Abstract
Many paired comparison data sets reported in the literature are obtained in a multiple judgment setting where each judge compares all possible item pairs one at a time. Despite the repeated measures structure of the data, typically the multiple judgments are analyzed under the strong assumption of independence. This disregard for dependencies in the paired comparison judgments is a serious model misspecification that may lead to incorrect statistical and substantive conclusions. Building on Takane's (1987, Cognition and Communication, 20, 45-62) analysis of covariance structures models, we present a variant of the Monte Carlo expectation maximization (MCEM) algorithm for estimating probabilistic paired comparison models of multiple paired comparison judgments. The MCEM algorithm is straightforward to implement and converges quickly even when the paired comparison data are sparse. A detailed analysis of a paired comparison experiment illustrates the usefulness of this approach for the interpretation of similarity and individual difference effects in preference data.
| Original language | English |
|---|---|
| Pages (from-to) | 795-811 |
| Number of pages | 17 |
| Journal | Journal of Mathematical Psychology |
| Volume | 45 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2001 Jan 1 |
Fingerprint
Keywords
- Maximum likelihood estimation
- Paired comparison data
- Wandering ideal point model
ASJC Scopus subject areas
- Psychology(all)
- Applied Mathematics
Cite this
Maximum likelihood estimation of factor and ideal point models for paired comparison data. / Tsai, Rung-Ching; Böckenholt, Ulf.
In: Journal of Mathematical Psychology, Vol. 45, No. 6, 01.01.2001, p. 795-811.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Maximum likelihood estimation of factor and ideal point models for paired comparison data
AU - Tsai, Rung-Ching
AU - Böckenholt, Ulf
PY - 2001/1/1
Y1 - 2001/1/1
N2 - Many paired comparison data sets reported in the literature are obtained in a multiple judgment setting where each judge compares all possible item pairs one at a time. Despite the repeated measures structure of the data, typically the multiple judgments are analyzed under the strong assumption of independence. This disregard for dependencies in the paired comparison judgments is a serious model misspecification that may lead to incorrect statistical and substantive conclusions. Building on Takane's (1987, Cognition and Communication, 20, 45-62) analysis of covariance structures models, we present a variant of the Monte Carlo expectation maximization (MCEM) algorithm for estimating probabilistic paired comparison models of multiple paired comparison judgments. The MCEM algorithm is straightforward to implement and converges quickly even when the paired comparison data are sparse. A detailed analysis of a paired comparison experiment illustrates the usefulness of this approach for the interpretation of similarity and individual difference effects in preference data.
AB - Many paired comparison data sets reported in the literature are obtained in a multiple judgment setting where each judge compares all possible item pairs one at a time. Despite the repeated measures structure of the data, typically the multiple judgments are analyzed under the strong assumption of independence. This disregard for dependencies in the paired comparison judgments is a serious model misspecification that may lead to incorrect statistical and substantive conclusions. Building on Takane's (1987, Cognition and Communication, 20, 45-62) analysis of covariance structures models, we present a variant of the Monte Carlo expectation maximization (MCEM) algorithm for estimating probabilistic paired comparison models of multiple paired comparison judgments. The MCEM algorithm is straightforward to implement and converges quickly even when the paired comparison data are sparse. A detailed analysis of a paired comparison experiment illustrates the usefulness of this approach for the interpretation of similarity and individual difference effects in preference data.
KW - Maximum likelihood estimation
KW - Paired comparison data
KW - Wandering ideal point model
UR - http://www.scopus.com/inward/record.url?scp=0035713501&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035713501&partnerID=8YFLogxK
U2 - 10.1006/jmps.2000.1353
DO - 10.1006/jmps.2000.1353
M3 - Article
AN - SCOPUS:0035713501
VL - 45
SP - 795
EP - 811
JO - Journal of Mathematical Psychology
JF - Journal of Mathematical Psychology
SN - 0022-2496
IS - 6
ER -