Maximum softly-penalized likelihood for mixed effects logistic regression

06/06/2022
by   Philipp Sterzinger, et al.
0

Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite variance components, can cause havoc to numerical estimation procedures and inference. We introduce an appropriately scaled additive penalty to the log-likelihood function, or an approximation thereof, which penalizes the fixed effects by the Jeffreys' invariant prior for the model with no random effects and the variance components by a composition of negative Huber loss functions. The resulting maximum penalized likelihood estimates are shown to lie in the interior of the parameter space. Appropriate scaling of the penalty guarantees that the penalization is soft enough to preserve the optimal asymptotic properties expected by the maximum likelihood estimator, namely consistency, asymptotic normality, and Cramér-Rao efficiency. Our choice of penalties and scaling factor preserves equivariance of the fixed effects estimates under linear transformation of the model parameters, such as contrasts. Maximum softly-penalized likelihood is compared to competing approaches on two real-data examples, and through comprehensive simulation studies that illustrate its superior finite sample performance.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/25/2022

Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions

The purpose of this article is to develop a general parametric estimatio...
research
11/13/2017

MM Algorithms for Variance Component Estimation and Selection in Logistic Linear Mixed Model

Logistic linear mixed model is widely used in experimental designs and g...
research
06/02/2022

Soft calibration for selection bias problems under mixed-effects models

Calibration weighting has been widely used for correcting selection bias...
research
02/08/2013

Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models

It has been shown that AIC-type criteria are asymptotically efficient se...
research
08/08/2019

Analysis of Networks via the Sparse β-Model

Data in the form of networks are increasingly available in a variety of ...
research
10/03/2018

Semiparametric Regression using Variational Approximations

Semiparametric regression offers a flexible framework for modeling non-l...
research
01/22/2023

Penalized estimation for non-identifiable models

We derive asymptotic properties of penalized estimators for singular mod...

Please sign up or login with your details

Forgot password? Click here to reset