Two-level linear paired comparison models

Estimation and identifiability issues

Rung-Ching Tsai, Ulf Böckenholt

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

The method of paired comparisons became popular in psychological research with Thurstone's [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.

Original languageEnglish
Pages (from-to)429-449
Number of pages21
JournalMathematical Social Sciences
Volume43
Issue number3
DOIs
Publication statusPublished - 2002 Aug 12

Fingerprint

model comparison
Matched-Pair Analysis
Paired Comparisons
Identifiability
comparison of methods
linear model
Monte Carlo EM Algorithm
Mixed Effects
Individual Differences
Covariance Structure
Generalized Linear Model
Individuality
interpretation
Parameter Estimation
Linear Models
Continuum
Model
Specification
Psychology
Values

Keywords

  • Maximum likelihood estimation
  • Ordinal data
  • Probit models
  • Random effects models

ASJC Scopus subject areas

  • Sociology and Political Science
  • Social Sciences(all)
  • Psychology(all)
  • Statistics, Probability and Uncertainty

Cite this

Two-level linear paired comparison models : Estimation and identifiability issues. / Tsai, Rung-Ching; Böckenholt, Ulf.

In: Mathematical Social Sciences, Vol. 43, No. 3, 12.08.2002, p. 429-449.

Research output: Contribution to journalArticle

@article{d0739b7dbe80470b8c7b628793fea9f0,
title = "Two-level linear paired comparison models: Estimation and identifiability issues",
abstract = "The method of paired comparisons became popular in psychological research with Thurstone's [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.",
keywords = "Maximum likelihood estimation, Ordinal data, Probit models, Random effects models",
author = "Rung-Ching Tsai and Ulf B{\"o}ckenholt",
year = "2002",
month = "8",
day = "12",
doi = "10.1016/S0165-4896(02)00019-7",
language = "English",
volume = "43",
pages = "429--449",
journal = "Mathematical Social Sciences",
issn = "0165-4896",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Two-level linear paired comparison models

T2 - Estimation and identifiability issues

AU - Tsai, Rung-Ching

AU - Böckenholt, Ulf

PY - 2002/8/12

Y1 - 2002/8/12

N2 - The method of paired comparisons became popular in psychological research with Thurstone's [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.

AB - The method of paired comparisons became popular in psychological research with Thurstone's [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.

KW - Maximum likelihood estimation

KW - Ordinal data

KW - Probit models

KW - Random effects models

UR - http://www.scopus.com/inward/record.url?scp=0036339745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036339745&partnerID=8YFLogxK

U2 - 10.1016/S0165-4896(02)00019-7

DO - 10.1016/S0165-4896(02)00019-7

M3 - Article

VL - 43

SP - 429

EP - 449

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 3

ER -