Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

Sieve maximum likelihood estimation for generalized linear mixed models with an unknown link function

Pages: 39 – 49



Guoqing Diao (Department of Biostatistics and Bioinformatics, George Washington University, Washington, District of Columbia, U.S.A.)

Mengdie Yuan (Department of Statistics, George Mason University, Fairfax, Virginia, U.S.A.)


We study the generalized linear mixed models with an unknown link function for correlated outcome data. We propose sieve maximum likelihood estimation procedures by using B‑splines. Specifically, we estimate the unknown link function in a sieve space spanned by the B‑spline basis of the linear predictor that includes both the fixed and random terms. We establish the consistency and asymptotic normality of the proposed sieve maximum likelihood estimators. Extensive simulation studies, along with an application to an epileptic study, are provided to evaluate the finite-sample performance of the proposed method.


b-splines, GLMM, longitudinal data, semiparametric models, single index model

2010 Mathematics Subject Classification

62G08, 62J12

Received 15 December 2022

Accepted 12 August 2023

Published 27 November 2023