Adaptive EAP Estimation of Ability in a Microcomputer Environment

Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random-intercept models under a range of conditions.

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“…Ten Have and Localio (1999)) and item response theory (e.g. Bock and Mislevy (1982) and Embretson and Reise (2000)). …”

Section: Posterior Standard Deviationsmentioning

confidence: 99%

Prediction in Multilevel Generalized Linear Models

Skrondal

Rabe‐Hesketh

2009

Journal of the Royal Statistical Society Series A: Statistics in Society

185

142

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“…After the model parameters are calibrated, point estimates for individual persons can be obtained from either the mean vector of the marginal posterior distribution, Equation A.6, called the expected a posteriori estimates [51], or the maximum point of conditional likelihood, called the maximum likelihood estimates.…”

Section: ðA:5þmentioning

confidence: 99%

Validating, Improving Reliability, and Estimating Correlation of the Four Subscales in the WHOQOL-BREF using Multidimensional Rasch Analysis

et al. 2006

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Objective: This study examined the construct validity, and improved the test reliability and the estimation accuracy for the correlation between domains of the WHOQOL-BREF using multidimensional Rasch analysis. Method: A total of 13,083 adults were administered the 28-item WHOQOL-BREF Taiwan version, which consists of 4 subscales (domains). The multidimensional form of the partial credit model was used to examine the fit of the 4 subscales. For comparison, each subscale individually was also fitted to the unidimensional partial credit model. Standard item fit statistics and analysis of differential item functioning (DIF) were used to check model-data fit. Results: After excluding 2 overall items and deleting 7 DIF items, the remaining items of each subscale in the WHOQOL-BREF constituted a single construct. The test reliabilities and correlations between domains obtained from the multidimensional approach, (0.82-0.86) and (0.79-0.89), respectively, were much higher than those obtained from the unidimensional approach, (0.67-0.75) and (0.53-0.65), respectively. Conclusion: The 19-item WHOQOL-BREF measures more succinct latent traits than the original design. The multidimensional approach yields not only more accurate estimates for the correlation between domains but also substantially higher reliabilities, than the standard unidimensional approach.

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“…Second, we used the BILOG FLOAT command to allow the means of the prior distributions on the item parameters to be estimated and to change between estimation cycles. Finally, we used the expected a posteriori (EAP) method to estimate latent trait scores (Bock & Mislevy, 1982). Table 2 provides summaries of the item parameter estimates.…”

Section: Item Parameter Estimationmentioning

confidence: 99%

How many IRT parameters does it take to model psychopathology items?

Reise¹,

Waller²

2003

Psychological Methods

103

127

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The authors compared the fit of the 2-and 3-parameter logistic models (2PLM; 3PLM) on 15 unidimensional factor scales derived from the Minnesota Multiphasic Personality Inventory-Adolescent item pool. Log-likelihood chi-square deviance tests indicated that a 3PLM provided an improved fit. However, residual statistics indicated that the difference in fit between the 2 models was negligible. An unexpected finding was that from 10% to 30% of the items had substantial lower asymptote parameters (c Ն .10) when the scales were scored in the pathology or nonpathology directions. The authors argue that the large lower asymptote parameters are attributable to item-content ambiguity possibly caused by item-level multidimensionality. These findings suggest that the direction of scoring can critically affect an item response theory analysis.

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Adaptive EAP Estimation of Ability in a Microcomputer Environment

Cited by 486 publications

References 5 publications

Prediction in Multilevel Generalized Linear Models

Prediction in Multilevel Generalized Linear Models

Validating, Improving Reliability, and Estimating Correlation of the Four Subscales in the WHOQOL-BREF using Multidimensional Rasch Analysis

How many IRT parameters does it take to model psychopathology items?

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