Quest Journals Journal of Research in Applied Mathematics Volume 3 ~ Issue 5 (2017) pp: 01-10 ISSN(Online) : 2394-0743 ISSN (Print): 2394-0735 www.questjournals.org *Corresponding Author: Neha Jain 1 | Page Rahul Gupta Department of Statistics, University Of Jammu, Jammu, J and K, India Research Paper Generalized Additive and Generalized Linear Modeling for Children Diseases Neha Jain, Roohi Gupta and Rahul Gupta* Rahul Gupta Department of Statistics, University Of Jammu, Jammu, J and K, India Received 03 Feb, 2017; Accepted 18 Feb, 2017 © The author(s) 2017. Published with open access at www.questjournals.org ABSTRACT: This paper is necessarily restricted to application of Generalised Linear Models(GLM) and Generalised Additive Models(GAM), and is intended to provide readers with some measure of the power of these mathematical tools for modeling Health/Illness data systems. We are all aware that illness, in general and children illness, in particular is amongst the most serious socio-economic and demographic problems in developing countries, and they have great impact on future development. In this paper we focus on some frequently occurring diseases among children under fourteen years of age, using data collected from various hospitals of Jammu district from 2011 to 2016.The success of any policy or health care intervention depends on a correct understanding of the socio economic environmental and cultural factors that determine the occurrence of diseases and deaths. Until recently, any morbidity information available was derived from clinics and hospitals. Information on the incidence of diseases, obtained from hospitals represents only a small proportion of the illness, because many cases do not seek medical attention .Thus, the hospital records may not be appropriate from estimating the incidence of diseases from programme developments. The use of DHS data in the understanding of the childhood morbidity has expanded rapidly in recent years. However, few attempts have been made to address explicitly the problems of non linear effects on metric covariates in the interpretation of results .This study shows how the GAM model can be adapted to extent the analysis of GLM to provide an explanation of non linear relationship of the covariate. Incorporation of non linear terms in the model improves the estimates in the terms of goodness of fit. The GLM model is explicitly specified by giving symbolic description of the linear predictor and a description of the error distribution and the GAM model is fit using the local scoring algorithm, which iteratively fits weighted additive models by back fitting. The back fitting algorithm is a Gauss-Seidel method of fitting additive models by the iteratively smoothing partial residuals. The algorithm separates the parametric from the non parametric parts of the fit, and fits the parametric part using weighted linear least squares within the back fitting algorithm. Keywords: Generlised additive model, Generalised linear model, weighted linear least squares I. INTRODUCTION Generalized additive model (GAM) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. Generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression , logistic regression and Poisson regression . They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian approaches and least squares fits to variance stabilized responses, have been developed. Significant statistical development in the last three decades has been the advances in regression analysis provided by generalized additive models (GAM) and generalized linear models (GLM).These three alphabet acronyms translate into a great scope for application in many areas of applied scientific research. Based on developments by Cox and Snell[1] in the late sixties, the first seminal publications, also providing the link with practice (through software availability), were