Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Xinmin Li, Haiyan Su, Hua Liang

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

Original languageEnglish
Pages (from-to)1303-1318
Number of pages16
JournalScience China Mathematics
Volume61
Issue number7
DOIs
StatePublished - 1 Jul 2018

Fingerprint

Generalized P-value
Linear Mixed Effects Model
Variance Components
Testing
Zero
Components of Variance
Additive Models
Longitudinal Data
Likelihood Ratio Test
Random Effects
Linearity
Justification
Simulation Experiment
Likelihood
Evaluate

Keywords

  • 62G10
  • 62J10
  • fiducial distribution
  • generalized pivotal quantity
  • generalized test variable
  • penalized spline additive models
  • restricted likelihood ratio test
  • structural equation
  • zero-variance components

Cite this

@article{4304caf9bc4e456483a1abd71cfb7fcf,
title = "Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models",
abstract = "Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.",
keywords = "62G10, 62J10, fiducial distribution, generalized pivotal quantity, generalized test variable, penalized spline additive models, restricted likelihood ratio test, structural equation, zero-variance components",
author = "Xinmin Li and Haiyan Su and Hua Liang",
year = "2018",
month = "7",
day = "1",
doi = "10.1007/s11425-016-9068-8",
language = "English",
volume = "61",
pages = "1303--1318",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science in China Press",
number = "7",

}

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models. / Li, Xinmin; Su, Haiyan; Liang, Hua.

In: Science China Mathematics, Vol. 61, No. 7, 01.07.2018, p. 1303-1318.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

AU - Li, Xinmin

AU - Su, Haiyan

AU - Liang, Hua

PY - 2018/7/1

Y1 - 2018/7/1

N2 - Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

AB - Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

KW - 62G10

KW - 62J10

KW - fiducial distribution

KW - generalized pivotal quantity

KW - generalized test variable

KW - penalized spline additive models

KW - restricted likelihood ratio test

KW - structural equation

KW - zero-variance components

UR - http://www.scopus.com/inward/record.url?scp=85044940984&partnerID=8YFLogxK

U2 - 10.1007/s11425-016-9068-8

DO - 10.1007/s11425-016-9068-8

M3 - Article

VL - 61

SP - 1303

EP - 1318

JO - Science China Mathematics

JF - Science China Mathematics

SN - 1674-7283

IS - 7

ER -