I will specify some thought, and you decide whether to use them ;)
First of all there are definitely several levels of the problem solution to look out:
- the obvious one is based on direct dependencies of number of installations, duration, prices, so you should start by using these features;
- first hidden area to consider when working on additional features is your typical customer profile and everything that can be related to it, so if you gather more data about the person who actually buys you will be able to target better when doing marketing/sales for the app;
- second hidden area to consider is data about your direct and/or indirect competitors, if you manage to get data related to their marketing/sales strategy it may help you to better understand what can be/should be a target for analysis and prediction;
- third area is seasonality-related parameters, possibly the in-app purchase decisions that were taken were seasonable, and possibly there are criterions by changes which you can change the influence of seasonability.
- and of course the part related to the product itself... possibly there is a lack of value for those who rejected to buy and opposite - those who bought definitely found something very valuable there.
As for the model and algorithm: it is more important to clarify the goal at this stage, and decompose it into all sub-parts and sub-parameters( purchase may contain not just payment decision but also a lot of parts from previous 'stage' of purchase process like search for solution, awareness of the existing demand etc.). That could be any: classification, regression type of a solution needed, or may be you should start from customer segmentation let's say with a help of SOM.
Be creative and approach with a more complex view of the problem that you are solving.
And Good uck!