Alternatives to Ordinary Least Squares Regression

OLS regression is the most basic regression modeling strategy and is generally the starting point for the study of regression. Recall that OLS can be used only when a DV is continuous and (reasonably) normally distributed. As you might have already guessed, researchers often confront DVs that do not meet one or both of these criteria. A DV might be nominal or ordinal, or it could be heavily skewed. It might contain a substantial number of zeros, which throws the OLS calculations off.

Various regression techniques are available for situations when the DV violates the OLS assumptions. We will not go into them in detail, but it is worth knowing the names of at least some of the most common models. Each one is specific to a certain kind of DV.

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When a DV is dichotomous (i.e., categorical with two classes), binary logistic regression is used. Binary logistic regression calculates the probability of any given case in the data set falling into the category of interest. The DV might be, for instance, whether a defendant was sentenced to prison. Binary logistic regression would tell the user whether and to what extent each of the IVs (offense type, prior record, and so on) increases the probability of a defendant being sent to prison. Additionally, a severely skewed DV can sometimes be dichotomized (i.e., split in half) and put through binary logistic rather than OLS. Binary logistic regression is very popular. There are two other types of logistic regression that are used for categorical DVs. For a nominal DV with three or more classes, multinomial logistic is available. For an ordinal DV with three or more classes, ordered logistic can be employed. Each of these types of models functions by sequentially comparing pairs of classes.

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