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      Question

      The Likelihood Ratio (LR) Test is often preferred over

      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. Correct Answer Incorrect Answer
      B The ratio of the restricted likelihood function to the unrestricted likelihood function. Correct Answer Incorrect Answer
      C Twice the difference between the logarithm of the restricted likelihood function and the unrestricted likelihood function. Correct Answer Incorrect Answer
      D The difference between the R2 of the restricted model and the unrestricted model. Correct Answer Incorrect Answer

      Solution

      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). Β· The test statistic (LR) is: LR=2Γ—[ln(LU)βˆ’ln(LR)] Β· Since the logarithm of the unrestricted likelihood (ln(LU)) will always be greater than or equal to the restricted likelihood (ln(LR)), the LR statistic is always non-negative and measures how much the restrictions degrade the fit of the model. It follows a Ο‡2 distribution under the null hypothesis.

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