Estimation and software

Tuerlinckx, Francis; Rijmen, Frank; Molenberghs, Geert; Verbeke, Geert; Briggs, Derek C.; Noortgate, Wim Van Den; Meulders, Michel; Boeck, Paul De

doi:10.1007/978-1-4757-3990-9_12

Cited by 16 publications

(15 citation statements)

References 35 publications

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“…The packages from the above categories 2 and 3 are based on MCMC and therefore may be expected to yield variance estimates which are about the same as the Gauss-Hermite based programs. When WinBUGS was used to estimate the 1PL for the example data, it was found indeed that the variance estimate was very similar (Tuerlinckx et al 2004).…”

Section: Two Packages For Rasch Families Of Modelsmentioning

confidence: 90%

“…For the 1PL applied to the dataset, the results of the lmer function are compared with the six programs described by Tuerlinckx et al (2004) for the same dataset. The lmer variance is 1.90, which is lower than the estimate obtained with the three Gauss-Hermite quadrature based algorithms among the six (estimates of 1.98), but higher than PQL and PQL2 based estimates from the other three (estimates of 1.70 and 1.87, respectively).…”

Section: A Comparison With Other Irt Packages In Rmentioning

confidence: 99%

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The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

Boeck¹,

Bakker²,

Zwitser³

et al. 2011

J. Stat. Soft.

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251

254

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In this paper we elaborate on the potential of the lmer function from the lme4 package in R for item response (IRT) modeling. In line with the package, an IRT framework is described based on generalized linear mixed modeling. The aspects of the framework refer to (a) the kind of covariates -their mode (person, item, person-by-item), and their being external vs. internal to responses, and (b) the kind of effects the covariates have -fixed vs. random, and if random, the mode across which the effects are random (persons, items). Based on this framework, three broad categories of models are described: Item covariate models, person covariate models, and person-by-item covariate models, and within each category three types of more specific models are discussed. The models in question are explained and the associated lmer code is given. Examples of models are the linear logistic test model with an error term, differential item functioning models, and local item dependency models. Because the lme4 package is for univariate generalized linear mixed models, neither the two-parameter, and three-parameter models, nor the item response models for polytomous response data, can be estimated with the lmer function.

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Section: Two Packages For Rasch Families Of Modelsmentioning

confidence: 90%

Section: A Comparison With Other Irt Packages In Rmentioning

confidence: 99%

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

Boeck¹,

Bakker²,

Zwitser³

et al. 2011

J. Stat. Soft.

Self Cite

251

254

View full text Add to dashboard Cite

show abstract

“…The integral in the marginal likelihood is intractable. The MMLE with the EM algorithm is an approximation to the integral with numerical integration techniques (Tuerlinckx et al, ). A numerical approximation to the likelihood then is maximized with respect to the fixed‐effects parameters and the parameters related to the population densities of the random effects.…”

Section: Estimation Methodsmentioning

confidence: 99%

Estimation Methods for One‐Parameter Testlet Models

Jiao

Wang

2013

J Educational Measurement

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This study demonstrated the equivalence between the Rasch testlet model and the three‐level one‐parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE) with the expectation‐maximization algorithm in ConQuest and the sixth‐order Laplace approximation estimation in HLM6. The results indicated that the estimation methods had significant effects on the bias of the testlet variance and ability variance estimation, the random error in the ability parameter estimation, and the bias in the item difficulty parameter estimation. The Laplace method best recovered the testlet variance while the MMLE best recovered the ability variance. The Laplace method resulted in the smallest random error in the ability parameter estimation while the MCMC method produced the smallest bias in item parameter estimates. Analyses of three real tests generally supported the findings from the simulation and indicated that the estimates for item difficulty and ability parameters were highly correlated across estimation methods.

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“…() for samples of 100 and 200 subjects. This bias is probably due to the rather small number of quadrature nodes ( n = 7) used by the diffIRT package by default in order to approximate the MML (Tuerlinckx et al ., ). Increasing the number of quadrature points should resolve the problem, at the cost of computation time.…”

Section: Simulation Studymentioning

confidence: 97%

Limited information estimation of the diffusion‐based item response theory model for responses and response times

Ranger

Kuhn

Szardenings

2016

Brit J Math & Statis

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Psychological tests are usually analysed with item response models. Recently, some alternative measurement models have been proposed that were derived from cognitive process models developed in experimental psychology. These models consider the responses but also the response times of the test takers. Two such models are the Q-diffusion model and the D-diffusion model. Both models can be calibrated with the diffIRT package of the R statistical environment via marginal maximum likelihood (MML) estimation. In this manuscript, an alternative approach to model calibration is proposed. The approach is based on weighted least squares estimation and parallels the standard estimation approach in structural equation modelling. Estimates are determined by minimizing the discrepancy between the observed and the implied covariance matrix. The estimator is simple to implement, consistent, and asymptotically normally distributed. Least squares estimation also provides a test of model fit by comparing the observed and implied covariance matrix. The estimator and the test of model fit are evaluated in a simulation study. Although parameter recovery is good, the estimator is less efficient than the MML estimator.

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Estimation and software

Cited by 16 publications

References 35 publications

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

Estimation Methods for One‐Parameter Testlet Models

Limited information estimation of the diffusion‐based item response theory model for responses and response times

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Estimation and software

Cited by 16 publications

References 35 publications

The Estimation of Item Response Models with thelmerFunction from thelme4Package inR

The Estimation of Item Response Models with thelmerFunction from thelme4Package inR

Estimation Methods for One‐Parameter Testlet Models

Limited information estimation of the diffusion‐based item response theory model for responses and response times

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Product

Resources

About

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR