psychometrics package, including structural equation model, confirmatory factor analysis, unidimensional item response theory, multidimensional item response theory, cognitive diagnosis model, factor analysis and adaptive testing. The package is still a doll. will be finished in future.
- binary response data IRT (two parameters, three parameters).
- grade respone data IRT (GRM model)
- EM algorithm (2PL, GRM)
- MCMC algorithm (3PL）
The approximate polychoric correlation is calculated, and the slope initial value is obtained by factor analysis of the polychoric correlation matrix.
- E step uses GH integral.
- M step uses Newton algorithm (sparse matrix is divided into non sparse matrix).
Gradient projection algorithm
GH integrals can only estimate low dimensional parameters.
- Dina
- ho-dina
- EM algorithm
- MCMC algorithm
- maximum likelihood estimation (only for estimating skill parameters of subjects)
- contains three parameter estimation methods(ULS, ML and GLS).
- based on gradient descent
- can be used for continuous data, binary data and ordered data.
- based on gradient descent
- binary and ordered data based on Polychoric correlation matrix.
For the time being, only for the calculation of full information item factor analysis, it is very simple.
principal component analysis
gradient projection
Thurston IRT model (multidimensional item response theory model for personality test)
Maximum information method for multidimensional item response theory
- numpy
- progressbar2
See demo in detail
- theta parameterization of CCFA
- parameter estimation of structural equation models for multivariate data
- Bayesin knowledge tracing (Bayesian knowledge tracking)
- multidimensional item response theory (full information item factor analysis)
- high dimensional computing algorithm (adaptive integral, etc.)
- various item response models
- cognitive diagnosis model
- G-DINA model
- Q matrix correlation algorithm
- Factor analysis
- maximum likelihood estimation
- various factor rotation algorithms
- adaptive
- adaptive cognitive diagnosis
- other adaption model
- standard error and P value
- code annotation, testing and documentation.
- DINA Model and Parameter Estimation: A Didactic
- Higher-order latent trait models for cognitive diagnosis
- Full-Information Item Factor Analysis.
- Multidimensional adaptive testing
- Derivative free gradient projection algorithms for rotation
自编心理测量库，包含结构方程模型，验证性因子分析，单维项目反应理论，多维项目反应理论，认知诊断，因子分析和自适应测验等等，还在整理中，仅供学习
- 二级计分IRT（双参数，三参数）
- 多级计分IRT（GRM模型）
- EM算法（双参数，GRM）
- MCMC算法（三参数）
计算近似polychoric correlation, 对这个相关矩阵进行因子分析，获得斜率初值
- E步用GH积分
- M步用牛顿算法（把稀疏矩阵拆成不稀疏的矩阵计算）
基于梯度投影算法
GH积分只能计算低维度的参数估计
- dina
- ho-dina
- EM算法
- MCMC算法
- 极大似然估计（仅限估计被试技能掌握参数）
- 包含ULS, ML, GLS三种参数估计方法
- 基于梯度下降
- 支持连续数据、二分数据和有序数据
- 基于梯度下降
- 二分数据和有序数据基于Polychoric相关矩阵
暂时只为计算全息项目因子分析而存在，很简单的实现
主成分分析
梯度投影
瑟斯顿IRT模型（用于人格测验的多维项目反应理论模型）
多维项目反应理论的最大信息法
- numpy
- progressbar2
详见demo
- CCFA的theta参数化
- 多样化数据的结构方程模型参数估计
- 贝叶斯知识追踪(Bayesin knowledge tracing)
- 多维项目反应理论（全息项目因子分析）
- 高维度计算算法（自适应积分等）
- 各类项目反应模型
- 认知诊断
- G-DINA模型
- Q矩阵相关算法
- 因子分析
- 极大似然估计
- 各类因子旋转算法
- 自适应
- 自适应认知诊断
- 其他自适应
- 标准误、P值
- 代码注释、测试和文档