The measure of the degree to which the particular model differs from the saturated model for the data set. Explicitly in terms of the likelihoods of the two models can be defined as follows

 

  are the likelihoods of the current and the saturated model, correspondingly. Large values of d are encountered when Lc is small relative to Ls, signifying that the current model is a poor one. Small values of d are attained in the overturn case. The deviance has asymptotically a chi-squared distribution with the degrees of freedom equal to the difference in the number of parameters in the two models when the current model is correct.