So I'm currently trying to use a multinomial logistic regression model in R on a data set with 13 variables (mix of continuous and categorical) and 33,000 observations, where the dependent variable has 4 different categories. To do this properly though I need to test the following assumption:
"There needs to be a linear relationship between any continuous independent variable and the logit transformation of the dependent variable"
I'm not sure on how best to carry this out. After a bit of research I found a possible solution where I could create a simple logistic regression model for each individual category in the outcome variable and then look at the plot of binned residuals against the estimated probabilities. Still in need of some further advice on whether this is a correct solution or if there is a better way to do this. Thanks