### Abstract

Original language | Undefined |
---|---|

Place of Publication | Newton, PA, USA |

Publisher | Law School Admission Council |

Number of pages | 14 |

Publication status | Published - 2005 |

### Publication series

Name | LSAC research report series |
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Publisher | Law School Admission Council |

No. | 05-03 |

### Keywords

- IR-104248

### Cite this

*Likelihood-based statistics for validating continuous response models*. (LSAC research report series; No. 05-03). Newton, PA, USA: Law School Admission Council.

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*Likelihood-based statistics for validating continuous response models*. LSAC research report series, no. 05-03, Law School Admission Council, Newton, PA, USA.

**Likelihood-based statistics for validating continuous response models.** / Glas, Cornelis A.W.; Korobko, O.B.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Likelihood-based statistics for validating continuous response models

AU - Glas, Cornelis A.W.

AU - Korobko, O.B.

PY - 2005

Y1 - 2005

N2 - The theory for the estimation and testing of item response theory (IRT) models for items with discrete responses is by now very thoroughly developed. In contrast, the estimation and testing theory for IRT models for items with continuous responses has hardly received any attention. This is mainly due to the fact that the continuous response format is seldom used. An exception may be the so-called analogous-scale item format where a respondent marks the position on a line to express his or her opinion about a topic. Recently, continuous responses have attracted interest as covariates accompanying discrete responses. One may think of the response time needed to answer an item in a computerized adaptive testing situation. In the present report, the theory of estimating and testing a model for continuous responses, the model proposed by Mellenbergh in 1994, is developed in a marginal maximum likelihood framework. It is shown that the fit to the model can be evaluated using Lagrange multiplier tests. Simulation studies show that these tests have excellent properties in terms of control of Type I error rate and power.

AB - The theory for the estimation and testing of item response theory (IRT) models for items with discrete responses is by now very thoroughly developed. In contrast, the estimation and testing theory for IRT models for items with continuous responses has hardly received any attention. This is mainly due to the fact that the continuous response format is seldom used. An exception may be the so-called analogous-scale item format where a respondent marks the position on a line to express his or her opinion about a topic. Recently, continuous responses have attracted interest as covariates accompanying discrete responses. One may think of the response time needed to answer an item in a computerized adaptive testing situation. In the present report, the theory of estimating and testing a model for continuous responses, the model proposed by Mellenbergh in 1994, is developed in a marginal maximum likelihood framework. It is shown that the fit to the model can be evaluated using Lagrange multiplier tests. Simulation studies show that these tests have excellent properties in terms of control of Type I error rate and power.

KW - IR-104248

M3 - Report

T3 - LSAC research report series

BT - Likelihood-based statistics for validating continuous response models

PB - Law School Admission Council

CY - Newton, PA, USA

ER -