Suppose we have two Binomial proportion GLMs Model 1 and Model 2, where one of t

Question

Suppose we have two Binomial proportion GLMs Model 1 and Model 2, where one of the models is nested within the other. I provide you with the following information. On the basis of this information, which model is preferred if you only consider an approximate hypothesis test that we have discussed in class? Within your answer, you must clearly write: Your null and alternative hypotheses in terms of these two models (i.e.. specify which model corresponds to H_0 and which model corresponds to H_a), based on the information that one of the models is nested within the other). the theoretical form of the random test statistic and its approximate distribution if the null distribution is true, your decision rule if testing at significance level alpha = 0.01 (i.e., specify your rejection region), the actual observed value of your test statistic based on the numeric values within the table above, the p-value of your test, and your hypothesis testing decision.

Explanation / Answer

H0: One model is not nested within the other model

H1: One model is nested within the other model

This test follows chisquare distribution with alpha los and n-1 df

If P value > alpha 0.01, we accept H0 otherwise we reject H0

Here P-value < alpha 0.05, we reject H0

Thus we conclude that One model is nested within the other model

residual residual Model Deviation df deviation df P-value Model 1 8.9 8 Model 2 25.2 11 16.3 3 0.000984

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