Say you have a design that looks like a 2 by 2
factorial ANCOVA, but your dependent variable is a 0/1 variable. In such
a case, using a normal ANCOVA is not really appropriate since the variable is
0/1, so instead you use probit. You code the data using dummy
codes to indicate the main effect of factor 1 (b1) the main effect of factor 2
(b2) and the interaction (b1 * b2 = b3), and you have a covariate. You then
run the probit as shown below
clear
input y cell b1 b2 b3 cov1
0 1 0 0 0 43
1 1 0 0 0 54
0 1 0 0 0 44
0 2 0 1 0 49
1 2 0 1 0 45
1 2 0 1 0 42
0 3 1 0 0 54
1 3 1 0 0 34
1 3 1 0 0 56
0 4 1 1 1 45
0 4 1 1 1 67
1 4 1 1 1 54
endprobit y b1 b2 b3 cov1
Probit estimates Number of obs = 12
LR chi2(4) = 1.48
Prob > chi2 = 0.8300
Log likelihood = -7.5772029 Pseudo R2 = 0.0890——————————————————————————
y | Coef. Std. Err. z P>|z| [95% Conf. Interval] ———+——————————————————————–
b1 | .8854965 1.063108 0.833 0.405 -1.198157 2.96915
b2 | .8240042 1.060277 0.777 0.437 -1.2541 2.902108
b3 | -1.575389 1.551571 -1.015 0.310 -4.616412 1.465635
cov1 | -.0188094 .0544449 -0.345 0.730 -.1255194 .0879006
_cons | .466865 2.699602 0.173 0.863 -4.824257 5.757987
——————————————————————————
Then, if you want to get predicted probabilities for
each cell, but adjusted for the covariate, you use the adjust command
below. Note that by(cell) is just giving you the probabilities
for the 4 cells of the 2 by 2.
adjust cov, by(cell) pr ci
The output is shown below, with the predicted
probabilities and the confidence intervals.
——————————————————————————-
Dependent variable: y Command: probit
Variables left as is: b1, b2, b3
Covariate set to mean: cov1 = 48.916668
——————————————————————————-———-+———————————–
cell | pr lb ub
———-+———————————–
1 | .325193 [.028601 .840207] 2 | .644598 [.125401 .970618] 3 | .667227 [.144304 .97293] 4 | .37482 [.028089 .898211] ———-+———————————–
Key: pr = Probability
[lb , ub] = [95% Confidence Interval]