STEPWISE SELECTION OF PREDICTOR VARIABLES

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The next stage is to fit a generalized additive model involving all three of the predictors, and use a stepwise selection strategy with different combinations of predictors in the model to see if there is significant difference in the goodness of fit.

The goodness of fit is gauged by the residual deviance. The lower the residual deviance, the better the model fits the data. 

Model                         Residual df(err) Change in Change 
                              Deviance         Deviance   in df

s(age) + s(number) + s(start)  45.1     71.1      
age + s(number) + s(start)     52.7     73.1     7.6      2.0
s(number) + s(start)           57.6     74.3    12.5      3.2
s(age) + number + s(start)     48.2     73.1     3.1      2.0
s(age) + number + s(start)     50.4     74.1     5.3      3.0
s(age) + s(number) + start     51.0     73.2     5.9      2.1
s(age) + s(number)             61.9     74.1    16.8      3.0
In the above table, the variables occuring with an s in front, e.g. s(age), indicates where the variable has been included using a non-parametric smoother, whilst a variable occuring without an s in front indicates that the variable has been included as a linear term.

The Chi-squared value at the 5% significance level is 5.99 for 2 degrees of freedom, and 7.82 for 3 degrees of freedom.

As a result, it can be seen that the model produces a significantly inferior fit when either age or start is dropped from the model.

Dropping number from the model doesn't give a significantly inferior fit, so it can be concluded that no extra information is gained by including number in the model.

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Generalized Additive Models 23.4.96 Page : 11d of 15