A lot of web-based companies are obsessed with funnel analysis, that is, how the number of people who visit a given page of their site changes as a function of the actions the people had to take to get to that page (e.g. highest number of people on the home page, fewer people on the "account creation page", even fewer on the "enter credit card information for paid subscription" page, etc).
Most of the analyses that I see predict how the total number of people changes from one page to the next, but I feel it would be more informative to model these changes more granularly, utilizing information about the individual users (e.g. whether they've visited the site before, whether they're using desktop or mobile, etc). I think the most natural way to capture this would be with a series of logistic regressions, where each term in the logistic regression for page $n$ is the value of a variable of interest (e.g. browser type) multiplied by the expected value of the conditional bernoulli random variable resulting from the logistic regression for page $n-1$.
However this seems like it would get very messy very fast (especially when we consider tree-structured page branchings), and require a very large number of users to keep the error bounds on the parameter estimates reasonably tight, so I was wondering if anyone knows of a simpler/more standard way of performing this sort of analysis, or can otherwise suggest a better approach? Thanks!