In an auctions website I maintain, auctions are listed most-recent-first. There are 20 auctions per page. A user can click next
in the footer to view older auctions.
It's early days so there's currently no other way to search an auction. The most-recent-first view is the only discovery mechanism. I do provide a filter along cities, but that too in most-recent-first ordering.
I need to infer which features are driving bid submission in this auction website (so that I can improve bid submission rates).
My dataset comprises auctions that were all alive for 7 whole days. My initial plan was to apply logistic regression to this dataset with unique_bids_per_day
as the dependent variable. I had a very useful discussion about that here.
In a nutshell, I was advised that if the dependent variable followed the Bernoulli or Binomial distribution, then logistic/binomial regression could be useful. So I did a quick analysis to check distribution of unique_bids
across the 7 days an auction is live. Results suggest that most bids come within 24 hours of auction submission (or creation). I.e.
This is unsurprising given how the website is organized (described at the start).
So wouldn't this mean that unique_bids_per_day
is not following a binomial distribution (the probability of getting a bid is not uniformly distributed over the life of an auction)? And if that is the case, that would jeopardize using logistic regression in this type of scenario. So then what should I do to infer which features are driving bids? Would be great to get an illustrative answer.
Note: features are categorical and numeric both
This is the head of the data (summarized; the actual data has more features). unique_clicks_per_day
is actually unique_bids_per_day
.
This is the natural log of days_since_submission
. Looks slightly bi-modal:
unique_bids_per_day
can take on? If it is not 0 and 1 then without recoding, you cannot use this variable in a logistic regression. If you could provide a snapshot of the first few lines of your data it would help folks at the site better address your modeling questions. $\endgroup$head
at the end of the question. One way to recodeunique_bids_per_day
could be to calculatemedian_bids_per_day
, and then classify all values above median as1
, and0
otherwise. However, this way, I'd lose some information. Could there be a better way to accomplish the inference I want? Responders to the question I've linked to seemed to imply Binomial regression is the way to go (which I assume is the same as logistic in this case). $\endgroup$unique_clicks_per_day
? It can't be number of clicks because it is not an integer and it doesn't seem like it is a proportion as there is a value in the same vector that exceeds 1. (it is also repeated in the third row of data though that could be a coincidence). $\endgroup$total unique clicks
garnered in 7 days, divided by7
. 7 days is the life of a single auction. $\endgroup$total unique clicks
. Each auction sounds like it last for the same length of time so there is nothing to be gained by standardizing to a daily click rate from an analytical standpoint (it only alters the interpretation). The untransformed variable is now a count variable (has to be an integer between 0 and infinity), and you can now use a generalized linear model (specifically using the Poisson link function). $\endgroup$