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A comparison of correlation and regression approaches for multinomial processing tree models
Journal of Mathematical Psychology ( IF 2.2 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.jmp.2020.102400
Lisa J. Jobst , Daniel W. Heck , Morten Moshagen

Abstract Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. The present study compares different approaches regarding their ability to estimate both types of correlations. For parameter–parameter correlations, we considered two Bayesian hierarchical MPT models – the beta-MPT approach and the latent-trait approach – and two frequentist approaches that fit the data of each participant separately, either involving a correction for attenuation or not (corrected and uncorrected individual-model approach). Regarding parameter-covariate correlations, we additionally considered the latent-trait regression. Recovery performance was determined via a Monte Carlo simulation varying sample size, number of items, extent of heterogeneity, and magnitude of the true correlation. The results indicate the smallest bias regarding parameter–parameter​ correlations for the latent-trait approach and the corrected individual-model approach and the smallest bias regarding parameter-covariate correlations for the latent-trait regression and the corrected individual-model approach. However, adequately recovering correlations of MPT parameters generally requires a sufficiently large number of observations and sufficient heterogeneity.

中文翻译:

多项式处理树模型的相关性和回归方法的比较

摘要 多项处理树 (MPT) 模型是一类用于分类数据的随机模型,最近已扩展到通过假设每个参与者的不同参数来解释个体的异质性。这些扩展能够估计模型参数之间的相关性以及模型参数与外部协变量之间的相关性。本研究比较了不同方法估计两种类型相关性的能力。对于参数-参数相关性,我们考虑了两种贝叶斯分层 MPT 模型——beta-MPT 方法和潜在特征方法——以及两种分别适合每个参与者数据的频率论方法,要么涉及衰减校正(校正和未修正的个体模型方法)。关于参数-协变量相关性,我们还考虑了潜在特征回归。回收性能是通过蒙特卡罗模拟确定的,改变样本大小、项目数量、异质性程度和真实相关性的大小。结果表明,潜在特征方法和校正个体模型方法的参数-参数相关性偏差最小,潜在特征回归和校正个体模型方法的参数-协变量相关性偏差最小。然而,充分恢复 MPT 参数的相关性通常需要足够多的观察和足够的异质性。回收性能是通过蒙特卡罗模拟确定的,改变样本大小、项目数量、异质性程度和真实相关性的大小。结果表明,潜在特征方法和校正个体模型方法的参数-参数相关性偏差最小,潜在特征回归和校正个体模型方法的参数-协变量相关性偏差最小。然而,充分恢复 MPT 参数的相关性通常需要足够多的观察和足够的异质性。回收性能是通过蒙特卡罗模拟确定的,改变样本大小、项目数量、异质性程度和真实相关性的大小。结果表明,潜在特征方法和校正个体模型方法的参数-参数相关性偏差最小,潜在特征回归和校正个体模型方法的参数-协变量相关性偏差最小。然而,充分恢复 MPT 参数的相关性通常需要足够多的观察和足够的异质性。结果表明,潜在特征方法和校正个体模型方法的参数-参数相关性偏差最小,潜在特征回归和校正个体模型方法的参数-协变量相关性偏差最小。然而,充分恢复 MPT 参数的相关性通常需要足够多的观察和足够的异质性。结果表明,潜在特征方法和校正个体模型方法的参数-参数相关性偏差最小,潜在特征回归和校正个体模型方法的参数-协变量相关性偏差最小。然而,充分恢复 MPT 参数的相关性通常需要足够多的观察和足够的异质性。
更新日期:2020-09-01
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