All Subsets Regression - Linear Models

This menu can be used to search through linear regression models. There are various methods for choosing a regression model when there are many candidate model terms. The Change Model menu on the Linear Regression menu provides forward selection, backward elimination and stepwise regression. However these methods result in only one model and alternative models, with an equivalent or even better fit, are easily overlooked. Especially in observational studies with many non-orthogonal terms there are frequently a number of alternative models, and then selection of just one well-fitting model is unsatisfactory and possibly misleading. A preferable method is to fit all possible regression models, and to evaluate these according to some criterion. In this way a number of best regression models can be selected. However the fitting of all possible regression models is very computer intensive. It should also be used with caution, because models can be selected which appear to have a lot of explanatory power, but contain noise variables only. This may occur particularly when the number of parameters is large in comparison with the number of units. Terms should therefore not be selected on the basis of a statistical analysis alone. This menu can be used to perform these model selection methods.

Available Data

This lists data structures appropriate to the current input field. The contents will change as you move from one field to the next. Double-click on a name to copy it to the current input field; alternatively, you can type the name directly into the input field.

Response Variate

Provides a space for you to specify a response variate containing the data.

Model formula of List of explanatory data

Specifies the model candidate terms in the fitted model, which may be set using a model formula or using a list of terms separated by commas.

Terms always included in the model

It is sometimes desirable to include specific terms in every model. Such terms may be specified by in this box, which may be set using a model formula or using a list of terms separated by commas.

Operators

This provides a quick way of entering operators in the Model Terms formula. Double-click on the required symbol to copy it to the current input field. You can also type in operators directly. See model formula for a description of each.

Factorial

You can control the maximum order of interaction to be generated when you use model-formula operators like '*'.

Method

Specifies the model selection methods to be used.

Accumulated	an accumulated analysis of deviance in which all model terms are added one by one to the model in the given order
Pooled	an accumulated analysis of deviance in which terms with the same number of identifiers, e.g. main effects or two-factor interactions, are pooled
Forward Selection	an accumulated analysis of deviance resulting from forward selection
Backwards Elimination	an accumulated analysis of deviance resulting from backward elimination
Forward Stepwise	an accumulated analysis of deviance resulting from stepwise regression starting with no candidate terms in the model
Backward Stepwise	an accumulated analysis of deviance resulting from stepwise regression starting with all candidate terms in the model
All Possible	summary statistics for a number of best models among all possible models