54,897 research outputs found
Fixed effects selection in the linear mixed-effects model using adaptive ridge procedure for L0 penalty performance
This paper is concerned with the selection of fixed effects along with the
estimation of fixed effects, random effects and variance components in the
linear mixed-effects model. We introduce a selection procedure based on an
adaptive ridge (AR) penalty of the profiled likelihood, where the covariance
matrix of the random effects is Cholesky factorized. This selection procedure
is intended to both low and high-dimensional settings where the number of fixed
effects is allowed to grow exponentially with the total sample size, yielding
technical difficulties due to the non-convex optimization problem induced by L0
penalties. Through extensive simulation studies, the procedure is compared to
the LASSO selection and appears to enjoy the model selection consistency as
well as the estimation consistency
Regularization for Generalized Additive Mixed Models by Likelihood-Based Boosting
With the emergence of semi- and nonparametric regression the
generalized linear mixed model has been expanded to account for additive predictors. In the present paper an approach to variable selection is proposed that works for generalized additive mixed models. In contrast to common procedures it can be used in high-dimensional settings where many covariates are available and the form of the influence is unknown. It is constructed as a componentwise boosting method and hence is able to perform variable selection. The complexity of the resulting estimator is determined by information criteria. The method is nvestigated in simulation studies for binary and Poisson responses and is illustrated by using real data sets
Regularization for Generalized Additive Mixed Models by Likelihood-Based Boosting
With the emergence of semi- and nonparametric regression the
generalized linear mixed model has been expanded to account for additive predictors. In the present paper an approach to variable selection is proposed that works for generalized additive mixed models. In contrast to common procedures it can be used in high-dimensional settings where many covariates are available and the form of the influence is unknown. It is constructed as a componentwise boosting method and hence is able to perform variable selection. The complexity of the resulting estimator is determined by information criteria. The method is nvestigated in simulation studies for binary and Poisson responses and is illustrated by using real data sets
S-estimation and a robust conditional Akaike information criterion for linear mixed models.
We study estimation and model selection on both the fixed and the random effects in the setting of linear mixed models using outlier robust S-estimators. Robustness aspects on the level of the random effects as well as on the error terms is taken into account. The derived marginal and conditional information criteria are in the style of Akaike's information criterion but avoid the use of a fully specified likelihood by a suitable S-estimation approach that minimizes a scale function. We derive the appropriate penalty terms and provide an implementation using R. The setting of semiparametric additive models fit with penalized regression splines, in a mixed models formulation, fits as a specific application. Simulated data examples illustrate the effectiveness of the proposed criteria.Akaike information criterion; Conditional likelihood; Effective degrees of freedom; Mixed model; Penalized regression spline; S-estimation;
Fence methods for mixed model selection
Many model search strategies involve trading off model fit with model
complexity in a penalized goodness of fit measure. Asymptotic properties for
these types of procedures in settings like linear regression and ARMA time
series have been studied, but these do not naturally extend to nonstandard
situations such as mixed effects models, where simple definition of the sample
size is not meaningful. This paper introduces a new class of strategies, known
as fence methods, for mixed model selection, which includes linear and
generalized linear mixed models. The idea involves a procedure to isolate a
subgroup of what are known as correct models (of which the optimal model is a
member). This is accomplished by constructing a statistical fence, or barrier,
to carefully eliminate incorrect models. Once the fence is constructed, the
optimal model is selected from among those within the fence according to a
criterion which can be made flexible. In addition, we propose two variations of
the fence. The first is a stepwise procedure to handle situations of many
predictors; the second is an adaptive approach for choosing a tuning constant.
We give sufficient conditions for consistency of fence and its variations, a
desirable property for a good model selection procedure. The methods are
illustrated through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS517 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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