# Logistic Regression Model building (dropping p-values)

I'm researching factors that influence how bookable a certain room is with data similar to that of Airbnb. The idea is to look at what has been filled out in a listing of a room (i.e. utilities included, kitchen shared/private, toilet shared/private...) to make a prediction on the probability of booking for a room, as opposed to just taking the average booking. A secondary (and more applied goal) would be to say that certain criteria can be made mandatory as they make the room x-times more bookable. So by including x,y,z the room would be i.e. double as likely to get booked. I have experience with regression but am fairly new to logistic regression, so I'm not 100% sure if this is the most sensible use of this method to get to the above mentioned outcome.

To establish the probability of a booking I have ca. 40 possible criteria that could be predictors in the model which are taken from the listing process of roughly 7000 rooms (I can 'zoom' into different cities and compare to adjust for confounding factors), and after analyzing them and basing it on previous knowledge I came up with around 7-8 that should have the largest effect size.

I figured I would use logistic regression to build the model as I have both continuous predictors and categorical ones, and of course my categorical dependent (booking: either 0 no booking, or 1 booking). My problem is that if I test the significance of those individual predictors on the dependent (booking) they are all significant, but once I start fitting them into a model together the significance drops and only 2 or 3 (and not even the ones with the largest effect size) remain. I assume this is often due to multicollinearity (i.e. bed & desk in a room are usually both filled out together if they happen to be filled out). Another issue is that the data varies a bit across datasets, so some predictors are significant in one dataset (e.g. London), and then they are insignificant when looking at the world dataset. I suppose as this is not an experimental setting it makes it all a bit more complicating.

My questions are:

1. Is logistic regression the most appropriate method?
2. How much do p-values matter when assessing whether a predictor should be fit into the model (I read on some other posts that it shouldn't be your all-or-nothing criterion in selecting predictors, but rather that you should look at changes in pseudo R^2 and goodness of fit). In the end even if the lower bound of the CI of the Odds is below 1 it shouldn't matter to much as in reality if I think about it I doubt adding useful information such as specifications of the kitchen will decrease the bookability of a room.

Btw I'm running it on SPSS

Thanks a lot in advance.

• Can you elaborate on the statement that their significance falls when entered together? Are you using a certain p-value threshold? Apr 25, 2017 at 19:44
• I would say you should be sidestepping the p-value stuff entirely and doing something like penalized logistic regression; don't know if it's available in SPSS. Apr 25, 2017 at 19:52
• @earthlink, I'm just using the standard .05 significance level. So whilst as a single predictor I get something in the range of .00 something, once I add multiple predictors into the model they mostly shoot up beyond .05.
– Jan
Apr 26, 2017 at 7:48
• @benbolker, thanks for the tip. A quick google search didn't yield me much of an answer in regards to it being included in the SPSS package (guess it's time to switch), but I'll look into it a bit better later. Also cross validation and ROC curve should point me into a better direction. Thank you.
– Jan
Apr 26, 2017 at 7:52