Estimation of Nonparametric Ordinal Logistic Regression Model using Generalized Additive Models (GAM) Method Based on Local Scoring Algorithm

One of the statistical methods used to describe the relationship between categorical scale response variable and categorical or continuous variable of predictors is logistic regression analysis. If the response variable has ordinal scale, it is called ordinal logistic regression. The ordinal response variables is common used in scientific research. There are two approaches to the regression model, i.e. parametric and nonparametric approach. We develop the nonparametric ordinal logistic regression which is an expansion of the ordinal logistic regression model where the regression function is estimated using a nonparametric approach. The aim of this study is determine the regression function estimators of the nonparametric ordinal logistic regression model using Generalized Additive Models (GAM) method based on local scoring algorithm. The GAM method assumes that the regression function is expressed as the sum of the regression functions of each component predictor variables. The local scoring algorithm consists of two loops, namely the scoring step (outer loop) which is iterated until the deviance value converges and the backfitting step (inner loop) is iterated until the Residual Sum of Squares (RSS) value converges.