### Abstract

Log-multiplicative association (LMA) models have been proposed as uni- and multidimensional item response models for dichotomous and/or polytomous items. A problem that prevents more widespread use of LMA models is that current estimation methods for moderate to large problems are computationally prohibitive. As a special case of a log-linear model, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns, the number of which increases exponentially as the number of items and/or response options per item increases. Anderson et al. (J. Stat. Softw. 20, 2007, doi:10.18637/jss.v020.i06) used pseudo-likelihood estimation for linear-by-linear models, which are special cases of LMA models, but in their proposal, the category scores are fixed to specific values. The solution presented here extends pseudo-likelihood estimation to more general LMA models where category scores are estimated. Our simulation studies show that parameter estimates from the new algorithm are nearly identical to parameter estimates from MLE, work for large numbers of items, are insensitive to starting values, and converge in a small number of iterations.

Original language | English (US) |
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Title of host publication | Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016 |

Editors | Wen-Chung Wang, Marie Wiberg, Steven A. Culpepper, Jeffrey A. Douglas, L. Andries van der Ark |

Publisher | Springer New York LLC |

Pages | 21-30 |

Number of pages | 10 |

ISBN (Print) | 9783319562933 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 81st annual meeting of the Psychometric Society, 2016 - Asheville, United States Duration: Jul 11 2016 → Jul 15 2016 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 196 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 81st annual meeting of the Psychometric Society, 2016 |
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Country | United States |

City | Asheville |

Period | 7/11/16 → 7/15/16 |

### Fingerprint

### Keywords

- Formative measurement models
- Log linear-by-linear models
- Log-multiplicative association models
- Multidimensional item response theory
- Second-order exponential models

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016*(pp. 21-30). (Springer Proceedings in Mathematics and Statistics; Vol. 196). Springer New York LLC. https://doi.org/10.1007/978-3-319-56294-0_3

**Pseudo-likelihood estimation of multidimensional response models : Polytomous and dichotomous items.** / Paek, Youngshil; Anderson, Carolyn Jane.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016.*Springer Proceedings in Mathematics and Statistics, vol. 196, Springer New York LLC, pp. 21-30, 81st annual meeting of the Psychometric Society, 2016, Asheville, United States, 7/11/16. https://doi.org/10.1007/978-3-319-56294-0_3

}

TY - GEN

T1 - Pseudo-likelihood estimation of multidimensional response models

T2 - Polytomous and dichotomous items

AU - Paek, Youngshil

AU - Anderson, Carolyn Jane

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Log-multiplicative association (LMA) models have been proposed as uni- and multidimensional item response models for dichotomous and/or polytomous items. A problem that prevents more widespread use of LMA models is that current estimation methods for moderate to large problems are computationally prohibitive. As a special case of a log-linear model, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns, the number of which increases exponentially as the number of items and/or response options per item increases. Anderson et al. (J. Stat. Softw. 20, 2007, doi:10.18637/jss.v020.i06) used pseudo-likelihood estimation for linear-by-linear models, which are special cases of LMA models, but in their proposal, the category scores are fixed to specific values. The solution presented here extends pseudo-likelihood estimation to more general LMA models where category scores are estimated. Our simulation studies show that parameter estimates from the new algorithm are nearly identical to parameter estimates from MLE, work for large numbers of items, are insensitive to starting values, and converge in a small number of iterations.

AB - Log-multiplicative association (LMA) models have been proposed as uni- and multidimensional item response models for dichotomous and/or polytomous items. A problem that prevents more widespread use of LMA models is that current estimation methods for moderate to large problems are computationally prohibitive. As a special case of a log-linear model, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns, the number of which increases exponentially as the number of items and/or response options per item increases. Anderson et al. (J. Stat. Softw. 20, 2007, doi:10.18637/jss.v020.i06) used pseudo-likelihood estimation for linear-by-linear models, which are special cases of LMA models, but in their proposal, the category scores are fixed to specific values. The solution presented here extends pseudo-likelihood estimation to more general LMA models where category scores are estimated. Our simulation studies show that parameter estimates from the new algorithm are nearly identical to parameter estimates from MLE, work for large numbers of items, are insensitive to starting values, and converge in a small number of iterations.

KW - Formative measurement models

KW - Log linear-by-linear models

KW - Log-multiplicative association models

KW - Multidimensional item response theory

KW - Second-order exponential models

UR - http://www.scopus.com/inward/record.url?scp=85020841828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020841828&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-56294-0_3

DO - 10.1007/978-3-319-56294-0_3

M3 - Conference contribution

AN - SCOPUS:85020841828

SN - 9783319562933

T3 - Springer Proceedings in Mathematics and Statistics

SP - 21

EP - 30

BT - Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016

A2 - Wang, Wen-Chung

A2 - Wiberg, Marie

A2 - Culpepper, Steven A.

A2 - Douglas, Jeffrey A.

A2 - van der Ark, L. Andries

PB - Springer New York LLC

ER -