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say i measured the same subjects, in two different times:

I measured for PB variable: which is binary: "yes", "no".

and measured their willingness to save money: which is "continuous" (Likert-scale 1 to 5, actually not continues but I will regard it as like that).

what model can i use, to predict willingness to save money by the predictor PB.?

if it wasn't two measures i would probably just do T-test or something like that. but i have two measurments, in different points of time for the same subjects.

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A crude approach would be to treat "willingness" as normally distributed with constant variance and fit a linear mixed model with PB as the predictor and a random effect for subject. You should of course construct residual plots to make sure that the constant variance assumption, especially, isn't truly outrageous. If not -- and if you have a large sample size and roughly equal numbers of PB=yes and PB=no values -- inference based on this model should be approximately valid.

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