Fits all subsets of the fixed terms in a `REML`

analysis (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`results` ); default `resu` |

`FORCED` = formula |
Terms to include in every model |

`FACTORIAL` = scalar |
Limit for expansion of `FORCED` terms; default 3 |

`SELECTION` = string tokens |
One or two criteria to be printed with the models (`r2` , `adjusted` , `cp` , `ep` , `aic` , `sic` , `bic` , `rss` , `rms` ); default `aic` , `sic` |

`NBESTMODELS` = scalar |
Number of models to print; default * i.e. all |

`BESTMODEL` = pointer |
Saves the best model according to the selected criteria |

`RESULTS` = pointer |
Pointer to save variates containing the criteria for the sets, and F and Wald statistics for the terms that they contain |

`MARGINALTERMS` = string token |
How to treat terms that are marginal to other terms (`forced` , `free` ); default `forc` |

`SAVE` = REML save structure |
Specifies the analysis whose fixed terms are to be tested; by default this will be the most recent `REML` |

### No parameters

### Description

`VALLSUBSETS`

fits all subsets of the fixed terms in a `REML`

analysis. It does this by a generalized regression analysis, with a weight matrix based on the variances estimated from the `REML`

analysis (i.e. with the full fixed model). The subsets are thus assessed using identical estimates of the variance components, allowing statistics such as the Akaike information criterion to be used to assess which subset may be best.

By default, `VALLSUBSETS`

uses the most recent `REML`

analysis. However, you can take an earlier analysis, by using the `SAVE`

option of `VALLSUBSETS`

to specify its save structure (saved using the `SAVE`

parameter of the earlier `REML`

command).

The subsets are formed from all the fixed terms, but you can use the `FORCED`

option to specify terms that should always be included. Terms that are marginal to another fixed term are usually also treated as forced. However, you can set option `MARGINALTERMS`

to free to retain them in the “free” terms that are used to form the subsets. Note that `VALLSUBSETS`

considers only models that obey the principle of marginality. This states that a model that includes an interaction term must also include all its marginal terms. For example, a model that includes the interaction `A.B`

must also include the main effects `A`

and `B`

.

The `SELECTION`

option selects one or two criteria to be printed with the sets, with the settings:

`r2`

% sum of squares accounted for (taking the total sum of squares as the residual from the forced model),

`adjusted`

% variance accounted for (compared to the residual mean square from the forced model),

`cp`

Mallows Cp,

`ep`

mean squared error of prediction,

`aic`

Akaike information criterion,

`sic`

or `bic`

Schwarz (Bayesian) information criterion,

`rss`

residual sum of squares, and

`rms`

residual mean square.

For more details, see the `RSEARCH`

procedure (which is used to do the analyses). `VALLSUBSETS`

reports which subset is best, according to each of the selected criteria. The default selects the Akaike and Schwarz (Bayesian) information criteria.

In addition to the selected criteria, the output shows the number of degrees of freedom fitted in the subset, and probabilities assessing the effect of dropping each of its terms from the subset. The probabilities are obtained from F statistics if the denominator degrees of freedom are available from the original `REML`

analysis. Otherwise they are based on Wald statistics. Terms that are marginal to another term in the subset cannot be dropped. This is indicated by printing `marg`

instead of a probability. Also, terms that are aliased are indicated by printing `aaa`

. By default, all the subsets are printed, but you can set the `NBESTMODELS`

to a scalar, *n* say, to print only the *n* best subsets according to the first criterion specified by the `SELECTION`

option.

The results are printed by default. However, you can set option `PRINT=*`

if you want only to save them, using the `RESULTS`

option. This saves a pointer containing variates storing all the available criteria and the numbers of degrees of freedom, then the Wald statistics for the terms, followed by their probabilities, and then the F statistics and their probabilities.

You can also use the `BESTMODEL`

option to save the best model according to each of the selected criteria. It saves them in a pointer containing either one or two model formulae (according to the number of selected criteria). The formulae are stored in the order in which the criteria were specified by the `SELECTION`

option, and are labelled in the pointer by the names of the criteria.

Options: `PRINT`

, `FORCED`

, `FACTORIAL`

, `SELECTION`

, `NBESTMODELS`

, `BESTMODELS`

, `RESULTS`

, `MARGINALTERMS`

, `SAVE`

.

Parameters: none.

### Method

`VALLSUBSETS`

defines a weighted regression, with weight matrix given by the inverse of the unit-by-unit variance-covariance matrix (obtained using the `UVCOVARIANCE`

option of `VKEEP`

). It then calls the `RSEARCH`

procedure to fit the subsets.

### Action with `RESTRICT`

Any restriction applied to vectors used in the `REML`

analysis will apply also to the results from `VALLSUBSETS`

.

### See also

Directive: `REML`

.

Procedures: RSEARCH, VRFIT, VSCREEN.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VALLSUBSETS example','Guide Part 2, Example 5.3.6a'; STYLE=meta,plain FACTOR [NVALUES=322; LEVELS=27] Dam & [LEVELS=18] Pup FACTOR [LEVELS=2; LABELS=!T('M','F')] Sex FACTOR [LEVELS=3; LABELS=!T('C','Low','High')] Dose VARIATE [NVALUES=322] Littersize,Weight OPEN '%GENDIR%/Examples/GuidePart2/Rats.dat'; CHANNEL=2 READ [CHANNEL=2] Dose,Sex,Littersize,Dam,Pup,Weight; \ FREPRESENTATION=2(labels),4(levels) CLOSE 2 VCOMPONENTS [FIXED=Littersize+Dose*Sex] RANDOM=Dam/Pup REML Weight VALLSUBSETS [MARGINALTERMS=free]