Antunes, PatríciaFerreira, Sandra S.Ferreira, DárioMexia, João T.2020-02-102020-02-102020Patrícia Antunes, Sandra S. Ferreira, Dário Ferreira and João T. Mexia (2020). Multiple Additive Models. Communications in Statistics – Theory and Methodshttp://hdl.handle.net/10400.6/9180The models constituting a multiple model will correspond to d treatments of a base design. Using a classic result on cumulant generation function we show how to obtain least square estimators for cumulants and generalized least squares estimators for vectors \beta, l=1,...,d, in the individual models. Next we carry out ANOVA-like analysis for the action of the factors in the base design. This is possible since the estimators \tilde{\beta }(l) of \beta (l). l=1,...,d, have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions \epsilon_{i}^{\top} \beta (l) i=1,...,k, l=1,...,d, for the individual models. The ANOVA-like analysis will consider homologue components on principal estimable functions. To apply our results we assume the factors in the base design to have fixed effects. Moreover if w=1, and Z(1) has covariance matrix \sigma^{2} \m I_{n}, our treatment generalizes that previously given for multiple regression designs. In them we have a linear regression for each treatment of a base design. We then study the action of the factors on that design on the vectors \beta(l), l=1,...,d. An example of application of the proposed methodology is given.engANOVACumulantsMixed Modelsjournal articleDOI: 10.1080/03610926.2020.1723636