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Psychology research focuses on interactions, and this has deep implicationsfor inference from non-representative samples. For the goal of estimatingaverage treatment effects, we propose to fit a model allowing treatment tointeract with background variables and then average over the distribution ofthese variables in the population. This can be seen as an extension ofmultilevel regression and poststratification (MRP), a method used in politicalscience and other areas of survey research, where researchers wish togeneralize from a sparse and possibly non-representative sample to the generalpopulation. In this paper, we discuss areas where this method can be used inthe psychological sciences. We use our method to estimate the normingdistribution for the Big Five Personality Scale using open source data. Weargue that large open data sources like this and other collaborative datasources can be combined with MRP to help resolve current challenges ofgeneralizability and replication in psychology.

Know your population and know your model: Using model-based regression and poststratification to generalize findings beyond the observed sample