General Model (Generalized Linear Models)

This menu allows you to use any of GenStat's standard range of link functions and error distributions; these are selected using the Distribution and Link function boxes. (If, however, you have a non-standard model, others can be defined by using the MODEL directive in command mode or by using the GLM procedure.) If you choose the negative binomial distribution, you must also specify a fixed value for the aggregation parameter (the parameter k in the formula for the variance in terms of the mean: v = m + m*m/k). You can choose a general power link, in which case you need to specify the exponent; the logratio link, log(m / (m+k)), also requires you to specify the parameter k.

Response Variate

Specifies a variate for the response. This can be entered in directly or can be selected from those within the Available Data list.

Maximal Model

This allows you to specify the most complicated model that you are likely to want to consider. It may be left blank, but this may lead to subsequent inability to compare models because of data that are missing for some explanatory variates but not for others.

Model to be fitted

The model to be fitted is specified by entering a model formula into the Model to be fitted box. The formula can involve both variates and factors which can be selected from the Available Data window, and operators from the Operators window.

Distribution

List of available error distributions. If you select the binomial distribution then you must supply the binomial totals in the space provided. Alternatively, if you select the negative binomial you must supply the aggregation in the space provided or select the estimate aggregation parameter option.

Link Function

Lists the available link functions. If you select the power link function then you must supply the exponent in the space provided. Similarly, if you select the Logratio link function then you must supply the logratio in the space provided.

Change Model

After fitting the model you can investigate other models by using Change Model to add or drop terms. If you specified a maximal model, all new terms must have appeared in that model. If you did not specify a maximal model and a term is introduced with a missing value for a unit previously used in the regression, the model sequence is interrupted and information will be available only for the current model (excluding that unit) and the new model. In command mode, you can also use STEP for stepwise regression.

A generalized linear model can be modified to take account of a fixed contribution to the linear effects for each unit, supplied in a variate referred to as the offset. A variate of weights can also be specified: both of these are available in the Options Menu.