The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Generalized Additive Models: Some Applications
Abstract
Generalized additive models have the form η(x) = α + σ fj (x j ), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj (xj ) nonparametrically, using a scatterplot smoother as a building block. We demonstrate the models in two different analyses: a nonparametric analysis of covariance and a logistic regression. The procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis. A variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions: these include confidence curves, degrees of freedom estimates, and approximate hypothesis tests. The local scoring algorithm is analogous to the iterative reweighted least squares algorithm for solving likelihood and nonlinear regression equations. At each iteration, an adjusted dependent variable is formed and an additive regression model is fit using the backfitting algorithm. The backfitting algorithm cycles through the variables and estimates each coordinated function by smoothing the partial residuals.
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Cites
Robust Locally Weighted Regression and Smoothing Scatterplots
Cleveland, W. S. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481038 · Cited by 11,594
Cross validatory choice and assessment of statistical predictions
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Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
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Self-citationFriedman, J. H., & Stuetzle, W. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477729 · Cited by 2,216
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Residuals and Influence in Regression.
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Linardatos, P., Papastefanopoulos, V., & Kotsiantis, S. (2020) · Entropy · doi:10.3390/e23010018 · Cited by 2,922
Smoothing reference centile curves: The lms method and penalized likelihood
Cole, T. J., & Green, P. J. (1992) · Statistics in Medicine · doi:10.1002/sim.4780111005 · Cited by 2,781
Taylor, S. J., & Letham, B. (2018) · The American Statistician · doi:10.1080/00031305.2017.1380080 · Cited by 2,737
Hastie, T., & Tibshirani, R. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01939.x · Cited by 1,902
Self-citationPenalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
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Metadata
- Authors
- Hastie, T., & Tibshirani, R.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1987-06
- Volume
- 82
- Issue
- 398
- Pages
- 371-386
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W4238293282
- Cited by
- 870
- References
- 28
- FWCI
- 3.31
- Type
- journal article
- Language
- en
- Open access
- closed
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