Multiple marginal independence testing for pick any/c variables

Christopher R. Bilder, Thomas M. Loughin, Dan Nettleton

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Many survey questions allow respondents to pick any number out of c possible categorical responses or "items". These kinds of survey questions often use the terminology "choose all that apply" or "pick any". Often of interest is determining if the marginal response distributions of each item differ among r different groups of respondents. Agresti and Liu (1998, 1999) call this a test for multiple marginal independence (MMI). If respondents are allowed to pick only 1 out of c responses, the hypothesis test may be performed using the Pearson chi-square test of independence. However, since respondents may pick more or less than 1 response, the test's assumptions that responses are made independently of each other is violated. Recently, a few MMI testing methods have been proposed. Loughin and Scherer (1998) propose using a bootstrap method based on a modified version of the Pearson chi-square test statistic. Agresti and Liu (1998, 1999) propose using marginal logit models, quasi-symmetric loglinear models, and a few methods based on Pearson chi-square test statistics. Decady and Thomas (1999) propose using a Rao-Scott adjusted chi-squared test statistic. There has not been a full investigation of these MMI testing methods. The purpose here is to evaluate the proposed methods and propose a few new methods. Recommendations are given to guide the practitioner in choosing which MMI testing methods to use.

Original languageEnglish (US)
Pages (from-to)1285-1316
Number of pages32
JournalCommunications in Statistics - Theory and Methods
Volume29
Issue number4
StatePublished - Apr 1 2000

Fingerprint

Chi-squared test
Statistics
Testing
Test Statistic
Terminology
Test of Independence
Marginal Model
Logit Model
Log-linear Models
Bootstrap Method
Hypothesis Test
Categorical
Independence
Recommendations
Choose
Evaluate

Keywords

  • Bootstrap
  • Categorical data
  • Chi-square test
  • Correlated binary data
  • Multiple response
  • Surveys

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Multiple marginal independence testing for pick any/c variables. / Bilder, Christopher R.; Loughin, Thomas M.; Nettleton, Dan.

In: Communications in Statistics - Theory and Methods, Vol. 29, No. 4, 01.04.2000, p. 1285-1316.

Research output: Contribution to journalArticle

@article{ccd76bb64c594b6bbb97f02646e52bdd,
title = "Multiple marginal independence testing for pick any/c variables",
abstract = "Many survey questions allow respondents to pick any number out of c possible categorical responses or {"}items{"}. These kinds of survey questions often use the terminology {"}choose all that apply{"} or {"}pick any{"}. Often of interest is determining if the marginal response distributions of each item differ among r different groups of respondents. Agresti and Liu (1998, 1999) call this a test for multiple marginal independence (MMI). If respondents are allowed to pick only 1 out of c responses, the hypothesis test may be performed using the Pearson chi-square test of independence. However, since respondents may pick more or less than 1 response, the test's assumptions that responses are made independently of each other is violated. Recently, a few MMI testing methods have been proposed. Loughin and Scherer (1998) propose using a bootstrap method based on a modified version of the Pearson chi-square test statistic. Agresti and Liu (1998, 1999) propose using marginal logit models, quasi-symmetric loglinear models, and a few methods based on Pearson chi-square test statistics. Decady and Thomas (1999) propose using a Rao-Scott adjusted chi-squared test statistic. There has not been a full investigation of these MMI testing methods. The purpose here is to evaluate the proposed methods and propose a few new methods. Recommendations are given to guide the practitioner in choosing which MMI testing methods to use.",
keywords = "Bootstrap, Categorical data, Chi-square test, Correlated binary data, Multiple response, Surveys",
author = "Bilder, {Christopher R.} and Loughin, {Thomas M.} and Dan Nettleton",
year = "2000",
month = "4",
day = "1",
language = "English (US)",
volume = "29",
pages = "1285--1316",
journal = "Communications in Statistics - Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",
number = "4",

}

TY - JOUR

T1 - Multiple marginal independence testing for pick any/c variables

AU - Bilder, Christopher R.

AU - Loughin, Thomas M.

AU - Nettleton, Dan

PY - 2000/4/1

Y1 - 2000/4/1

N2 - Many survey questions allow respondents to pick any number out of c possible categorical responses or "items". These kinds of survey questions often use the terminology "choose all that apply" or "pick any". Often of interest is determining if the marginal response distributions of each item differ among r different groups of respondents. Agresti and Liu (1998, 1999) call this a test for multiple marginal independence (MMI). If respondents are allowed to pick only 1 out of c responses, the hypothesis test may be performed using the Pearson chi-square test of independence. However, since respondents may pick more or less than 1 response, the test's assumptions that responses are made independently of each other is violated. Recently, a few MMI testing methods have been proposed. Loughin and Scherer (1998) propose using a bootstrap method based on a modified version of the Pearson chi-square test statistic. Agresti and Liu (1998, 1999) propose using marginal logit models, quasi-symmetric loglinear models, and a few methods based on Pearson chi-square test statistics. Decady and Thomas (1999) propose using a Rao-Scott adjusted chi-squared test statistic. There has not been a full investigation of these MMI testing methods. The purpose here is to evaluate the proposed methods and propose a few new methods. Recommendations are given to guide the practitioner in choosing which MMI testing methods to use.

AB - Many survey questions allow respondents to pick any number out of c possible categorical responses or "items". These kinds of survey questions often use the terminology "choose all that apply" or "pick any". Often of interest is determining if the marginal response distributions of each item differ among r different groups of respondents. Agresti and Liu (1998, 1999) call this a test for multiple marginal independence (MMI). If respondents are allowed to pick only 1 out of c responses, the hypothesis test may be performed using the Pearson chi-square test of independence. However, since respondents may pick more or less than 1 response, the test's assumptions that responses are made independently of each other is violated. Recently, a few MMI testing methods have been proposed. Loughin and Scherer (1998) propose using a bootstrap method based on a modified version of the Pearson chi-square test statistic. Agresti and Liu (1998, 1999) propose using marginal logit models, quasi-symmetric loglinear models, and a few methods based on Pearson chi-square test statistics. Decady and Thomas (1999) propose using a Rao-Scott adjusted chi-squared test statistic. There has not been a full investigation of these MMI testing methods. The purpose here is to evaluate the proposed methods and propose a few new methods. Recommendations are given to guide the practitioner in choosing which MMI testing methods to use.

KW - Bootstrap

KW - Categorical data

KW - Chi-square test

KW - Correlated binary data

KW - Multiple response

KW - Surveys

UR - http://www.scopus.com/inward/record.url?scp=0000834955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000834955&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000834955

VL - 29

SP - 1285

EP - 1316

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 4

ER -