Copula-based Local Dependence Framework

2018 ◽  
Author(s):  
Zaixin Huang
Keyword(s):  
Local Dependence

scholarly journals Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification

2021 ◽  
pp. 001316442110203
Author(s):  
Lucia Guastadisegni ◽  
Silvia Cagnone ◽  
Irini Moustaki ◽  
Vassilis Vasdekis
Keyword(s):  
Lagrange Multiplier ◽  
False Positive ◽  
Latent Variable ◽  
Model Misspecification ◽  
Cross Product ◽  
Small Sample ◽  
Type I ◽  
Local Dependence ◽  
Lagrange Multiplier Test ◽  
Product Approach

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

Local Dependence in an Operational CAT: Diagnosis and Implications

2008 ◽  
Vol 45 (3) ◽  
pp. 201-223 ◽  
Author(s):  
Mary Pommerich ◽  
Daniel O. Segall
Keyword(s):  
Local Dependence

Investigating Local Dependence with Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Local Dependence ◽  
Conditional Covariance ◽  
Covariance Functions

Local-dependence and Accumulated-local Profiles

2021 ◽  
pp. 229-246
Author(s):  
Przemyslaw Biecek ◽  
Tomasz Burzykowski
Keyword(s):  
Local Dependence

Investigating Local Dependence With Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129-151 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Kernel Smoothing ◽  
Item Difficulty ◽  
Estimation Procedure ◽  
Local Dependence ◽  
Function Estimation ◽  
Conditional Covariance ◽  
Monotonic Transformation ◽  
Covariance Functions ◽  
Latent Space ◽  
Latent Ability

The local dependence of item pairs is investigated via a conditional covariance function estimation procedure. The conditioning variable used in the procedure is obtained by a monotonic transformation of total score on the remaining items. Intuitively, the conditioning variable corresponds to the unidimensional latent ability that is best measured by the test. The conditional covariance functions are estimated using kernel smoothing, and a standardization to adjust for the confounding effect of item difficulty is introduced. The particular standardization chosen is an adaptation of Yule’s coefficient of colligation. Several models of local dependence are discussed to explain special situations, such as speededness and latent space multidimensionality, in which the assumptions of unidimensionality and local independence are violated.

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