R is especially well suited for psychometrics. A long list of packages can be found in Psychometric Models and Methods, under the following categories:
- Item Response Theory (IRT). (e.g, eRm, ltm, mirt, lordif packages)
- Correspondence Analysis (CA), Optimal Scaling.
- Factor Analysis (FA), Principal Component Analysis (PCA). (e.g., psych packages)
- Structural Equation Models (SEM). (e.g., lavaan, sem packages)
- Multidimensional Scaling (MDS)
- Classical Test Theory (CTT). (e.g., CTT, psych, and ICC)
- Knowledge Structure Analysis
- Latent Class and Profile Analysis
- Paired Comparisons, Rankings, Ratings.
- Network Psychometrics.
- Bayesian Psychometrics (e.g., blavaan)
- Other Related Packages. (e.g.,psychotools, cNORM)
You could be interested in:
- Modern Psychometrics with R, by Patrick Mair.
- An introduction to psychometric theory with applications in R from the R Core Team.
- Using R for psychological research from the personality-project. Part of a series of tutorials for using R in psychological research.
- Psychometrics in R Journal of Statistical Software.
- Psychometric Models and Methods Patrick Mair & Reinhold Hatzinger, The Comprehensive R Archive Network (CRAN). See a list of packages by categories.
- Personality Project which is a collection of web pages devoted to the academic study of personality.
References
Image off ICC plots adapted from the eRm manual.