Estimating item parameters in multistage designs with the tmt package in R

Jan Steinfeld, Alexander Robitzsch
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Abstract

Various likelihood-based methods are available for the parameter estimation of item response theory models (IRT), leading to comparable parameter estimates. Considering multistage testing (MST) designs, Glas (1988; https://doi.org/10.2307/1164950) stated that the conditional maximum likelihood (CML) method in its original formulation leads to severely biased parameter estimates. A modified CML estimation method for MST designs proposed by Zwitser and Maris (2015; https://doi.org/10.1007/s11336-013-9369-6) finally provides asymptotically unbiased item parameter estimates. Steinfeld and Robitzsch (2021b; https://doi.org/10.31234/osf.io/ew27f) complemented this method to MST designs with probabilistic routing strategies. For both proposed modifications additional software solutions are required since design-specific information must be incorporated into the estimation process. An R package that has implemented both modifications is "tmt". In this article, first, the proposed solutions of the CML estimation in MST designs are illustrated, followed by the main part, the demonstration of the CML item parameter estimation with the R package "tmt". The demonstration includes the process of model specification, data simulation, and item parameter estimation, considering two different routing types of deterministic and probabilistic MST designs.

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在R语言中使用tmt包估算多级设计中的项目参数
项目反应理论模型(IRT)的参数估计有多种基于似然的方法,导致参数估计具有可比性。考虑到多级测试(MST)设计,Glas (1988;https://doi.org/10.2307/1164950)指出,条件最大似然(CML)方法在其原始公式中导致参数估计严重偏倚。Zwitser和Maris(2015)提出的MST设计改进CML估计方法;https://doi.org/10.1007/s11336-013-9369-6)最后提供渐近无偏的项目参数估计。斯坦菲尔德和罗比奇(2021b;https://doi.org/10.31234/osf.io/ew27f)用概率路由策略将该方法补充到MST设计中。对于这两种建议的修改都需要额外的软件解决方案,因为特定于设计的信息必须纳入评估过程。一个实现了这两个修改的R包是“tmt”。本文首先阐述了MST设计中CML估计的解决方案,然后是正文部分,用R包“tmt”演示了CML项目参数估计。该演示包括模型规范、数据仿真和项目参数估计过程,考虑了两种不同的路由类型的确定性和概率MST设计。
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Independent validation as a validation method for classification Estimating item parameters in multistage designs with the tmt package in R
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