# Stepwise binary logit regression - help for bootstrapping in Stata

I am running a stepwise binary logit regression in Stata using 14 independent variables. Two of the independent variables are dummies (assuming a value of 0 or 1). I've tested the independent variables for multicollinearity and adapted them by standardizing or using the natural logarithm of their values in order to mitigate this issue (VIF<2.5). The normal model runs smoothly; however, when I want to bootstrap the sample (# of observations: 73) with 1000 replications I receive p-values of 1.0000. Furthermore, the results conclude with the note: "one or more parameters could not be estimated in 314 bootstrap replicates; standard-error estimates include only complete replications."

Two questions: 1. Is the VIF threshold that I used correct (VIF<2.5)? Which other ways are there to get rid of multicollinearity, without dropping one of the variables? 2. Since I don't assume that multicollinearity is an issue anymore, what else could I have done wrong concerning my bootstraping methodology?

Best! Tim

• Your approach is not honest about the number of parameters estimated. The transformation estimation process needs to be part of the bootstrap as does every other modeling step that utilized $Y$. Collinearity on the other handle, can often ignore $Y$ and can be dealt with pre-outcome modeling. There is no need to compute $P$-values using the bootstrap as you already have those from the original model fit. May 13 '14 at 12:43
• Frank, thanks a lot for your quick reply. To put it into the words of a layperson: this means that I do not need to bootstrap my sample? Isn't the initial sample size of 73 too small to receive appropriate results? Furthermore, what do you mean by "not honest"? That the transformations I chose are not consistent with each other? Unfortunately, the issue of multicollinearity appears when I use a consistent approach.
– Tim
May 13 '14 at 13:04
• You are effectively estimating several more parameters when you try different transformations. You need to let the bootstrap repeate from scratch all the modeling steps each time, including examining transformations. [This is why just fitting regression splines if often a great approach. The bootstrap just refits the regression splines for each re-sample.] May 13 '14 at 16:26
• Concerning your question about $n=73$, I wouldn't expect the bootstrap to improve on the accuracy. May 13 '14 at 17:11