A linear model-based test for the heterogeneity of conditional correlations

Gregory E. Wilding, Xueya Cai, Alan Hutson, Zhangsheng Yu

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.

Original languageEnglish
Pages (from-to)2355-2366
Number of pages12
JournalJournal of Applied Statistics
Volume38
Issue number10
DOIs
StatePublished - Oct 2011

Fingerprint

Covariates
Linear Model
Model-based
Hypothesis Testing
Robust Inference
Restricted Maximum Likelihood
Pearson Correlation
Maximum Likelihood Method
Survey Data
Likelihood Ratio Test
Correlation coefficient
Parameter Estimation
Equality
Conditional correlation
Simulation Study
Testing
Prediction
Hypothesis testing

Keywords

  • Correlation coefficient
  • Heterogeneity
  • Linear model
  • Mos sf-36
  • Multivariate normal distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

A linear model-based test for the heterogeneity of conditional correlations. / Wilding, Gregory E.; Cai, Xueya; Hutson, Alan; Yu, Zhangsheng.

In: Journal of Applied Statistics, Vol. 38, No. 10, 10.2011, p. 2355-2366.

Research output: Contribution to journalArticle

Wilding, Gregory E. ; Cai, Xueya ; Hutson, Alan ; Yu, Zhangsheng. / A linear model-based test for the heterogeneity of conditional correlations. In: Journal of Applied Statistics. 2011 ; Vol. 38, No. 10. pp. 2355-2366.
@article{d65b9496aaef4c93ad23f5b333767edc,
title = "A linear model-based test for the heterogeneity of conditional correlations",
abstract = "Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.",
keywords = "Correlation coefficient, Heterogeneity, Linear model, Mos sf-36, Multivariate normal distribution",
author = "Wilding, {Gregory E.} and Xueya Cai and Alan Hutson and Zhangsheng Yu",
year = "2011",
month = "10",
doi = "10.1080/02664763.2011.559201",
language = "English",
volume = "38",
pages = "2355--2366",
journal = "Journal of Applied Statistics",
issn = "0266-4763",
publisher = "Routledge",
number = "10",

}

TY - JOUR

T1 - A linear model-based test for the heterogeneity of conditional correlations

AU - Wilding, Gregory E.

AU - Cai, Xueya

AU - Hutson, Alan

AU - Yu, Zhangsheng

PY - 2011/10

Y1 - 2011/10

N2 - Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.

AB - Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.

KW - Correlation coefficient

KW - Heterogeneity

KW - Linear model

KW - Mos sf-36

KW - Multivariate normal distribution

UR - http://www.scopus.com/inward/record.url?scp=84860392624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860392624&partnerID=8YFLogxK

U2 - 10.1080/02664763.2011.559201

DO - 10.1080/02664763.2011.559201

M3 - Article

VL - 38

SP - 2355

EP - 2366

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 0266-4763

IS - 10

ER -