# Should predicted probabilities from Logistic Regression correspond with percentages?

I have conducted a logistic regression in order to identify whether student status (student/non-student), time period (time 1, 2 or 3), or condition (condition 1 or condition 2) predict a binary outcome (buying lunch or purchasing lunch).

I have plotted the predicted probabilities that are saved as a result of the logistic regression to visualise the data. These show a decrease in probability of lunch being bought in time 2 for one of the conditions. However, when looking at the percentages of people who bought their lunch (rather than the predicted probabilities), there is an increase at time 2.

Is it possible for there to be an increase in terms of percentages but a decrease in terms of probabilities, or does this indicate that something has gone wrong with the model?

• There's an "increase" at time 2 relative to what? A multivariate model simultaneously considers the influence of all 3 factors. Simpson's paradox indicates that marginal and conditional differences may be of opposite sign. The general answer to your question is that probs and percents should probably be the same thing. Commented Jul 7, 2017 at 16:48
• @AdamO - Thanks for your comment! I mean an increase from Time 1 to Time 2 Commented Jul 7, 2017 at 17:22
• calculate stratified proportions by time / condition / student and look at the conditional totals. Commented Jul 7, 2017 at 17:24