The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models

The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models In educational and psychological measurement when short test forms are used, the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold. As a result, hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic. Inferences based on the exact distribution, on the other hand, do not suffer from this limitation. However, the computation involved for the exact distribution approach is often prohibitively expensive. In this paper, we propose a general framework for constructing hypothesis tests and confidence intervals for IRT models within the exponential family based on exact distribution. In addition, an efficient branch and bound algorithm for calculating the exact p value is introduced. The type-I error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation. We also demonstrate its practical use by analyzing three real data sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models

Loading next page...
 
/lp/springer_journal/the-ump-exact-test-and-the-confidence-interval-for-person-parameters-PVH0j0N6SO
Publisher
Springer Journals
Copyright
Copyright © 2017 by The Psychometric Society
Subject
Psychology; Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Statistical Theory and Methods
ISSN
0033-3123
eISSN
1860-0980
D.O.I.
10.1007/s11336-017-9580-y
Publisher site
See Article on Publisher Site

Abstract

In educational and psychological measurement when short test forms are used, the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold. As a result, hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic. Inferences based on the exact distribution, on the other hand, do not suffer from this limitation. However, the computation involved for the exact distribution approach is often prohibitively expensive. In this paper, we propose a general framework for constructing hypothesis tests and confidence intervals for IRT models within the exponential family based on exact distribution. In addition, an efficient branch and bound algorithm for calculating the exact p value is introduced. The type-I error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation. We also demonstrate its practical use by analyzing three real data sets.

Journal

PsychometrikaSpringer Journals

Published: Aug 23, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off