# interpretation of deviance in logistic model

In logistic regression model for binary data,

If the residual deviance(2*(likelihood of saturated model-likelihood of my model)) is 56.728 with df=117, what can I say about the lack of fit of the model?

I don't know whether the deviance should be small, or similar to the degree of freedom when the model fits well.

• The deviance is interpreted in comparison to the null (intercept-only) model. ¿What is the deviance of the null model for your dependent variable? – Gregg H Apr 14 '18 at 16:18

Deviance is a model's goodness-of-fit statistic.

You first need to fit the null model. The difference between the deviances for the null model and your model follows an approximate chi-squared distribution with k-degrees of freedom(df). (k is the difference of dfs between two models.)

For example,

your model deviance (df) = 56.728 (117)

null model deviacne (df) = 70 (120)

=> 70-56.728=13.272 ~ chi_squred (3)

and then you can test the significance of your model.