Log-multiplicative association models as item response models

Carolyn Jane Anderson, Hsiu Ting Yu

Research output: Contribution to journalArticle

Abstract

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson & Vermunt, 2000; Anderson & Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.

Original languageEnglish (US)
Pages (from-to)5-23
Number of pages19
JournalPsychometrika
Volume72
Issue number1
DOIs
StatePublished - Mar 1 2007

Fingerprint

Association Model
Multiplicative Model
Statistical Models
Linear Models
Model Theory
Model
model theory
Log-linear Models
Continuous Variables
Latent Variables
Graphical Models
Response Function
Numerical integration
Statistical Model
Multiplicative
Model-based
linear model

Keywords

  • Conditionally specified models
  • Graphical models
  • Multivariate logistic regression
  • The Dutch Identity

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Psychology(all)
  • Psychology (miscellaneous)
  • Social Sciences (miscellaneous)

Cite this

Log-multiplicative association models as item response models. / Anderson, Carolyn Jane; Yu, Hsiu Ting.

In: Psychometrika, Vol. 72, No. 1, 01.03.2007, p. 5-23.

Research output: Contribution to journalArticle

@article{01aa81e5106248b980a71837a3e1973b,
title = "Log-multiplicative association models as item response models",
abstract = "Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson & Vermunt, 2000; Anderson & B{\"o}ckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.",
keywords = "Conditionally specified models, Graphical models, Multivariate logistic regression, The Dutch Identity",
author = "Anderson, {Carolyn Jane} and Yu, {Hsiu Ting}",
year = "2007",
month = "3",
day = "1",
doi = "10.1007/s11336-005-1419-2",
language = "English (US)",
volume = "72",
pages = "5--23",
journal = "Psychometrika",
issn = "0033-3123",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Log-multiplicative association models as item response models

AU - Anderson, Carolyn Jane

AU - Yu, Hsiu Ting

PY - 2007/3/1

Y1 - 2007/3/1

N2 - Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson & Vermunt, 2000; Anderson & Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.

AB - Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson & Vermunt, 2000; Anderson & Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.

KW - Conditionally specified models

KW - Graphical models

KW - Multivariate logistic regression

KW - The Dutch Identity

UR - http://www.scopus.com/inward/record.url?scp=34249933116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249933116&partnerID=8YFLogxK

U2 - 10.1007/s11336-005-1419-2

DO - 10.1007/s11336-005-1419-2

M3 - Article

AN - SCOPUS:34249933116

VL - 72

SP - 5

EP - 23

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 1

ER -