In case of a linear regression, it's easy to test a linear relationship between a continuous dependent variable and each independent variable. For example, I can plot a scatter plot between the dependent variable on Y-axis and one of independent variables on X-axis to visualize the relationship before using the linear regression.
But, a logistic regression is different, it assumes a linear relationship between log odds of a binary dependent variable and independent variables. I want to test this assumption to determine if the logistic regression is appropriate for my dataset. Can I test it? and How?
Besides, is there any package in R to do the task?
Best Answer
Nice question. In practice, very few people pretest this assumption, or test it at all. To do so you could divide each independent variable (X) into perhaps 8 or 10 or 15 equal-interval categories. Then compute log-odds as ln(p/[1-p]) within each category, where p = the proportion of cases for which the dependent variable = 1 rather than 0. Finally, use ANOVA or, informally, view a scatterplot to assess the linearity of the relationship between log-odds and this X.