the table of predictions.

The prediction calculations consist of two steps. The first step is to calculate a table of fitted values. The `MODEL`

, `OMITTERMS`

and `FACTORIAL`

options specify the model to use for this. The formula specified by `MODEL`

is expanded into a list of model terms, deleting any that contain more variates of factors than the limit specified by the `FACTORIAL`

option. Then, any terms in the formula specified by `OMITTERMS`

are removed.

The second step averages the fitted values over the classifications that are not in the list that was supplied by the `CLASSIFY`

parameter. The `WEIGHTS`

option can supply one-way tables classified by any of the factors in the model. These are used to calculate the weight to be used for each fitted value when calculating the averages. Equal weights are assumed for any factor for which no table of weights has been supplied. (Note, this differs from the default in `PREDICT`

, which uses *marginal weights*; see the `PREDICT`

option `ADJUSTMENT`

for details.) In the averaging all the fitted values are generally used. However, if you define a list of factors using the `PRESENTCOMBINATIONS`

option, any combination of levels of these factors that does not occur in the data will be omitted from the averaging. Where a prediction is found to be inestimable, i.e. not invariant to the model parameterization, a missing value is given.

Printed output is controlled by settings of the `PRINT`

option with settings:

`description` |
describes the terms and standardization policies used when forming the predictions, |
---|---|

`predictions` |
prints the predictions, |

`se` |
produces predictions and standard errors, |

`sed` |
prints standard errors for differences between the predictions, |

`avesed` |
prints the average standard error of difference of the predictions, and |

`vcovariance` |
prints the variance and covariances of the predictions. |

By default descriptions, predictions, standard errors and an average standard error of differences are printed. You can also save the results, using the `PREDICTIONS`

, `SE`

, `SED`

and `VCOVARIANCE`

options. You can send the output to another channel, or to a text structure, by setting the `CHANNEL`

option.

Options: `PRINT`

, `CHANNEL`

, `MODEL`

, `OMITTERMS`

, `FACTORIAL`

, `PRESENTCOMBINATIONS`

, `WEIGHTS`

, `PREDICTIONS`

, `SE`

, `SED`

, `VCOVARIANCE`

, `SAVE`

.

Parameters: `CLASSIFY`

, `LEVELS`

, `PARALLEL`

.

### See also

Directives: `REML`

, `VCOMPONENTS`

, `VDISPLAY`

, `VKEEP`

, `PREDICT`

.

Procedures: `VFUNCTION`

, `VLSD`

, `VMCOMPARISON`

, `HGPREDICT`

.

Commands for: REML analysis of linear mixed models.

### Example

" Examples 2:5.3.1-4, 2:5.5.1, 2:5.5.2, 2:5.9.1a, 2:5.9.2 " " Split-plot design (Yates 1937, p.74; also John 1971, p.99)." UNITS [NVALUES=72] FACTOR [LEVELS=6] Blocks & [LEVELS=3] Wplots & [LEVELS=4] Subplots GENERATE Blocks,Wplots,Subplots FACTOR [LABELS=!T(Victory,'Golden rain',Marvellous)] Variety & [LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen VARIATE Yield; EXTRA=' of oats' READ [SERIAL=yes] Nitrogen,Variety,Yield 4 3 2 1 1 2 4 3 1 2 3 4 3 1 2 4 4 1 2 3 2 1 3 4 2 3 4 1 4 2 3 1 1 4 2 3 3 4 1 2 1 3 4 2 2 3 4 1 4 1 3 2 3 4 1 2 3 4 2 1 3 1 4 2 4 3 1 2 1 2 3 4 : 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 : 156 118 140 105 111 130 174 157 117 114 161 141 104 70 89 117 122 74 89 81 103 64 132 133 108 126 149 70 144 124 121 96 61 100 91 97 109 99 63 70 80 94 126 82 90 100 116 62 96 60 89 102 112 86 68 64 132 124 129 89 118 53 113 74 104 86 89 82 97 99 119 121 : VCOMPONENTS [Nitrogen*Variety] Blocks/Wplots/Subplots REML [METHOD=Fisher] Yield VDISPLAY [PRINT=means,stratumvariances] VLSD Nitrogen VGRAPH VDISPLAY [PRINT=effects; PTERMS=Nitrogen] VDEFFECTS [PSE=alleffects] Nitrogen VPLOT VARIATE [VALUES=2(1...18)2] Row & [VALUES=(1,2)18,(3,4)18] Column VDFIELDRESIDUALS Y=Row; X=Column REML [PRINT=*] Yield VPREDICT [PRINT=description,prediction,avesed] Nitrogen VPREDICT [PRINT=description,prediction,avesed] Variety VPREDICT [PRINT=description,prediction,sed] Variety,Nitrogen TABLE [CLASSIFICATION=Nitrogen; VALUES=-3,1,1,1] Ncomp CALCULATE Ncomp = Ncomp / 3 VTCOMPARISONS Ncomp VKEEP TERMS=Variety; MEANS=MV; SEDMEANS=SedV; VARMEANS=VarV & [SIGMA2=Sigma2] Blocks/Wplots; COMPONENTS=Cb,Cwp PRINT MV PRINT [RLPRINT=integers,labels; CLPRINT=integers; RLWIDTH=20] SedV PRINT [RLPRINT=integers,labels; CLPRINT=integers] VarV PRINT Cb,Cwp,Sigma2 VFRESIDUALS [RESIDUALS=residual; SERESIDUALS=seresidual;\ FITTEDVALUES=fittedvalue; SEFITTEDVALUES=sefittedvalue] PRINT Yield,fittedvalue,sefittedvalue,residual,seresidual VFIXEDTESTS [FIXEDTESTS=Drop] PRINT Drop[] VFIXEDTESTS [FIXEDTESTS=Add; WMETHOD=add] PRINT Add[]