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:


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


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


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


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.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s