Asymptotic Standard Errors of Observed-Score Equating With Polytomous IRT Models

2016 ◽  
Vol 53 (4) ◽  
pp. 459-477 ◽  
Author(s):  
Björn Andersson
Keyword(s):  
Standard Errors ◽  
Asymptotic Standard Errors ◽  
Irt Models ◽  
Polytomous Irt Models ◽  
Observed Score

Polytomous IRT models and monotone likelihood ratio of the total score

Psychometrika ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 679-693 ◽  
Author(s):  
Bas T. Hemker ◽  
Klaas Sijtsma ◽  
Ivo W. Molenaar ◽  
Brian W. Junker
Keyword(s):  
Likelihood Ratio ◽  
Monotone Likelihood Ratio ◽  
Irt Models ◽  
Polytomous Irt Models

Item Response Theory True Score Equatings and Their Standard Errors

2001 ◽  
Vol 26 (1) ◽  
pp. 31-50 ◽  
Author(s):  
Haruhiko Ogasawara
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Standard Errors ◽  
Simultaneous Estimation ◽  
True Score ◽  
Response Theory ◽  
Asymptotic Standard Errors ◽  
Item Parameters ◽  
Irt Equating ◽  
Equating Coefficients

The asymptotic standard errors of the estimates of the equated scores by several types of item response theory (IRT) true score equatings are provided. The first group of equatings do not use IRT equating coefficients. The second group of equatings use the IRT equating coefficients given by the moment or characteristic curve methods. The equating designs considered in this article cover those with internal or external common items and the methods with separate or simultaneous estimation of item parameters of associated tests. For the estimates of the asymptotic standard errors of the equated true scores, the method of marginal maximum likelihood estimation is employed for estimation of item parameters.

ASYMPTOTIC INFERENCE ON THE MOVING AVERAGE IMPACT MATRIX IN COINTEGRATED I (2) VAR SYSTEMS

2002 ◽  
Vol 18 (3) ◽  
pp. 673-690 ◽  
Author(s):  
Paolo Paruolo
Keyword(s):  
Moving Average ◽  
Impact Factors ◽  
Standard Errors ◽  
Linear Combinations ◽  
Asymptotic Standard Errors ◽  
Vector Autoregressive ◽  
Average Impact ◽  
The Common ◽  
Row Space ◽  
Asymptotic Variances

This paper provides asymptotic standard errors for the moving average (MA) impact matrix for the second differences of a vector autoregressive (VAR) process integrated of order 2, I(2). Standard errors of the row space of the MA impact matrix are also provided; bases of this row space define the common I(2) trends linear combinations. These standard errors are then used to formulate Wald-type tests. The MA impact matrix is shown to be linked to impact factors that measure the total effect of disequilibrium errors on the growth rate of the system. Most of the relevant limit distributions are Gaussian, and we report artificial regressions that can be used to calculate the estimators of the asymptotic variances. The use of the techniques proposed in the paper is illustrated on UK money data.

scholarly journals Efficient Standard Errors in Item Response Theory Models for Short Tests

2019 ◽  
Vol 80 (3) ◽  
pp. 461-475
Author(s):  
Lianne Ippel ◽  
David Magis
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Standard Errors ◽  
Response Theory ◽  
Asymptotic Standard Error ◽  
Irt Models ◽  
Global Comparison ◽  
Wide Range ◽  
Item Response Theory Models ◽  
Theory Framework

In dichotomous item response theory (IRT) framework, the asymptotic standard error (ASE) is the most common statistic to evaluate the precision of various ability estimators. Easy-to-use ASE formulas are readily available; however, the accuracy of some of these formulas was recently questioned and new ASE formulas were derived from a general asymptotic theory framework. Furthermore, exact standard errors were suggested to better evaluate the precision of ability estimators, especially with short tests for which the asymptotic framework is invalid. Unfortunately, the accuracy of exact standard errors was assessed so far only in a very limiting setting. The purpose of this article is to perform a global comparison of exact versus (classical and new formulations of) asymptotic standard errors, for a wide range of usual IRT ability estimators, IRT models, and with short tests. Results indicate that exact standard errors globally outperform the ASE versions in terms of reduced bias and root mean square error, while the new ASE formulas are also globally less biased than their classical counterparts. Further discussion about the usefulness and practical computation of exact standard errors are outlined.

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