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

Authors:

Vinai George Biju, Prashant CM,

DOI NO:

https://doi.org/10.26782/jmcms.2020.07.00021

Keywords:

Generalized Additive Model,Newton Approximation, Laplace,Diabetic Retinopathy,

Abstract

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 of 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.

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