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Generalized Additive Models (GAMs) - GitHub Pages

Generalized Additive Models (GAMs)Israel BorokiniAdvanced Analysis Methods in Natural Resources and Environmental Science (NRES 746)October 3, 2016 Outline Quick refresher on linear regression Generalized Additive Models Statistical expression Operations Research Applications R packages for GAMs Examples K selectionRegression Regression methods are used to investigate relationships between predictors and response variables A good model should perform three functions: description, inference and predictionsLinear Regression model Bivariate regression: Y = + X + Multivariate regression: Y = + 1X1+ 2X2+ .. + nXn+ Quadratic regression: Y = + 1X1+ 2X22+ Polynomial regression:Y = + 1X1+ 2X22+ 3X33+ nXnn+ Y-response variable X-explanatory variable -residual error, to cover unexplained information, assumed to be normally distributed with mean of 0 and 2 and are intercept and slope respectively, to be determined at CI = 95% N sample size OLS regression computes values of and that best fit the response by minimizing sum of squared errors (assuming linearity and homoscedasticity)where ~ N (0, 2)Assumptions of linear regression Models Linearity (sensitive to outliers & data inaccuracy) Multivariate normality Little or no multicollinearity& singularity No auto-correlation Homosceda

•A unique aspect of generalized additive models is the non-parametric (unspecified) function f of the predictor variables x •Generalized additive models are very flexible, and provide excellent fit for both linear and nonlinear relationships (multiple link functions) •GAMs can be applied normal distribution as well as Poisson, binomial,

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