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Usually when fitting a logit or probit model to data, one has a dependent binary outcome variable (say, university attendance = [0, 1]) and the usual set of independent variables (for the sake of it, say, parent income, gender and some measure of ability).

In my case, things are a bit different. To stay within the example, for my main data set I do not know whether people attended university. The only aspects I have information about are parent income, gender and other independent variables. However, I was able to obtain data on university attendance for a random subset of the data. Using this subset I fitted a logistic model, obtaining coefficients for all independent variables.

How can I use these coefficients to predict the probability of university attendance for everyone else?

[Please note that the education example is only made to simplify things.]

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  • $\begingroup$ i don't believe that you can say somethng like "given that your family income is a, the probability to attend at university is b". I believe coeeficients can be interpreted as "given the income a, the probability a student attend at a university is b times higher/lower than someone else with an income c" $\endgroup$ – Yorgos Jan 16 '17 at 20:08
  • $\begingroup$ I think that there is a group here (cross validated) where there are myuch more xperienced members who can help you with statistical inference $\endgroup$ – Yorgos Jan 16 '17 at 20:11
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    $\begingroup$ @Yorgos: if it is a logistic model then it is multiplying the odds rather than the probability. But given the data and a decent model you can make predictions about the odds and thus the probabilities for other individuals for whom you have the independent data though not the outcome $\endgroup$ – Henry Jan 16 '17 at 21:23
  • $\begingroup$ What do you mean exactly by: "I was able to obtain data on university attendance for a random subset of the data." - do you have specific attendance data for individuals, or not? How do you know that the subset is "random", and what do you mean by "random" in this case? $\endgroup$ – EnergyNumbers Feb 17 '17 at 2:02
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If I understood you correctly, $\Lambda(x_i'\hat\beta)$, where $\Lambda(x) = e^x / (1+e^x)$. You can use predict in both R and Stata. Try in Stata:

clear all
*** Generate data
set obs 10
set seed 1
gen x = rnormal()
gen y = 1+x+rnormal() > 0
replace y = . in 7/10
list
*** Estimate
logit y x
*** Predict
predict phat, p
list

For clarification, I presumed that your outcome variable is in $\{0,1 \}$ (not in $[0,1]$). You observe $y_i$ for some $i$ but not for all, you fitted a logit regression, and then you want to predict the probability for every $i$. Please let me know if I misinterpreted your question.

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