Likelihood ratio test for Logistic Regression

Using a previous example on logistic regression, the likelihood ratio can be calculated for an estimate of goodness of fit of the parameters in the regression model. Assuming a confidence level of 95%, and hypothesis setting below:

Null hypothesis: A1=A2=0.
Alternative hypothesis: Not A1=A2=0.

Firstly, recall the parameters of the logistic regression are obtained by the Nelder-Mead method:

lr-likelihood-ratio1

Since the maximum likelihood approach is used, the maximum likelihood value, L, is obtained:

lr-likelihood-ratio2

The success and failure count are obtained, and then substituted into the equation below together with the maximum likelihood.

lr-likelihood-ratio3

Finally, the χ² distribution for the value obtained above is determined, with degree of freedom of 2.

lr-likelihood-ratio4

Since P-value is smaller than 0.05, therefore the conclusion is reject the null hypothesis A1=A2=0 and accept Not A1=A2=0.

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