Do estimated probabilities obtained after logistic regression sum up to the total number of observed successes?

Question

I have a sequence of observed outcomes from independent but not identically distributed Bernoulli trials, and some covariate data. I perform logistic regression, and use it to estimate the probability of each trial succeeding. If I sum these estimates up, do they always add up to the total number of observed successes?

I know that in the absence of covariate data, the MLE of the constant term is the number of successes divided by the number of trials.

i mean, summing estimated probabilities for all observations, i.e. successes and failures. — Alex, Sep 02 '16 at 07:06

score 2 · Accepted Answer · answered Sep 06 '17 at 17:10

2

Yes, assuming there is an intercept in the model, then the fitted probabilities sum to the number of ones in the sample. This can be seen from the likelihood equations.

answered Sep 06 '17 at 17:10

kjetil b halvorsen

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Maybe worth noting that it isn't true for the probit model. – Bill Sep 06 '17 at 20:16

Do estimated probabilities obtained after logistic regression sum up to the total number of observed successes?

1 Answers1