Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

Battauz, Michela; Bellio, Ruggero

doi:10.1007/s11336-010-9195-z

Cited by 6 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our theoretical development addressed the case where the ME is homoskedastic with variance σ 2 . However, heteroskedastic measurement error commonly arises in applications, including psychometrics (Battauz and Bellio, 2011), economics (Sullivan, 2001) and biostatistics (see Delaigle & Meister, 2007 and references therein). SIMEX extends straightforwardly to the case where the ME variance is heteroskedastic with known variances σ 2 i for each unit by using σ 2 i to generate the synthetic data for each unit.…”

Section: Discussionmentioning

confidence: 99%

“…ME in key covariates is commonplace. For example, scores from standardized achievement tests commonly are used to adjust for non-equivalent student groups in observational studies in educational research (Battauz and Bellio, 2011;Lockwood and McCaffrey, 2014), including the estimation of individual school and teacher "value-added" effects for accountability purposes (Braun, 2005;Harris, 2011;McCaffrey et al, 2004a). Test scores are errorprone measures of latent achievement (Lord, 1980).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

Lockwood¹,

McCaffrey²

2015

Observational Studies

View full text Add to dashboard Cite

Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with error. We review approaches to consistent estimation of a population mean of an incompletely observed variable using error-prone covariates, noting difficulties with applying these methods. We consider the application of Simulation-Extrapolation (SIMEX) as a simple and effective alternative. We provide technical conditions under which SIMEX will lead to a consistent estimator of a population mean and argue why it may function well in common settings. We use a simulation study to demonstrate its potential for removing nearly all of the bias in regression, weighting and doubly robust estimators for a population mean while maintaining precision competitive with what would be obtained without measurement error. We also discuss and evaluate options for estimating the standard error of the SIMEX mean estimator. Finally, we present an empirical example of estimating middle school effects on student achievement.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

Lockwood¹,

McCaffrey²

2015

Observational Studies

View full text Add to dashboard Cite

show abstract

“…Specifically, this simultaneous approach allows us to detect the group difference on the error‐free latent variable scale (i.e., the ability parameter in IRT is equal to an (unbiased) estimator minus (random) error) at post‐test, by controlling for the possible measurement error in the pre‐test scores and by mapping pre‐test scores and post‐test scores on the latent variable scales. However, in previous studies, measurement error was mainly adjusted for the response variable (e.g., Fox, ) or for the covariate (e.g., Battauz & Bellio, ; Carroll et al ., ; Fox & Glas, ; Goldstein et al ., ). That is, in these previous applications, either a measurement model for the response variable (e.g., equation or a classical true score model) or a measurement model for the covariate (e.g., equation or a classical true score model) was used.…”

Section: Mmirm With a Multilevel Latent Covariatementioning

confidence: 99%

“…Up to this point, MMIRMs have been mainly applied to response variables (see Muthén & Asparouhov, , sections 7 and 8). There are examples of researchers correctly accounting for measurement error in covariate(s) using unidimensional item response models (Battauz & Bellio, ; Fox & Glas, ). There are also a few examples of measurement error adjustment in response variables and covariates.…”

Section: Introductionmentioning

confidence: 99%

Multilevel multidimensional item response model with a multilevel latent covariate

Cho

Bottge

2015

Brit J Math & Statis

View full text Add to dashboard Cite

In a pre-test-post-test cluster randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores, ignoring measurement error, are used as response variable and covariate, respectively, to estimate the intervention effect. However, these test scores are frequently subject to measurement error, and statistical inferences based on the model ignoring measurement error can yield a biased estimate of the intervention effect. When multiple domains exist in test data, it is sometimes more informative to detect the intervention effect for each domain than for the entire test. This paper presents applications of the multilevel multidimensional item response model with measurement error adjustments in a response variable and a covariate to estimate the intervention effect for each domain.

show abstract

“…For example, Stefanski and Carroll (1985) developed a bias-adjusted estimator, a functional maximum likelihood estimator and an estimator exploiting the consequences of sufficiency for a logistic regression when covariates were subject to MEs; Stefanski and Carroll (1987) studied parameter estimation in GLM with canonical form when the explanatory vector was measured with an independent normal error; Buzas and Stefanski (1996) investigated instrumental variable estimation in GLMEMs with canonical link functions; Aitkin and Rocci (2002) presented an EM algorithm for maximum likelihood estimation in GLMs with continuous MEs in the explanatory variables; Battauz (2011) developed a Laplace-based estimator for GLMEMs; Battauz and Bellio (2011) proposed a structural analysis for GLMs when some explanatory variables were measured with error and the ME variance was a function of the true variables.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Bayesian inference on generalized linear measurement error models

Tang

2016

Stat Papers

View full text Add to dashboard Cite

The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback-Leibler divergence and Cook's distance. Computationally feasible formulae for evaluating Bayesian casedeletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies.

show abstract

Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

Abstract: heteroscedastic error, IRT, maximum likelihood estimation, measurement error, Rasch model, structural model,

Cited by 6 publications

References 24 publications

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

Multilevel multidimensional item response model with a multilevel latent covariate

Semiparametric Bayesian inference on generalized linear measurement error models

Contact Info

Product

Resources

About