A note on applying the BCH method under linear equality and inequality constraints

L. Boeschoten, M. A. Croon, D. L. Oberski

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Researchers often wish to relate estimated scores on latent variables to exogenous covariates not previously used in analyses. The BCH method corrects for asymptotic bias in estimates due to these scores’ uncertainty and has been shown to be relatively robust. When applying the BCH approach however, two problems arise. First, negative cell proportions can be obtained. Second, the approach cannot deal with situations where marginals need to be fixed to specific values, such as edit restrictions. The BCH approach can handle these problems when placed in a framework of quadratic loss functions and linear equality and inequality constraints. This research note gives the explicit form for equality constraints and demonstrates how solutions for inequality constraints may be obtained using numerical methods.
LanguageEnglish
JournalJournal of Classification
DOIs
Publication statusPublished - 2019

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Equality Constraints
Linear Constraints
Inequality Constraints
equality
Quadratic Loss Function
Asymptotic Bias
Latent Variables
loss of function
Covariates
Proportion
Numerical Methods
Restriction
Uncertainty
Cell
uncertainty
Estimate
Demonstrate
trend
Inequality constraints
Equality

Cite this

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title = "A note on applying the BCH method under linear equality and inequality constraints",
abstract = "Researchers often wish to relate estimated scores on latent variables to exogenous covariates not previously used in analyses. The BCH method corrects for asymptotic bias in estimates due to these scores’ uncertainty and has been shown to be relatively robust. When applying the BCH approach however, two problems arise. First, negative cell proportions can be obtained. Second, the approach cannot deal with situations where marginals need to be fixed to specific values, such as edit restrictions. The BCH approach can handle these problems when placed in a framework of quadratic loss functions and linear equality and inequality constraints. This research note gives the explicit form for equality constraints and demonstrates how solutions for inequality constraints may be obtained using numerical methods.",
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A note on applying the BCH method under linear equality and inequality constraints. / Boeschoten, L.; Croon, M. A.; Oberski, D. L.

In: Journal of Classification, 2019.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A note on applying the BCH method under linear equality and inequality constraints

AU - Boeschoten, L.

AU - Croon, M. A.

AU - Oberski, D. L.

PY - 2019

Y1 - 2019

N2 - Researchers often wish to relate estimated scores on latent variables to exogenous covariates not previously used in analyses. The BCH method corrects for asymptotic bias in estimates due to these scores’ uncertainty and has been shown to be relatively robust. When applying the BCH approach however, two problems arise. First, negative cell proportions can be obtained. Second, the approach cannot deal with situations where marginals need to be fixed to specific values, such as edit restrictions. The BCH approach can handle these problems when placed in a framework of quadratic loss functions and linear equality and inequality constraints. This research note gives the explicit form for equality constraints and demonstrates how solutions for inequality constraints may be obtained using numerical methods.

AB - Researchers often wish to relate estimated scores on latent variables to exogenous covariates not previously used in analyses. The BCH method corrects for asymptotic bias in estimates due to these scores’ uncertainty and has been shown to be relatively robust. When applying the BCH approach however, two problems arise. First, negative cell proportions can be obtained. Second, the approach cannot deal with situations where marginals need to be fixed to specific values, such as edit restrictions. The BCH approach can handle these problems when placed in a framework of quadratic loss functions and linear equality and inequality constraints. This research note gives the explicit form for equality constraints and demonstrates how solutions for inequality constraints may be obtained using numerical methods.

U2 - 10.1007/s00357-018-9298-2

DO - 10.1007/s00357-018-9298-2

M3 - Article

JO - Journal of Classification

T2 - Journal of Classification

JF - Journal of Classification

SN - 0176-4268

ER -