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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Parameter recovery and model selection in mixed Rasch models.

David Preinerstorfer¹, Anton K Formann

¹Department of Statistics and Operations Research, University of Vienna, Austria. david.preinerstorfer@univie.ac.at

The British Journal of Mathematical and Statistical Psychology

|June 17, 2011

Summary

This study on mixed Rasch models found that larger sample sizes and more items improve accuracy. The Bayesian Information Criterion (BIC) is a more reliable model selection tool than the Akaike Information Criterion (AIC).

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Area of Science:

Psychometrics
Statistical Modeling

Background:

Mixed Rasch models are used in educational and psychological measurement.
Assessing the precision of parameter estimates and model selection is crucial for accurate analysis.

Purpose of the Study:

To evaluate the precision of conditional maximum likelihood estimates in mixed Rasch models.
To compare the performance of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for model selection.

Main Methods:

A Monte Carlo simulation study was conducted.
Varied factors included test length, sample size, mixture conditions (one vs. two groups), and population homogeneity/heterogeneity.
Conditional maximum likelihood estimation and information criteria (AIC, BIC) were analyzed.

Main Results:

Increased sample size and item count enhance estimation accuracy.
Medium-range parameters were estimated more precisely than extreme values.
Homogeneous populations yielded higher accuracy than heterogeneous ones.
The minimum-BIC method demonstrated superior reliability over AIC.

Conclusions:

Model selection using BIC is more dependable than AIC for mixed Rasch models.
Practical guidelines for mixed Rasch model analysis are provided based on simulation findings.