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I have temporal twitter data, and I want to calculate propensity score for the treatment and control group. The problem is, the treatment happened at different time for different user, and I want to compare aggregated values for covariates. For example, for user a1, treatment occurred after six months of account creation, for user a2, treatment occurred after eight months. I want to take the average number of tweets posted by those users before the treatment (for first six and eight months respectively), and find similar users in the control group who posted similar number of tweets for six and eight months. I have other covariates (e.g. average number of hashtags used). Is propensity score matching a suitable approach for this? If so how can I do that?

One approach came to my mind is to find match for each sample in the treatment group individually. For example, first for a1 find match someone in the control group who has similar average tweet for first six months. Then for a2 someone in the control group who has similar average tweet for first eight months and so on. But not sure if this is a valid approach. If not what else I can do?

In our experiment, the treatment is the first tweet of an user that was retweeted more than a certain number of times. We want to compare for example, average number of tweets posted before and after the treatment by a user in treatment group with someone in the control group.

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You can restructure your covariate set so that time till treatment is accounted for. For example, your covariates can be average number of tweets per month, etc., and you can also include length of time till treatment as a covariate. Once you feel you have adequately adjusted for confounding in this way, you can perform a regular PSM analysis. You can also require exact (or coarsened exact) matching on time till treatment, thereby matching treated units with control units that have the same amount of time till treatment. Also, instead of or in addition to matching, you can include these variables in a regression model of your outcome on the treatment, perhaps including interactions between time-till-treatment and treatment.

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