Statistical Modeling and Inference for Social Science

Statistical inference and modeling are different topics. One involves expressing the properties of DGPs in terms of parameters and parameters as functions of other variables. The other involves making inferences from observable data back to DGPs, whether those inferences are structured by a model or not.

Statistical inference is necessary to learn about a social process broader than the mere data in front of a researcher any time the process that generates that data or makes it observable has a stochastic element. Statistical modeling is not a necessary implication of any particular metaphysical view about DGPs. But it is helpful to social scientists attempting to learn about stochastic ones. First, statistical models allow for crisp expressions of the link between the positive theory that is often of ultimate interest in social science and data-generating processes (DGPs). Second, statistical models narrow the range of possible DGPs that might have generated the data considerably. This does a great deal of work in structuring the estimation and inference problems that researchers face. In a sense, a model represents a sort of “prior belief” about the workings of the social process under analysis. The analysis precedes from and is informed by that prior belief. And in another sense, models represent “free” information: generating equally certain, equally strong conclusions without a model as are possible with the aid of a model requires a massive increase in available data.