Testing goodness-of-fit of a logistic regression model with case-control data

K. F. Cheng, L. C. Chen

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A new test is proposed for testing the validity of the logistic regression model based on case-control data. The proposed test does not need a partition of the space of explanatory variables to handle the case of nonreplication. The new test is consistent against very general alternatives. The asymptotic distribution of the test statistic under a sequence of local alternatives is derived so that the behavior of the asymptotic power function of the new test can be studied. This result also gives the approximated null distribution of the test statistic. For practical sample sizes, the adequacy of the large-sample approximation to the null distribution of the test statistic are carefully examined. Power comparisons with other goodness-of-fit tests are performed to show the advantages of the new method. The test statistic is very simple to compute and the new test will be illustrated with examples.

Original languageEnglish
Pages (from-to)409-422
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume124
Issue number2
DOIs
Publication statusPublished - Sep 1 2004
Externally publishedYes

Fingerprint

Case-control Data
Logistic Regression Model
Goodness of fit
Logistics
Statistics
Test Statistic
Testing
Null Distribution
Power Comparison
Asymptotic Power
Local Alternatives
Power Function
Goodness of Fit Test
Asymptotic distribution
Sample Size
Partition
Logistic regression model
Model-based
Test statistic
Alternatives

Keywords

  • Asymptotic distribution
  • Asymptotic power
  • Case-control data
  • Goodness of fit
  • Logistic regression

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Testing goodness-of-fit of a logistic regression model with case-control data. / Cheng, K. F.; Chen, L. C.

In: Journal of Statistical Planning and Inference, Vol. 124, No. 2, 01.09.2004, p. 409-422.

Research output: Contribution to journalArticle

@article{f25e6779e3254092a5ce335bb0ca84c3,
title = "Testing goodness-of-fit of a logistic regression model with case-control data",
abstract = "A new test is proposed for testing the validity of the logistic regression model based on case-control data. The proposed test does not need a partition of the space of explanatory variables to handle the case of nonreplication. The new test is consistent against very general alternatives. The asymptotic distribution of the test statistic under a sequence of local alternatives is derived so that the behavior of the asymptotic power function of the new test can be studied. This result also gives the approximated null distribution of the test statistic. For practical sample sizes, the adequacy of the large-sample approximation to the null distribution of the test statistic are carefully examined. Power comparisons with other goodness-of-fit tests are performed to show the advantages of the new method. The test statistic is very simple to compute and the new test will be illustrated with examples.",
keywords = "Asymptotic distribution, Asymptotic power, Case-control data, Goodness of fit, Logistic regression",
author = "Cheng, {K. F.} and Chen, {L. C.}",
year = "2004",
month = "9",
day = "1",
doi = "10.1016/S0378-3758(03)00207-6",
language = "English",
volume = "124",
pages = "409--422",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Testing goodness-of-fit of a logistic regression model with case-control data

AU - Cheng, K. F.

AU - Chen, L. C.

PY - 2004/9/1

Y1 - 2004/9/1

N2 - A new test is proposed for testing the validity of the logistic regression model based on case-control data. The proposed test does not need a partition of the space of explanatory variables to handle the case of nonreplication. The new test is consistent against very general alternatives. The asymptotic distribution of the test statistic under a sequence of local alternatives is derived so that the behavior of the asymptotic power function of the new test can be studied. This result also gives the approximated null distribution of the test statistic. For practical sample sizes, the adequacy of the large-sample approximation to the null distribution of the test statistic are carefully examined. Power comparisons with other goodness-of-fit tests are performed to show the advantages of the new method. The test statistic is very simple to compute and the new test will be illustrated with examples.

AB - A new test is proposed for testing the validity of the logistic regression model based on case-control data. The proposed test does not need a partition of the space of explanatory variables to handle the case of nonreplication. The new test is consistent against very general alternatives. The asymptotic distribution of the test statistic under a sequence of local alternatives is derived so that the behavior of the asymptotic power function of the new test can be studied. This result also gives the approximated null distribution of the test statistic. For practical sample sizes, the adequacy of the large-sample approximation to the null distribution of the test statistic are carefully examined. Power comparisons with other goodness-of-fit tests are performed to show the advantages of the new method. The test statistic is very simple to compute and the new test will be illustrated with examples.

KW - Asymptotic distribution

KW - Asymptotic power

KW - Case-control data

KW - Goodness of fit

KW - Logistic regression

UR - http://www.scopus.com/inward/record.url?scp=3042638488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042638488&partnerID=8YFLogxK

U2 - 10.1016/S0378-3758(03)00207-6

DO - 10.1016/S0378-3758(03)00207-6

M3 - Article

AN - SCOPUS:3042638488

VL - 124

SP - 409

EP - 422

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 2

ER -