4-12 3 Tests of Non-nested Hypotheses All of the hypothesis tests concluded thus far have been in the context of“ nested”, models But what if we wanted to compare between the following models? Model 1: y X +u 1+221 Model 2: y,=B,+B, xX2+1 3t We could use R2 or adjusted R, but what if the number of explanatory variables were different across the 2 models? ·还有一些其他的“信息准则” ·但很多情况下,不同的准则可能导致选取不同的模型。 An alternative approach is an encompassing test, based on examination of the hybrid model: Model 3:y,=n,+r,x,,+r3xa,+4-12 3 Tests of Non-nested Hypotheses • All of the hypothesis tests concluded thus far have been in the context of “nested” models. • But what if we wanted to compare between the following models? • We could use R2 or adjusted R2 , but what if the number of explanatory variables were different across the 2 models? • 还有一些其他的“信息准则”。 • 但很多情况下，不同的准则可能导致选取不同的模型。 • An alternative approach is an encompassing test, based on examination of the hybrid model: t t t t t t y x v y x u = + + = + + 1 2 3 1 2 2 Model 2 : Model1:     t t t wt Model 3: y =  1 + 2 x2 + 3 x3 +