Generalized Additive ModelsThis book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text. |
Contents
Smoothing | 9 |
Smoothing in detail | 39 |
Additive models | 82 |
Some theory for additive models | 105 |
Generalized additive models | 136 |
Response transformation models | 174 |
Extensions to other settings | 201 |
Further topics | 235 |
Case studies | 281 |
Appendices | 301 |
| 311 | |
| 325 | |
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Common terms and phrases
absent additive fit additive model analysis approximation asymptotic B-splines backfitting algorithm basis functions bias binary bootstrap C-peptide Chapter components computed concurvity convergence covariance criterion cross-validation cubic smoothing spline cubic spline curves defined degrees of freedom denote derived described deviance df err diagonal discuss distribution eigenvalues eigenvectors equivalent kernel estimating equations example Exercise exponential family f₁ fitted functions fitted values Gaussian interaction interior knots iterative kernel smoothers kyphosis least-squares likelihood linear model linear regression linear smoothers locally-weighted running-line logistic logistic regression logit mean squared error method minimize neighbourhood Newton-Raphson nonlinear nonparametric observations operator optimal ozone partial residuals penalized least-squares plot points pointwise predictor problem regression model regression splines response running-line smoother sample scatterplot scatterplot smoother shows simple simulated smoothing parameter solution span standard-error bands surface symmetric tr(S transformation variance vector virus level Wahba weights zero