Deviance difference

=> différence de déviance :
Quant on crée un modèle linéaire généralisé , un modèle qui a beaucoup de variables explicatives peut être simplifié sous réserve de ne pas perdre en information dans ce processus. On teste cela par la différence de déviance entre les deux modèles qu'on veut comparer :

G = D_sans (pour le modèle sans la variable) - D_avec (pour le modèle avec la variable)

Plus la différence de la déviance résiduelle est petite plus est petit l'impact de la variable éliminée. On peut en faire l'évaluation par un test du Chi² ou par un G-test.

In generalized linear modelling, models which have many explanatory variables may be simplified, provided information is not lost in this process. This is tested by the difference in deviance between any two nested models being compared:
G = D (for the model without the variable) - D (for the model with the variable)

The smaller the difference in (residual) deviance, the smaller the impact of the variables removed. This can be tested by the test.
In the simplest example (in simple linear regression), if the log-likelihood of a model containing only a constant term is and the model containing a single independent variable along with the constant term is multiplying the difference in these
log-likelihoods by -2 gives the deviance difference, i.e.,
G statistics (likelihood ratio test) can be compared with the distribution on df = 1, and it can be decided whether the model with the independent variable has a regression effect (if P < 0.05, it has). The same method can be used to detect the effect of the interaction by
adding any interaction to the model and obtaining the regression deviance. If this deviance is significantly higher than the one without the interaction in the model, there is interaction [the coefficient for the interaction, however, does not give the odds ratio in logistic regression].