在小到中型样本大小的分级响应模型的项目参数估计中使用辅助项目信息:实证对等级贝叶斯估计:实证对等级贝叶斯估计
Matthew Naveiras1, Sun-Joo Cho2
1Riverside Insights, IL, USA.
Applied psychological measurement
|November 29, 2023
概括
对于项目响应理论,经验贝叶斯和层次贝叶斯方法在小样本大小中提供准确的项目参数估计,在数据有限时超过边际最大概率估计. 层次贝叶斯比实证贝叶斯提供了比实证贝叶斯更准确的后方方差估值.
科学领域:
- 心理测量 心理测量 心理测量
- 教育测量教育的测量
- 统计 统计 统计 统计
背景情况:
- 项目响应理论 (IRT) 通常使用边际最大概率估计 (MMLE) 来估计项目参数.
- 小样本大小,通常在罕见种群中遇到,对MMLE的准确性和趋同性构成挑战.
研究的目的:
- 将实证贝叶斯 (EB) 和层次贝叶斯 (HB) 作为MMLE的替代方案,用于小样本尺寸的IRT项目参数估计.
- 将EB和HB与MMLE进行比较,以确定贝叶斯方法优于MMLE的情况,并在MMLE失败时评估HB的可行性.
- 评估EB和HB之间的后方方差估计的准确性,强调HB在捕获项目参数不确定性方面的优势.
主要方法:
- 为了评估拟议的EB和HB方法,进行了一项模拟研究.
- 在各种模拟测试条件下对MMLE,EB和HB方法进行比较.
- 在分级响应模型中使用辅助项目信息实现EB和HB.
主要成果:
- 层次贝叶斯方法在各种测试场景中证明了作为MMLE替代品的可接受性能.
- 与MMLE相比,EB和HB方法显示出项目参数估计准确度更高的潜力,特别是在有限的数据的情况下.
- 通过计算项目参数估计的不确定性,HB获得了比EB更准确的后方方差估计.
结论:
- 层次贝叶斯方法是MMLE的可行的替代方案,用于IRT中的项目参数估计,特别是当样本大小小时.
- 提供了指导方针,以帮助研究人员根据特定的研究条件选择最合适的估计方法.
- 有R函数可用于促进这些先进的贝叶斯估计技术的实施.
相关概念视频
What are Estimates?
5.1K
It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates.
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
5.1K
Mechanistic Models: Compartment Models in Individual and Population Analysis
43
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
43
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
56
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
56
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
133
Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
133
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
517
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
517
Parametric Survival Analysis: Weibull and Exponential Methods
448
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
448


