Psychometrics is concerned with the design and analysis of research and the measurement of human characteristics. Psychometricians have also worked collaboratively with those in the field of statistics and quantitative methods to develop improved ways to organize and analyze data. Since much functionality is already contained in base R and there is considerable overlap between tools for psychometry and tools described in other views, particularly in SocialSciences, we only give a brief overview of packages that are closely related to psychometric methodology. Recently, Journal of Statistical Software (JSS) published a special volume on Psychometrics in R in which some new R packages were published which are not yet on CRAN.

Please let us know if we have omitted something of importance, or if a new package or function should be mentioned here.

Item Response Theory (IRT):

• The eRm package fits extended Rasch models, i.e. the ordinary Rasch model for dichotomous data (RM), the linear logistic test model (LLTM), the rating scale model (RSM) and its linear extension (LRSM), the partial credit model (PCM) and its linear extension (LPCM) using conditional ML estimation. Missing values are allowed.
• The package ltm also fits the simple RM. Additionally, functions for estimating Birnbaum's 2- and 3-parameter models based on a marginal ML approach are implemented as well as the graded response model for polytomous data, and the linear multidimensional logistic model.
• Item and ability parameters can be calibrated using the package plink. It provides unidimensional and multidimensional methods such as Mean/Mean, Mean/Sigma, Haebara, and Stocking-Lord methods for dichotomous (1PL, 2PL and 3PL) and/or polytomous (graded response, partial credit/generalized partial credit, nominal, and multiple-choice model) items. The multidimensional methods include the Reckase-Martineau method and extensions of the Haebara and Stocking-Lord method.
• The difR package contains several traditional methods to detect DIF in dichotomously scored items. Both uniform and non-uniform DIF effects can be detected, with methods relying upon item response models or not. Some methods deal with more than one focal group.
• The package lordif provides a logistic regression framework for detecting various types of differential item functioning (DIF).
• The catR package allows for computarized adaptive testing using IRT methods.
• The package plRasch computes maximum likelihood estimates and pseudo-likelihood estimates of parameters of Rasch models for polytomous (or dichotomous) items and multiple (or single) latent traits. Robust standard errors for the pseudo-likelihood estimates are also computed.
• A multilevel Rasch model can be estimated using the package lme4 with functions for mixed-effects models with crossed or partially crossed random effects.
• Other packages of interest are: mokken to compute non-parametric item analysis, the RaschSampler allowing for the construction of exact Rasch model tests by generating random zero-one matrices with given marginals, and mprobit fitting the multivariate binary probit model. Simple Rasch computations such a simulating data and joint maximum likelihood are included in the MiscPsycho package.
• The irtProb is designed to estimate multidimensional subject parameters (MLE and MAP) such as personnal pseudo-guessing, personal fluctuation, personal inattention. These supplemental parameters can be used to assess person fit, to identify misfit type, to generate misfitting response patterns, or to make correction while estimating the proficiency level considering potential misfit at the same time.
• The package irtoys provides a simple common interface to the estimation of item parameters in IRT models for binary responses with three different programs (ICL, BILOG-MG, and ltm, and a variety of functions useful with IRT models.
• Gaussian ordination, related to logistic IRT and also approximated as maximum likelihood estimation through canonical correspondence analysis is implemented in various forms in the package VGAM.
• Two additional IRT packages (for Microsoft Windows only) are available and documented on the JSS site. The package mlirt computes multilevel IRT models, and cirt uses a joint hierarchically built up likelihood for estimating a two-parameter normal ogive model for responses and a log-normal model for response times.
• Bayesian approaches for estimating item and person parameters by means of Gibbs-Sampling are included in MCMCpack. In addition, the pscl package allows for Bayesian IRT and roll call analysis.
• The latdiag package produces commands to drive the dot program from graphviz to produce a graph useful in deciding whether a set of binary items might have a latent scale with non-crossing ICCs.

