![]() ![]() So the fit of S + B is not significantly better than S. Adding B to the S model (i.e., comparing S + B to S) drops the deviance by only.So the S model fits significantly better than the Null model. But the B model still is not a good fit since the goodness-of-fit chi-square value is very large. So the B model fits significantly better than the Null model. ![]() Adding B to the Null model drops the deviance by 36.41 − 28.80 = 7.61, which is highly significant because \(P(\chi^2_1 \geq 7.61)=0.006\).Here are the p-values associated with the G 2 statistics: For this purpose, it helps to add p-values to the analysis-of-deviance table. The goal is to find a simple model that fits the data. But the S model cannot be directly compared to the B model because they are not nested. The S model or B model may be compared to S + B. The Null (intercept-only) model can be compared to any model above it. The method described here holds ONLY for nested models.įor example, any model can be compared to the saturated model. Recall that full model has more parameters and setting some of them equal to zero the reduced model is obtained. This is exactly similar to testing whether a reduced model is true versus whether the full-model is true, for linear regression. To a χ 2 distribution with degrees of freedom equal to Δ X 2 = X 2 for smaller model − X 2 for larger model Δ G 2 = G 2 for smaller model − G 2 for larger model the smaller model is a special case of the larger one) then we can testīy doing likelihood ratio testing, and comparing In this case, we are checking for the change in deviance and if it is significant or not. F-statistic, due to dropping or adding a parameter. This is like ANOVA table you have seen in linear regressions or similar models, where we look at the difference in the fit statistics, e.g. The above table is an example of "analysis-of-deviance" table. ![]()
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