Carolyn J Anderson's Home Page

Anderson, C.J, Li, Z., & Vermunt, J.K. (2007). Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables. Journal of Statistical Software, 20.

This work was supported by NSF Grant #0351175 awarded to Anderson, and by the National Center for Supercomputing Applications and the University of Illinois under the auspices of the NCSA/UIUC Faculty Fellows Program and the Bureau of Educational Research in the College of Education at the University of Illinois.

This site is subject to change (i.e., up-dates).

An R package and SAS MACRO for pseudo-likelihood estimation of a log-linear-by-linear association models; that is, a family of Rasch models for dichotomous or polytomous items for uni- and multiple--latent traits. There are also links to alternative methods using SAS to fit Rasch models using pseudo-likelihood estimation.

The R package plRasch computes maximum likelihood estimates (MLE) and pseudo-likelihood estimattes (PLE) of parameters of Rasch models for poltyomous (or dichotomous) items and multiple (or single) latent traits. Robust standard errors for the pseudo-likelihood estimates are also computed

The R-package: plRasch_0.1.zip. This package and up-dates are published on the R web-site.
Examples:

Example code presented in the text:
- Simulates 1,000 response patterns from a 2-dimensional Rasch model for four dichotomous items.
- Fits the corresponding log-linear-by-linear association model using MLE and PLE.
- Anchors item parameters to latent variable using RaschPLE.
simulation.1D.small.R:
- Simulates 1,000 response patterns from a 1-dimensional Rasch model for four dichotomous items.
- Fits the corresponding log-linear-by-linear association model using MLE and PLE.
simulation.1D.large.R:
- Simulates 1,000 response patterns from a 1-dimensional Rasch model for 100 dichotomous items
- Fits the corresponding Log-linear-by-linear association model using PLE.
- Contains code for MLE, which is commented out, to demonstrate the problem with MLE of LLLA models for large problems.
simulation.1D.MC.large.R:
- Simulates 1,000 response patterns from a 1-dimensional Rasch model for 100 items with 3 reponse options per item.
- Fits the corresponding Log-linear-by-linear association model using PLE.
- Contains code for MLE, which is commented out, to demonstrate the problem with MLE of LLLA models for large problems.

SAS

SAS plgRasch macro that does bascially what the R plRasch package will do, except that there is no "wrapper". The "g" in "plgRasch" stands for "generalized". This macro
- Creates the SAS data set StackedData
- Fits the conditional multinomial logistic regression model using SAS/MDC from the SAS/ETS product.
- Computes robust estimates of the covariance matrix and standard errors of the parameter estimates.
Example using the plgRasch macro.
Simulated 2 dimensional data used by example. (2-dimensional, 30 items, dichotomous, sample size =1000, 10 items "load" on each to the two latent variables.
Simulated smallish dataset used by example. (1-dimensional, 5 items, 3 categories per item, sample size =500.
Note: I have SAS/IML code that will set up the design matrix for different parameterization of the Rasch model (i.e., partial credit, rating scale, and linear rating scale Rasch models.
SAS code using SAS/DATA STEPS to fit Rasch model for dichtomous data using pseudo-likelihood estimation (see "Figure 3"). This web-page page also includes
- Lem for fitting Rasch and 2PL using magrinal maximum likelihood estimation.
- SAS code for generated and simmulated data from the Rasch and 2PL models for dicthomous data.
- SAS and Lem studying the differences and similarties between standard IRT models and log-multiplicative ones

Report broken links and send email to cja@illinois.edu

Last revised June 17, 2008