Additional information paper Forecasting and Analyzing Insurance Companies’ Ratings by Tony Van Gestel, David Martens, Bart Baesens, Daniel Feremans, Johan Huysmans, Jan Vanthienen to be published in International Journal of Forecasting 1 Difference in Model Fit The quality of the model fit is assessed by the negative log likelihood. In infor- mation criteria, one often uses the model deviance, which is twice the negative log likelihood, as a main indicator. In the case of ordinary least squares regres- sion, the deviance is closely related to the sum squared error. The deviance 1 ) be- tween the full model M 1 (with inputs 1,...,i −1, i, i +1,...,m) and the reduced model M 0 without the corresponding input (inputs 1,...,i − 1,i +1,...,m) are compared. The Bayes factor B 10 is approximated via 2 log(B 10 ) ≈ dev(M 0 ) − dev(M 1 ) = Δdev (1) and indicates the model improvement. This has to be sufficiently large as indicated by Table 1 (Jeffreys (1961)). Table 1: Evidence against the H 0 hypothesis of no improvement of model M 1 over model M 0 for different values of the Bayes factor B 10 (Jeffreys (1961)). 2 log(B 10 ) B 10 Evidence against H 0 0 to 2 1 to 3 Not worth more than a bare mention 2 to 5 3 to 12 Positive 5 to 10 12 to 150 Strong > 10 > 150 Decisive 1 It is preferred to report the deviance as it is straightforward to compute the appropriate complexity criteria from the deviance. 1