Regularized Ordinal Regression and the ordinalNet R Package

Regularization techniques such as the lasso (Tibshirani 1996) and elastic net (Zou and Hastie 2005) can be used to improve regression model coefficient estimation and prediction accuracy, as well as to perform variable selection. Ordinal regression models are widely used in applications where the use of regularization could be beneficial; however, these models are not included in many popular software packages for regularized regression. We propose a coordinate descent algorithm to fit a broad class of ordinal regression models with an elastic net penalty. Furthermore, we demonstrate that each model in this class generalizes to a more flexible form, for instance to accommodate unordered categorical data. We introduce an elastic net penalty class that applies to both model forms. Additionally, this penalty can be used to shrink a non-ordinal model toward its ordinal counterpart. Finally, we introduce the R package ordinalNet, which implements the algorithm for this model class

Semiparametric generalized linear models

I propose a new class of generalized linear models. As with the existing models, these new models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. However, here, the “baseline” distribution of Y when the linear predictor is zero is left unspecified and is estimated from the data. The response distribution when the linear predictor differs from zero is then generated via exponential tilting of the baseline distribution, yielding a response model that is a member of the natural exponential family, with corresponding canonical link and variance functions. The resulting model has a similar level of flexibility as the proportional odds model. Maximum likelihood estimators are developed for response distribution with finite support, and the new model is studied and illustrated through simulations and example analyses from aging and psychiatry research.

Regularized Ordinal Regression and the ordinalNet R Package

Regularization techniques such as the lasso (Tibshirani 1996) and elastic net (Zou and Hastie 2005) can be used to improve regression model coefficient estimation and prediction accuracy, as well as to perform variable selection. Ordinal regression models are widely used in applications where the use of regularization could be beneficial; however, these models are not included in many popular software packages for regularized regression. We propose a coordinate descent algorithm to fit a broad class of ordinal regression models with an elastic net penalty. Furthermore, we demonstrate that each model in this class generalizes to a more flexible form, that can be used to model either ordered or unordered categorical response data. We call this the elementwise link multinomial-ordinal class, and it includes widely used models such as multinomial logistic regression (which also has an ordinal form) and ordinal logistic regression (which also has an unordered multinomial form). We introduce an elastic net penalty class that applies to either model form, and additionally, this penalty can be used to shrink a non-ordinal model toward its ordinal counterpart. Finally, we introduce the R package ordinalNet, which implements the algorithm for this model class

An Evolutionary Framework for Association Testing in Resequencing Studies

Sequencing technologies are becoming cheap enough to apply to large numbers of study participants and promise to provide new insights into human phenotypes by bringing to light rare and previously unknown genetic variants. We develop a new framework for the analysis of sequence data that incorporates all of the major features of previously proposed approaches, including those focused on allele counts and allele burden, but is both more general and more powerful. We harness population genetic theory to provide prior information on effect sizes and to create a pooling strategy for information from rare variants. Our method, EMMPAT (Evolutionary Mixed Model for Pooled Association Testing), generates a single test per gene (substantially reducing multiple testing concerns), facilitates graphical summaries, and improves the interpretation of results by allowing calculation of attributable variance. Simulations show that, relative to previously used approaches, our method increases the power to detect genes that affect phenotype when natural selection has kept alleles with large effect sizes rare. We demonstrate our approach on a population-based re-sequencing study of association between serum triglycerides and variation in ANGPTL4.</p

A latent variable approach to potential outcomes for emergency department admission decisions

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151329/1/sim8210.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151329/2/sim8210_am.pd