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I am currently collecting mobile device data about user location and the time at which an app is being used for a cohort of users and apps. I am trying to predict which apps are likely to be used at a given time by a given user.

Which model should i use in order to predict the apps that are likely to be used by a particular user? For example, should I collect data for 5 days a week then use the 3 days for training and then the other 2 days for testing? Given location, time of day, and day, what model should I use to predict which app is likely to be used?

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Much depends on the data available to you. Perhaps you can be more specific about the scale and scope.

Modelling time is the straightforward bit. To understand how to conceptualise time as useful features, see this excellent answer on Machine learning - features engineering from date/time data

Modelling the user is more complicated. You will likely not have enough data on each user, but you can build some user models. (Too few, then the system will make similar predictions for all users, without nuance. Too many and there will be sparsity, overfitting, and generally the same problems as having no profile models at all, ie one model per actual user.)

This can be done supervised or unsupervised, finding representative clusters.
(Search for user profile categorisation, user models, user model clustering)