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In SPSS, when performing binary logistic regression using multiple categorical predictors, a significance level is detailed for the variable overall in addition to each category. This strikes me as useful as the model is built up as the addition of a predictor may negate the effect of previously added variables. What is this overall significance a measure of?

In R, the summary of my GLMs do not include this information. As I am building models I can anova(model0, model1) to test the impact of a new addition. However, how would one then detect if a previous predictor had become insignificant overall? Is the significance of a single category sufficient to warrant inclusion?

I have read the following article which was helpful:

Significance of categorical predictor in logistic regression

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  • $\begingroup$ What do you mean exactly by previous predictors? Are they the predictors in model0? $\endgroup$ – Hotaka Dec 15 '15 at 17:06
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To test if your previous predictor has become non-significant you make a new model without it and do the anova(model0,model1). You might end up doing a lot of anovas, hence the issue with Type 1 errors that alesc mentions.

A better method might be to try model averaging - build all possible models, and then build a weighted average using the AIC scores. This is relatively quick/straightforward to do using the package MuMIn. One of the benefits is that it avoids decisions about what predictors to include, which can end up being somewhat arbitrary.

It also allows a rough significance test for each predictor based on the estimate, and whether the confidence intervals cross zero or not.

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So basically, you are chaining statistical tests. Then you need to consider the Multiple comparisons problem in order to avoid Type I errors.

There are multiple methods to take this into account, but IMO the most convenient way is to use the Holm-Bonferroni method.

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