From a behavioral study data was extracted. The study was about how people change their eating behavior, following visual cues. There were to groups of people: One was shown visual cues and then it was recorded what they chose to eat and the other group was just shown random stuff or nothing and then it was recorded was they chose to eat. This experiment was repeated with the same people a large number of occasions, at different times of day. I have a dataset that precisely recordes personal information about each individual as well as their eating behaviour during each time the experiment was carried out.
The goal is to predict whether the visual cue will make someone eat the stuff presented in the cue or not. The problem is that it is unclear to me how to separate the influence of the treatment from the behavior that they might have shown anyway. I.e., suppose a person sees an image of a cake and then, when he is presented with a variety of different foods, eats cake. How can we know that it was actually the image that influenced him and that he did not wanted to eat cake anyway, so the image change actually nothing?
Thus I can't directly treat it as a binary classification and define a categorical feature, where I assign "1" if someone ate what was in the picture and "0" if he didn't, since by that way I may also identify those who wanted to eat what was in the cue before it was shown to them. How can I solve this problem?