Solved – Testing nonlinearity in logistic regression (or other forms of regression)

assumptionslogisticreferencesregressionregression-strategies

One of the assumption of logistic regression is the linearity in the logit. So once I got my model up and running I test for nonlinearity using Box-Tidwell test. One of my continuous predictors (X) has tested positive for nonlinearity. What am I suppose to do next?

As this is a violation of the assumptions shall I get rid of the predictor (X) or include the nonlinear transformation (X*X). Or transform the variable into a categorical?
If you have a reference could you please point me to that too?

Best Answer

I would suggest to use restricted cubic splines (rcs in R, see the Hmisc and Design packages for examples of use), instead of adding power of $X$ in your model. This approach is the one that is recommended by Frank Harrell, for instance, and you will find a nice illustration in his handouts (§2.5 and chap. 9) on Regression Modeling Strategies (see the companion website).

You can compare the results with your Box-Tidwell test by using the boxTidwell() in the car package.

Transforming continuous predictors into categorical ones is generally not a good idea, see e.g. Problems Caused by Categorizing Continuous Variables.

Related Solutions

Solved – Steps of data analysis using logistic regression

Generally large beta coefficients signal multi-collinearity. You should look for marginals that are zero in your cross-tabulations. You should also pay attention to mpiktas's comment. Testing for linearity (and transforming to categorical) is not generally needed if you have been setting up your data correctly.

Solved – Investigating robustness of logistic regression against violation of linearity of logit

The linearity assumption is so commonly violated in regression that it should be called a surprise rather than an assumption. Like other regression models, the logistic model is not robust to nonlinearity when you falsely assume linearity. Rather than detect nonlinearity using residuals or omnibus goodness of fit tests, it is better to use direct tests. For example, expand continuous predictors using regression splines and do a composite test of all the nonlinear terms. Better still don't test the terms and just expect nonlinearity. This approach is much better than trying different single-slope choices of transformations such as square root, log, etc., because statistical inference arise after such analyses will be incorrect because it does not have large enough numerator degrees of freedom.

Here's an example in R.

require(rms)
f <- lrm(y ~ rcs(age,4) + rcs(blood.pressure,5) + sex + rcs(height,4))
# Fits restricted cubic splines in 3 variables with default knots
# 4, 5, 4 knots = 2, 3, 2 nonlinear terms
Function(f)   # display algebraic form of fit
anova(f)      # obtain individual + combined linearity tests

Best Answer

Related Solutions

Solved – Steps of data analysis using logistic regression

Solved – Investigating robustness of logistic regression against violation of linearity of logit

Related Question