I am using a logistic regression model to predict a binary decision (purchase, don't purchase) based on several independent variables (income, age, education, etc.) for a population of individuals (customers). I have data for individuals from one or more previous time periods, and I want to predict behavior for different individuals in a future time period. Unfortunately, my experience is with explanation, not prediction.
My real interest is in predicting aggregate behavior--for example, what are total predicted purchases by customers in a future time period based on their characteristics? I can see two ways of doing this. First, I could use the parameters from the logistic regression model to generate a probability [0-1] for each customer in the future time period, then use a cut value (0.5) to resolve those probabilities to either 0 or 1, then sum the 1s to generate an estimate of total purchases. Second, I could use the parameters from the logistic regression model to generate a probability [0-1] for each customer in the future time period (as before), then simply sum those probabilities to generate an estimate of total purchases (without using a cut value).
The second approach (adding the probabilities) makes the most sense to me, but the reference material I have consulted so far frames the prediction task in terms of cut values and classification tables. Is the second approach conceptually flawed? If so, why? Thanks very much.
ADDENDUM: With regard to the references I consulted, it was often suggested to use cut values and classification tables, with training and validation sets, to evaluate the real-world performance of a logit model. However, I would have thought that summing the probabilities would have been a better way to do that.