# Analyzing the added effect of an individual variable having fitted one variable already, using a generalized linear model

I am using a generalized linear model to analyse my data, there are 6 explanatory variables. I have added all different variable combinations in different models, and ranked them according to their AIC weights. Only one variable is really significant in any of the models, but different models with different combinations of variables rank reasonably closely behind the 'best' model with the highest AIC weight which only contains the explanatory variable that is significant.

I would now like to analyse the effect of the individual variables a bit further, in the sense that I would like to analyse what the effect is of the non-significant variables, while controlling for the significant one. So given the effect that variable $X_1$ (the significant one) has on $Y$, how much more effect does $X_2$ have for example?

I initially thought of fitting a generalized linear model to my data, using only $X_1$, and then fitting another generalized linear model using $X_2$, on the residuals from the first model, however, that method has some major disadvantages I understand. Does anybody have some advice on how else I can do this?

• If we change "generalized linear model" to "regression" will your question change? Oct 21, 2011 at 3:19
• I am not sure. Probably not. Oct 21, 2011 at 4:58

You might consider the added-variable plot or the component-plus-residual plot (of which the CERES plot is a better variant). If you're using R, the car package has these tools built in for both linear models and generalized linear models. The accompanying reference, An R Companion to Applied Regression, has more details, as do (I think) the authors' two regression texts that this reference accompanies.
If I understand your question correctly, you already have run 2^6 = 32 different models and ranked them by AIC. Then, in those 32 will be models with $X_1$ and $X_2$, $X_1$ and $X_3$, and so on. You could look at each of these to see how adding variables changed the effect of $X_1$.