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 language | English (US) |
|---|---|
| Pages (from-to) | 5-23 |
| Number of pages | 19 |
| Journal | Psychometrika |
| Volume | 72 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 1 2007 |
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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 journal › Article
}
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
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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 -