Question

The Likelihood Ratio (LR) Test is often preferred over

Q: Answer-The Likelihood Ratio (LR) Test is often preferred over the Wald Test or the Lagrange Multiplier (LM)...

Solution The Likelihood Ratio LR test compares the maximum likelihood achieved under the restricted hypothesis LR with the maximum likelihood achieved under the unrestricted full hypothesis LU. The test statistic LR is LR2lnLUlnLR Since the logarithm of the unrestricted likelihood lnLU will always be greater than or equal to the restricted likelihood lnLR, the LR statistic is always non-negative and measures how much the restrictions degrade the fit of the model. It follows a 2 distribution under the null hypothesis.

the Wald Test or the Lagrange Multiplier (LM) Test for hypothesis testing in models like Maximum Likelihood Estimation (MLE). The LR test statistic is given by:

A Twice the difference between the logarithm of the unrestricted likelihood function and the restricted likelihood function.

B The ratio of the restricted likelihood function to the unrestricted likelihood function.

C Twice the difference between the logarithm of the restricted likelihood function and the unrestricted likelihood function.

D The difference between the R2 of the restricted model and the unrestricted model.

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