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I have a dataset containing the outcomes of head-to-head matches of a game. I would like to fit a logistic regression model with target variable being the winner of the match and using var_a and var_b as two predictors. The first, var_a is a continuous variable and the second, var_b is a binary variable. For this, I am considering using the difference in var_a between the player and the other player in the match as a predictor rather than the raw values of var_a.

An example few rows might look like this:

match_id winner var_a var_b
1 0 80 1
1 1 76 0
2 0 54 0
2 1 68 0
3 0 71 0
3 1 78 1

As you can see, there are two observations per match.

I feel like if I simply fit a model using all rows of my data, I will run into problems based on the fact that each match would be included twice. This feels almost like a paired samples t-test except for the fact that I have a third variable, var_b which may or may not be present in a given match. For example, in match 2, neither player had var_b.

My thought was to do a bootstrap-esque procedure where I randomly select one observation per match, fit a model, and record the coefficients and then repeat a few thousand times to generate confidence intervals for my coefficient estimates. This is not the same as the bootstrap, since I would not be sampling with replacement, but I'm not sure if any kind of standard bootstrap approach would be appropriate. Perhaps a cluster bootstrap could work?

Is the procedure that I have outlined a reasonable approach or is there some other method which could give me better estimates for the coefficients?

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You could try fitting a logistic regression with 4 predictors: var_a[player_1], var_a[player_2], var_b[player_1], var_b[player_2], the target variable being 0 or 1 (0 if player_1 wins or 1 if player_2).

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