# psy

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## Package

3

### Categories

.. image:: https://img.shields.io/pypi/v/psy.svg :target: https://pypi.python.org/pypi/psy

# pypsy

`中文 <./README_ZH.rst>`_

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.

## unidimensional item response theory

models

``````
-  binary response data IRT (two parameters, three parameters).

-  grade respone data IRT (GRM model)

Parameter estimation algorithm
------------------------------

-  EM algorithm (2PL, GRM)

-  MCMC algorithm (3PL）

--------------

Multidimensional item response theory (full information item factor analysis)
-----------------------------------------------------------------------------

Parameter estimation algorithm
``````

The initial value ^^^^^^^^^^^^^^^^^

The approximate polychoric correlation is calculated, and the slope initial value is obtained by factor analysis of the polychoric correlation matrix.

EM algorithm ^^^^^^^^^^^^

• E step uses GH integral.

• M step uses Newton algorithm (sparse matrix is divided into non sparse matrix).

Factor rotation ^^^^^^^^^^^^^^^

The shortcomings

``````
GH integrals can only estimate low dimensional parameters.

--------------

Cognitive diagnosis model
-------------------------

models
~~~~~~

-  Dina

-  ho-dina

parameter estimation algorithms
``````
• EM algorithm

• MCMC algorithm

• maximum likelihood estimation (only for estimating skill parameters of subjects)

## Structural equation model

• contains three parameter estimation methods(ULS, ML and GLS).

## Confirmatory factor analysis

• can be used for continuous data, binary data and ordered data.

• binary and ordered data based on Polychoric correlation matrix.

## Factor analysis

For the time being, only for the calculation of full information item factor analysis, it is very simple.

The algorithm

``````
principal component analysis

The rotation algorithm
``````

model

``````
Thurston IRT model (multidimensional item response theory model for
personality test)

Algorithm
``````

Maximum information method for multidimensional item response theory

• numpy

• progressbar2

## How to use it

install

``````::

pip install psy

See demo

TODO LIST
---------

-  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

-  standard error and P value

-  code annotation, testing and documentation.

Reference
---------

-  `DINA Model and Parameter Estimation: A
-  `Higher-order latent trait models for cognitive
diagnosis <http://www.aliquote.org/pub/delatorre2004.pdf>`__
-  `Full-Information Item Factor
Analysis. <http://conservancy.umn.edu/bitstream/11299/104282/1/v12n3p261.pdf>`__
-  `Derivative free gradient projection algorithms for rotation <https://cloudfront.escholarship.org/dist/prd/content/qt9938p4wc/qt9938p4wc.pdf>`__
``````

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