Methods for evaluating empirical bayes point estimates of latent trait scores

Psychometrika ◽  
1975 ◽  
Vol 40 (3) ◽  
pp. 373-394 ◽  
Author(s):  
Jack Kearns ◽  
William Meredith
Keyword(s):  
Empirical Bayes ◽  
Latent Trait ◽  
Point Estimates

Approximation for Bayesian Ability Estimation

1988 ◽  
Vol 13 (2) ◽  
pp. 117-130 ◽  
Author(s):  
Robert K. Tsutakawa ◽  
Michael J. Soltys
Keyword(s):  
Standard Deviation ◽  
Empirical Bayes ◽  
Numerical Comparison ◽  
Item Response Model ◽  
Posterior Mean ◽  
Point Estimates ◽  
Item Parameters ◽  
Using Data ◽  
Math Test ◽  
Ability Parameter

An approximation is proposed for the posterior mean and standard deviation of the ability parameter in an item response model. The procedure assumes that approximations to the posterior mean and covariance matrix of item parameters are available. It is based on the posterior mean of a Taylor series approximation to the posterior mean conditional on the item parameters. The method is illustrated for the two-parameter logistic model using data from an ACT math test with 39 items. A numerical comparison with the empirical Bayes method using n = 400 examinees shows that the point estimates are very similar but the standard deviations under empirical Bayes are about 2% smaller than those under Bayes. Moreover, when the sample size is decreased to n = 100, the standard deviation under Bayes is shown to increase by 14% in some cases.

An IRT Investigation of the Validity of Non-Patient Analogue Research Using the Beck Depression Inventory

1995 ◽  
Vol 11 (1) ◽  
pp. 14-20 ◽  
Author(s):  
Sean M. Hammond
Keyword(s):  
Differential Item Functioning ◽  
Beck Depression Inventory ◽  
Rating Scale ◽  
Latent Trait ◽  
Scale Model ◽  
Item Functioning ◽  
Two Samples ◽  
Patient Groups ◽  
Analogue Research ◽  
Rating Scale Model

This paper presents an IRT analysis of the Beck Depression Inventory which was carried out to assess the assumption of an underlying latent trait common to non-clinical and patient samples. A one parameter rating scale model was fitted to data drawn from a patient and non-patient sample. Findings suggest that while the BDI fits the model reasonably well for the two samples separately there is sufficient differential item functioning to raise serious duobts of the viability of using it analogously with patient and non-patient groups.

The Orchard Plot: Cultivating a Forest Plot for Use in Ecology, Evolution and Beyond

2019 ◽  
Author(s):  
Shinichi Nakagawa ◽  
Malgorzata Lagisz ◽  
Rose E O'Dea ◽  
Joanna Rutkowska ◽  
Yefeng Yang ◽  
...  
Keyword(s):  
Meta Analysis ◽  
R Package ◽  
Effect Sizes ◽  
Forest Plot ◽  
Point Estimates ◽  
Aggregate Effect ◽  
The Individual ◽  
Meta Analyses ◽  
Heterogeneous Effect ◽  
Intuitive Interpretation

‘Classic’ forest plots show the effect sizes from individual studies and the aggregate effect from a meta-analysis. However, in ecology and evolution meta-analyses routinely contain over 100 effect sizes, making the classic forest plot of limited use. We surveyed 102 meta-analyses in ecology and evolution, finding that only 11% use the classic forest plot. Instead, most used a ‘forest-like plot’, showing point estimates (with 95% confidence intervals; CIs) from a series of subgroups or categories in a meta-regression. We propose a modification of the forest-like plot, which we name the ‘orchard plot’. Orchard plots, in addition to showing overall mean effects and CIs from meta-analyses/regressions, also includes 95% prediction intervals (PIs), and the individual effect sizes scaled by their precision. The PI allows the user and reader to see the range in which an effect size from a future study may be expected to fall. The PI, therefore, provides an intuitive interpretation of any heterogeneity in the data. Supplementing the PI, the inclusion of underlying effect sizes also allows the user to see any influential or outlying effect sizes. We showcase the orchard plot with example datasets from ecology and evolution, using the R package, orchard, including several functions for visualizing meta-analytic data using forest-plot derivatives. We consider the orchard plot as a variant on the classic forest plot, cultivated to the needs of meta-analysts in ecology and evolution. Hopefully, the orchard plot will prove fruitful for visualizing large collections of heterogeneous effect sizes regardless of the field of study.

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