Correspondence Analysis (CA):

• The package ca comprises two parts, one for simple correspondence analysis and one for multiple and joint correspondence analysis. Within each part, functions for computation, summaries and visualization in two and three dimensions are provided, including options to display supplementary points and perform subset analyses. Other features are visualization functions that offer features such as different scaling options for biplots and three-dimensional maps using the rgl package. Graphical options include shading and sizing plot symbols for the points according to their contributions to the map and masses respectively. A corresponding GUI is provided by the package caGUI.
• Simple and canonical CA are provided by the package anacor. It allows for diffenrent scaling methods such as standard scaling, Benzecri scaling, centroid scaling, and Goodman scaling. Along with well-known two- and three-dimensional joint plots including confidence ellipsoids, it offers alternative plotting possibilities in terms of transformation plots, Benzecri plots, and regression plots.
• A GUI (Windows only) that allows the user to construct interactive Biplots is offered by the package BiplotGUI.
• Homogeneity analysis aka multiple CA and various Gifi extensions can be computed by means of the homals package. Hull plots, span plots, Voronoi plots, star plots, projection plots and many others can be produced.
• Simple and multiple correspondence analysis can be performed using corresp() and mca() in package MASS.
• The package ade4 contains an extensive set of functions covering, e.g., principal components, simple and multiple, fuzzy, non symmetric, and decentered correspondence analysis. Additional functionality is provided at Bioconductor in the package made4 (see also here ).
• The package cocorresp fits predictive and symmetric co-correspondence analysis (CoCA) models to relate one data matrix to another data matrix.
• Apart from several factor analytic methods FactoMineR performs CA including supplementary row and/or column points and multiple correspondence analysis (MCA) with supplementary individuals, supplementary quantitative variables and supplementary qualitative variables.
• Package vegan supports all basic ordination methods, including non-metric multidimensional scaling. The constrained ordination methods include constrained analysis of proximities, redundancy analysis, and constrained (canonical) and partially constrained correspondence analysis.
• Other extensions of CA and MCA which also generalize many common IRT models can be found on the PsychoR page.

Structural Equation Models, Factor Analysis, PCA:

• Ordinary factor analysis (FA) is the package stats as function factanal(). Principal component analysis (PCA) can be fitted with prcomp() (based on svd(), preferred) as well as princomp() (based on eigen() for compatibility with S-PLUS). Additional rotation methods for FA based on gradient projection algorithms can be found in the package GPArotation. The package nFactors produces a non-graphical solution to the Cattell scree test. Some graphical PCA representations can be found in the psy package.
• The sem package fits general (i.e., latent-variable) SEMs by FIML, and structural equations in observed-variable models by 2SLS. Categorical variables in SEMs can be accommodated via the polycor package. The systemfit package implements a wider variety of estimators for observed-variables models, including nonlinear simultaneous-equations models. See also the pls package, for partial least-squares estimation, the gR task view for graphical models and the SocialSciences task view for other related packages.
• The package lavaan can be used to estimate a large variety of multivariate statistical models, including path analysis, confirmatory factor analysis, structural equation modeling and growth curve models. It includes the lavaan model syntax which allows users to express their models in a compact way and allows for ML, GLS, WLS, robust ML using Satorra-Bentler corrections, and FIML for data with missing values. It fully supports for meanstructures and multiple groups and reports standardized solutions, fit measures, modification indices and more as output.
• The package semPLS sits structural equation models using partial least squares (PLS). The PLS approach is referred to as soft-modeling technique requiring no distributional assumptions on the observed data.
• The plsRglm package is designed to provide PLS regression and PLS generalized linear regression. It includes various criteria to select the number of components, repeated k-fold cross-validation, bootstrap confidence intervals and significance testing.
• SEMModComp conducts tests of difference in fit for mean and covariance structure models as in structural equation modeling (SEM)
• The package FAiR performs factor analysis based on a genetic algorithm for optimization. This makes it possible to impose a wide range of restrictions on the factor analysis model, whether using exploratory factor analysis, confirmatory factor analysis, or a new estimator called semi-exploratory factor analysis (SEFA).
• FA and PCA with supplementary individuals and supplementary quantitative/qualitative variables can be performed using the FactoMineR package whereas MCMCpack has some options for sampling from the posterior for ordinal and mixed factor models.
• The homals package provides nonlinear PCA and, by defining sets, nonlinear canonical correlation analysis (models of the Gifi-family).
• Independent component analysis (ICA) can be computed using fastICA.
• A desired number of robust principal components can be computed with the pcaPP package.
• The package psych includes functions such as fa.parallel() and VSS() for estimating the appropriate number of factors/components as well as ICLUST() for item clustering.
• An interface between the EQS software for SEM and R is provided by the REQS package.
• The OpenMX package allows estimation of a wide variety of advanced multivariate statistical models. It consists of a library of functions and optimizers that allow you to quickly and flexibly define an SEM model and estimate parameters given observed data. It is available under this link .

