当前位置: X-MOL 学术Br. J. Math. Stat. Psychol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Revisiting dispersion in count data item response theory models: The Conway-Maxwell-Poisson counts model.
British Journal of Mathematical and Statistical Psychology ( IF 2.6 ) Pub Date : 2019-08-16 , DOI: 10.1111/bmsp.12184
Boris Forthmann 1 , Daniela Gühne 2 , Philipp Doebler 2
Affiliation  

Count data naturally arise in several areas of cognitive ability testing, such as processing speed, memory, verbal fluency, and divergent thinking. Contemporary count data item response theory models, however, are not flexible enough, especially to account for over- and underdispersion at the same time. For example, the Rasch Poisson counts model (RPCM) assumes equidispersion (conditional mean and variance coincide) which is often violated in empirical data. This work introduces the Conway-Maxwell-Poisson counts model (CMPCM) that can handle underdispersion (variance lower than the mean), equidispersion, and overdispersion (variance larger than the mean) in general and specifically at the item level. A simulation study revealed satisfactory parameter recovery at moderate sample sizes and mostly unbiased standard errors for the proposed estimation approach. In addition, plausible empirical reliability estimates resulted, while those based on the RPCM were biased downwards (underdispersion) and biased upwards (overdispersion) when the simulation model deviated from equidispersion. Finally, verbal fluency data were analysed and the CMPCM with item-specific dispersion parameters fitted the data best. Dispersion parameter estimates indicated underdispersion for three out of four items. Overall, these findings indicate the feasibility and importance of the suggested flexible count data modelling approach.

中文翻译:

重新审视计数数据项响应理论模型中的离散:Conway-Maxwell-Poisson 计数模型。

计数数据自然会出现在认知能力测试的几个领域,例如处理速度、记忆力、语言流畅性和发散性思维。然而,当代计数数据项响应理论模型不够灵活,尤其是不能同时考虑过度和不足。例如,Rasch Poisson 计数模型 (RPCM) 假设等分散(条件均值和方差重合),这在经验数据中经常被违反。这项工作介绍了 Conway-Maxwell-Poisson 计数模型 (CMPCM),该模型可以在一般情况下特别是在项目级别处理欠分散(方差低于平均值)、等分散和过度分散(方差大于平均值)。模拟研究表明,所提出的估计方法在中等样本量和大多数无偏标准误差下的参数恢复令人满意。此外,产生了合理的经验可靠性估计,而当模拟模型偏离等分散时,基于 RPCM 的那些估计会向下偏移(离散不足)和向上偏移(过度离散)。最后,对语言流畅度数据进行了分析,具有特定项目分散参数的 CMPCM 最适合数据。分散参数估计表明四分之三的分散不足。总的来说,这些发现表明了建议的灵活计数数据建模方法的可行性和重要性。当模拟模型偏离等分散时,基于 RPCM 的模型会向下偏置(分散不足)和向上偏置(过度分散)。最后,对语言流畅度数据进行了分析,具有特定项目分散参数的 CMPCM 最适合数据。分散参数估计表明四分之三的分散不足。总的来说,这些发现表明了建议的灵活计数数据建模方法的可行性和重要性。当模拟模型偏离等分散时,基于 RPCM 的模型会向下偏置(分散不足)和向上偏置(过度分散)。最后,对语言流畅度数据进行了分析,具有特定项目分散参数的 CMPCM 最适合数据。分散参数估计表明四分之三的分散不足。总的来说,这些发现表明了建议的灵活计数数据建模方法的可行性和重要性。
更新日期:2019-08-16
down
wechat
bug