Statistical software popular with psychometricians
Stata: Data analysis and statistical software
MPlus A wide choice of models, estimators and algorithms
R The R project.Collaborative freeware for statistical computing
Latent Gold A powerful latent class and finite mixture program
MLwiN Multilevel modelling software from the Centre for Multilevel Modelling at the University of Bristol (free download for UK academic staff)
R is an increasingly popular free software environment for statistical computing and graphics. Several authors have developed routines specifically for psychometric analysis using various Item Response Theory models.
Stata is a powerful general purpose statistical package much preferred by psychometricians because of its excellent graphic facilities and its ability to handle non-parametric aspects of ordinal and binary data of the form normally found in questionnaire responses.
Mplus is a syntax based statistical software package for estimating models containing latent, or unobserved, variables. It has grown out of the tradition in statistical modelling known as SEM - Structural Equation Models, sometimes called LISREL models (this stands for linear structural relations modelling). However Mplus is much more comprehensive that this and can handle models for multivariate analysis with both continuous and categorical observed and latent variables e.g. probit and logistic regression models and their SEM equivalents. It also has capabilities for estimating latent classification and trajectory models, multilevel models, conducting Monte Carlo simulations, combining multiply imputed data sets, and handling complex data from survey samples.