Multidimensional Scaling (MDS):

• The smacof package provides the following approaches of multidimensional scaling (MDS) based on stress minimization by means of majorization: Simple smacof on symmetric dissimilarity matrices, smacof for rectangular matrices (unfolding models), smacof with constraints on the configuration, three-way smacof for individual differences (including constraints for idioscal, indscal, and identity), and spherical smacof (primal and dual algorithm). Each of these approaches is implemented in a metric and nonmetric manner including primary, secondary, and tertiary approaches for tie handling.
• The PTAk package provides a multiway method to decompose a tensor (array) of any order, as a generalisation of SVD also supporting non-identity metrics and penalisations. 2-way SVD with these extensions is also available. Additionally, the package includes some other multiway methods: PCAn (Tucker-n) and PARAFAC/CANDECOMP with extensions.
• MASS and stats provide functionalities for computing classical MDS using the cmdscale() function. Sammon mapping sammon() and non-metric MDS isoMDS() are other relevant functions.
• Non-metric MDS can additionally be performed with metaMDS() in vegan. Furthermore, labdsv and ecodist provide the function nmds() and some routines can be found in xgobi.
• Principal coordinate analysis can be computed with capscale() in vegan; in labdsv and ecodist using pco() and with dudi.pco() in ade4.
• Individual differences in multidimensional scaling can be computed with indscal() in the SensoMineR package.
• The package MLDS allows for the computation of maximum likelihood difference scaling (MLDS).

Classical Test Theory (CTT):

• The CTT package can be used to perform a variety of tasks and analyses associated with classical test theory: score multiple-choice responses, perform reliability analyses, conduct item analyses, and transform scores onto different scales.
• Functions for correlation theory, meta-analysis (validity generalization), reliability, item analysis, inter-rater reliability, and classical utility are contained in the psychometric package.
• The CMC package calculates and plots the step-by-step Cronbach-Mesbach curve, that is a method, based on the Cronbach alpha coefficient of reliability, for checking the unidimensionality of a measurement scale.
• Cronbach alpha, kappa coefficients, and intra-class correlation coefficients (ICC) can be found in the psy package.
• A number of routines for scale construction and reliability analysis useful for personality and experimental psychology are contained in the packages psych and MiscPsycho.
• Additional measures for reliability and concordance can be computed with the concord package.

Other related packages:

• Recursive partitioning based on psychometric models, employing the general MOB algorithm (from package party) are implemented in psychotree. Currently, only Bradley-Terry trees are provided.
• The equate package contains functions for non-IRT equating under both random groups and nonequivalent groups with anchor test designs. Mean, linear, equipercentile and circle-arc equating are supported, as are methods for univariate and bivariate presmoothing of score distributions. Specific equating methods currently supported include Tucker, Levine observed score, Levine true score, Braun/Holland, frequency estimation, and chained equating.
• Latent class analysis with random effects can be performed with the package randomLCA. In addition, the package e1071 provides the function lca(). Another package is poLCA for polytomous variable latent class analysis.
• The cfa package allows for the computation of simple, more-sample, and stepwise configural frequency analysis (CFA).
• Coefficents for interrater reliability and agreements can be computed with the irr.
• prefmod generates design matrix for analysing real paired comparisons and derived paired comparison data (Likert type items / ratings or rankings) using a loglinear approach. Fits loglinear Bradley-Terry model (LLBT) exploting an eliminate feature. Computes pattern models for paired comparisons, rankings, and ratings. Some treatment of missing values (MCAR and MNAR).
• Bradley-Terry models for paired comparisons are implemented in the package BradleyTerry2 and in eba. The latter allowes for the computation of elimination-by-aspects models.
• DAKS provides functions and example datasets for the psychometric theory of knowledge spaces. This package implements data analysis methods and procedures for simulating data and transforming different formulations in knowledge space theory.
• Psychophysical data can be analyzed with the psyphy package. The MLCM package contains functions to estimate the contribution of the n scales to the judgment by a maximum likelihood method under several hypotheses of how the perceptual dimensions interact.
• Functions and example datasets for Fechnerian scaling of discrete object sets are provided by fechner. It computes Fechnerian distances among objects representing subjective dissimilarities, and other related information.
• Confidence intervals for standardized effect sizes: The MBESS package.
• Functions for data screening, testing moderation, mediation, and estimating power are contained in the QuantPsyc package.
• The qgraph package can be used to visualize data as networks.
• Fitting and testing multinomial processing tree models, a class of statistical models for categorical data with latent parameters, can be performed using the mpt package. These parameters are the link probabilities of a tree-like graph and represent the cognitive processing steps executed to arrive at observable response categories.