Database Reference
In-Depth Information
The pseudo-R
2
is a measure of how well the fitted model explains the data as
compared to the default model of no predictor variables and only an intercept
term. A
value near 1 indicates a good fit over the simple null model.
Deviance and the Log-Likelihood Ratio Test
In the calculation, the -2 multipliers simply divide out. So, it may
appear that including such a multiplier does not provide a benefit. However, the
multiplier in the deviance definition is based on the log-likelihood test statistic
shown in
Equation 6.14
:
where
T
is approximately Chi-squared distributed
with
The previous description of the log-likelihood test statistic applies to any
estimation using MLE. As can be seen in
Equation 6.15
,
in the logistic regression
case,
where p is the number of parameters in the fitted model.
So, in a hypothesis test, a large value of would indicate that the fitted model is
significantly better than the null model that uses only the intercept term.
In the churn example, the log-likelihood ratio statistic would be this:
with 2 degrees of freedom and a corresponding
p-value that is essentially zero.
So far, the log-likelihood ratio test discussion has focused on comparing a fitted
model to the default model of using only the intercept. However, the log-likelihood
