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I analyse purchase decisions on different products j over a duration of t days. I would like to include random or fixed effects. When I run a Hausman test and include only the time variant variables, then random effects are favored rejecting fixed effects by prob>chi2 =0.075. When I include my time invariant variables such as product category (which is constant over panel=product j), then prob>chi2= 0.000. I am now wondering whether to use random or fixed effects. I thought it makes more sense to include only the time variant variables as usually the invariant variables should be excluded by Stata. I appreciate any recommendations.

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