Question

When is the statistical regression test used in social science?

Answer 1

At its heart, regression describes systematic relationships between one or more predictor variables with (typically) one outcome. The flexibility of regression and its many extensions make it the primary statistical tool that social scientists use to model their substantive hypotheses with empirical data.If regression only summarised associations between two continuous variables, it would be a very limited tool for social scientists. However, regression has been extended in numerous ways. An initial and important expansion of the model allowed for multiple predictors and multiple types of predictors, including continuous, binary, and categorical. With the inclusion of categorical predictors, statisticians noted that analysis of variance models with a single error term and similar models are special cases of regression, and the two methods (i.e., regression and analysis of variance) are seen as different facets of a general linear model.

A second important expansion of regression allowed for different types of outcome variables such as binary, ordinal, nominal, and count variables. The basic linear regression model uses the normal distribution as its probability model. The generalized linear model, which includes non-normal outcomes, increases the flexibility of regression by allowing different probability models (e.g., binomial distribution for binary outcomes and Poisson distribution for count outcomes), and predictors are connected to the outcome through a link function (e.g., logit transformation for binary outcomes and natural logarithm for count outcomes).