scholarly journals Correcting measurement error bias in interaction models with small samples

2006 ◽  
Vol 3 (2) ◽  
Author(s):  
Josep Bisbe ◽  
Germà Coenders ◽  
Willem Saris ◽  
Joan Batista-Foguet
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Ordinary Least Squares ◽  
Alternative Methods ◽  
Small Samples ◽  
Least Squares Regression ◽  
Interaction Terms ◽  
Error Bias

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression.

scholarly journals Comparison of Competing Approaches to Analyzing Cross-Classified Data: Random Effects Models, Ordinary Least Squares, or Fixed Effects with Cluster Robust Standard Errors

2021 ◽  
Author(s):  
Young Ri Lee ◽  
James E Pustejovsky
Keyword(s):  
Least Squares ◽  
Random Effects ◽  
Fixed Effects ◽  
Good Alternative ◽  
Ordinary Least Squares ◽  
Alternative Methods ◽  
Least Squares Regression ◽  
Monte Carlo Simulation Study ◽  
Random Effects Models ◽  
Fixed Effects Regression

Cross-classified random effects modeling (CCREM) is a common approach for analyzing cross-classified data in education. However, when the focus of a study is on the regression coefficients at level one rather than on the random effects, ordinary least squares regression with cluster robust variance estimators (OLS-CRVE) or fixed effects regression with CRVE (FE-CRVE) could be appropriate approaches. These alternative methods may be advantageous because they rely on weaker assumptions than what is required by CCREM. We conducted a Monte Carlo Simulation study to compare the performance of CCREM, OLS-CRVE, and FE-CRVE in models with crossed random effects, including conditions where homoscedasticity assumptions and exogeneity assumptions held and conditions where they were violated. We found that CCREM performed the best when its assumptions are all met. However, when homoscedasticity assumptions are violated, OLS-CRVE and FE-CRVE provided similar or better performance than CCREM. FE-CRVE showed the best performance when the exogeneity assumption is violated. Thus, we recommend two-way FE-CRVE as a good alternative to CCREM, particularly if the homoscedasticity or exogeneity assumptions of the CCREM might be in doubt.

Domestic violence is associated with environmental suppression of IQ in young children

2003 ◽  
Vol 15 (2) ◽  
pp. 297-311 ◽  
Author(s):  
KARESTAN C. KOENEN ◽  
TERRIE E. MOFFITT ◽  
AVSHALOM CASPI ◽  
ALAN TAYLOR ◽  
SHAUN PURCELL
Keyword(s):  
Domestic Violence ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Population Sample ◽  
Animal Experiments ◽  
Ordinary Least Squares ◽  
Genetic Influences ◽  
Least Squares Regression ◽  
Extreme Stress ◽  
Lower Intelligence

Research suggests that exposure to extreme stress in childhood, such as domestic violence, affects children's neurocognitive development, leading to lower intelligence. But studies have been unable to account for genetic influences that might confound the association between domestic violence and lower intelligence. This twin study tested whether domestic violence had environmentally mediated effects on young children's intelligence. Children's IQs were assessed for a population sample of 1116 monozygotic and dizygotic 5-year-old twin pairs in England. Mothers reported their experience of domestic violence in the previous 5 years. Ordinary least squares regression showed that domestic violence was uniquely associated with IQ suppression in a dose–response relationship. Children exposed to high levels of domestic violence had IQs that were, on average, 8 points lower than unexposed children. Structural equation models showed that adult domestic violence accounted for 4% of the variation, on average, in child IQ, independent of latent genetic influences. The findings are consistent with animal experiments and human correlational studies documenting the harmful effects of extreme stress on brain development. Programs that successfully reduce domestic violence should also have beneficial effects on children's cognitive development.

Variation Sharing

2017 ◽  
Vol 8 (4) ◽  
pp. 46-68 ◽  
Author(s):  
Ned Kock ◽  
Shaun Sexton
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Partial Least Squares ◽  
Latent Variables ◽  
Structural Equation ◽  
Least Squares Method ◽  
Fundamental Problem ◽  
Equation Modeling ◽  
Path Coefficient ◽  
Least Squares Regression

The most fundamental problem currently associated with structural equation modeling employing the partial least squares method is that it does not properly account for measurement error, which often leads to path coefficient estimates that asymptotically converge to values of lower magnitude than the true values. This attenuation phenomenon affects applications in the field of business data analytics; and is in fact a characteristic of composite-based models in general, where latent variables are modeled as exact linear combinations of their indicators. The underestimation is often of around 10% per path in models that meet generally accepted measurement quality assessment criteria. The authors propose a numeric solution to this problem, which they call the factor-based partial least squares regression (FPLSR) algorithm, whereby variation lost in composites is restored in proportion to measurement error and amount of attenuation. Six variations of the solution are developed based on different reliability measures, and contrasted in Monte Carlo simulations. The authors' solution is nonparametric and seems to perform generally well with small samples and severely non-normal data.

scholarly journals Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics

1981 ◽  
Vol 18 (3) ◽  
pp. 382-388 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker
Keyword(s):  
Statistical Analysis ◽  
Measurement Error ◽  
Structural Equation ◽  
Goodness Of Fit ◽  
Structural Equation Models ◽  
Structural Equations ◽  
Testing System

Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or statistical analysis. The authors argue that the choice of interpretative statistic must be based on the research objective. They demonstrate that when this is done the Fornell-Larcker testing system is internally consistent and that it conforms to the rules of correspondence for relating data to abstract variables.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

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