Solved – Logistic regression: if only some classes of a categorical variable appear significant

categorical datalogistic

I am performing (rare events) logistic regression analyses in R and want to test several categorical variables consisting of more than two classes. I understood that I can do this by using factor(). However, I am not sure what to do in case some, but not all categories are significant. Can I (1) just leave out the ones that are not significant, assuming their coefficients equal 0, or (2) do I have to include them all in the model, or (3) do I somehow have to recalibrate the logistic regression model with only the significant dummies?

Thanks in advance!

Best Answer

The contrasts you mention are a function of the choice of reference cell, so are arbitrary. Removing dummy variables (combining categories) will ruin type I error, confidence interval coverage, and bias estimates. There is nothing wrong with having 'insignificant' effects in a model.

Related Solutions

Solved – Test independence between quantitative and categorical predictors for logistic regression

I have 8 categories and not ordered. In fact I have 2 categorical variables and multiple numerical variables and I want to train a logistic regression model. I want to test the independence between all my variables (only predictors), and remove the ones that are dependent, meaning that they are redundant in my model.

It would have helped you if you'd started with this information.

1) Pairs of variables with highly significant correlations (i.e. very small p-values) may both be needed in a model - indeed they may be very far from "redundant"; a significant pairwise correlation tells you very little about that. Indeed with large samples even trivially small correlations may be highly significant. Hypothesis tests answer the wrong question here (they don't tell you about the impact of the correlation on your inference).

2) If measures of association with categorical variables don't measure the same kind of dependency that matters in your model, it's not telling you what you need to know about.

3) It's quite possible for variables to be pairwise not all that correlated but highly dependent in larger groups; you can check every pairwise correlation and find it's almost zero, yet still have redundant variables across the whole set.

Your entire approach is simply misguided - it might help, but it might utterly fail to avoid redundancy and it might get you to throw out important variables for no good reason at all. You approach tells you less than you might think about redundancy of your variables.

You need to consider your variables as a collection. The right sort of thing to do is check the condition of your $X$-matrix, or something related to it. Sometimes people use things like variance inflation factors, or how completely each $X_j$ is predicted by the collection of previous (or even all other) $X$'s or various other measures. This sort of checking is fairly standard while doing regressions and GLMs.

Solved – Interpretation of logistic regression intercept with one dumthe coded categorical variable

I think you are making this hard on yourself. Make sure race is a factor variable so that the software provides the overall $\chi^2$ of association with $k-1$ d.f. for $k$ categories. Coding doesn't affect the value of $\chi^2$. Don't use a stepwise process for making inference about the importance of race. Use the overall "chunk" test as described above, which has a built-in perfect multiplicity adjustment besides being invariant to coding. In R this would look like (for a binary or ordinal logistic model predicting $Y$):

require(rms)
f <- lrm(Y ~ rcs(age, 4) + race)
anova(f)   # 3 d.f. test for age, k-1 for race
# also prints 2 d.f. test of linearity in age
# age fit is restricted cubic spline with 4 default knots

When doing multiple imputation with the Hmisc package aregImpute function or with the mice package, you would substitute the following for the 2nd line above:

f <- fit.mult.impute(Y ~ rcs(age, 4) + race, lrm, impute_object, n.impute=20)

which would adjust the covariance matrix for multiple imputation [n.impute recommended to be the percent of observations that have any variable missing].

Best Answer

Related Solutions

Solved – Test independence between quantitative and categorical predictors for logistic regression

Solved – Interpretation of logistic regression intercept with one dumthe coded categorical variable

Related Question