Dear all, Thank you for your remarks. The data under analysis were multiply-imputed using Mice. To compare the nested models, I used the following R codes by van Buuren: pool.compare (Model2, Model1, method = c("wald"), data = NULL) As far as I know the Wald statistic tests the null hypothesis that the extra parameters are all zero. But I might be wrong... -----Message d'origine----- De?: CHATTON Anne Envoy??: vendredi, 5 octobre 2018 10:46 ??: 'r-help at r-project.org' <r-help at r-project.org> Objet?: Strange paradox Hello, I am currently analysed two nested models using the same sample. Both the simpler model (Model 1 ~ x1 + x2) and the more complex model (Model 2 ~ x1 + x2 + x3 + x4) yield the same adjusted R-square. Yet the p-value associated with the deviance statistic is highly significant (p=0.0047), suggesting that the confounders (x3 and x4) account for the prediction of the dependent variable. Does anyone have an explanation of this strange paradox? Thank you for any suggestion. Anne