NON LINEAR GENERALIZED ADDITIVE MODELS USING LIKELIHOOD ESTIMATIONS WITH LAPLACE AND NEWTON APPROXIMATIONS

Vinai George Biju
2020 JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES  
The Generalized Additive Model is found to be a convenient framework due of its flexibility in non-linear predictor specification. It is possible to combine several forms of smooth plus Gaussian random effects and use numerically accurate and wide-ranging fitting smoothness estimates. The Newton interpretation of smoothing provides standardized interval approximations. The Model assortment through additional selection penalties and p-value estimates is proposed along with bivariate combination
more » ... f input variables capturing different non-linear relationship. The proposed extension includes, using non-exponential family distribution, orderly categorical models, negative binomial distributions, and multivariate additive models, log-likelihood based on Laplace and Newton models. The general problem is that there is not one particular architecture do everything with an exponential GAM family. 269 machinery is expanded for smooth configurations to include a stronger AIC model framework. This approach enables computationally accurate inferencing mechanisms using the GAM extensions. The approach also provides the benefit of allowing access for exponential family GAMs to the inferential machinery as proposed. The downside of this technique is that it requires derivatives of the likelihood of the parameters in the higher order to be evaluated. The simple penalty approach offers a wide range of seamless smoothing elements like random Gaussian model. The AIC measure estimates for the penalized regression is yet to be worked on in the near future. VI. Acknowledgement
doi:10.26782/jmcms.2020.07.00021 fatcat:oxcvixj3urdzxoag2dbmrsyzly