Penalized regression with individual deviance effects
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The present work addresses the problem of model estimation and computations for discrete data when some covariates are modeled smoothly using splines. We propose to introduce and explicitly estimate individual deviance effects (one for each observation), constrained by a ridge penalty. This turns out to be an effective way to absorb model excess variation and detect systematic patterns. Large but very sparse systems of penalized likelihood equations have to be solved. We present fast and compact algorithms for fitting, estimation and computation of the effective dimension. Applications to counts, binomial, and survival data illustrate practical use of this model.
KeywordsGeneralized linear models Smoothing Effective dimension Penalized regression
The authors would like to thank the two referees for their helpful suggestions and comments on the original manuscript.
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