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11 More Regression Methods > 11.7 Regression Interactions and Moderator Analysi... - Pg. 589

Chapter 11 More Regression Methods 589 of the sample size, using linear interpolation where necessary. By default, all components are tested. The argument jv can be used to limit which components are tested. For example, jv=2 would test only H 0 : g 2 (x 2 ) = 0. 11.7 Regression Interactions and Moderator Analysis As an application of the method in Section 11.6.3, note that it provides a flexible approach to the so-called regression interaction problem. Consider the two predictor case and let c 1 and c 2 be two distinct values for the second predictor, x 2 . Roughly, no interaction refers to a situation where the regression line between y and x 1 , given that x 2 = c 1 , is parallel to regression line between y and x 1 , given that x 2 = c 2 . An early approach to modeling interactions assumes that y = 0 + 1 x 1 + 2 x 2 + 3 x 1 x 2 + , (11.18) where an interaction is said to exist if 3 = 0 (e.g., Saunders, 1956). This model often plays a role in what is called a moderator analysis, roughly meaning that the goal is to determine the extent to which knowing the value of one variable, x 2 here, alters the association between y and x 1 . Note that Eq. (11.18) can be written as