Last updated on 20190520
by Patrick Mair
Psychometrics is concerned with theory and techniques of psychological measurement.
Psychometricians have also worked collaboratively with those in the field of statistics and
quantitative methods to develop improved ways to organize, analyze, and scale
corresponding 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.
Please let me know if I 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 3parameter 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.

The mirt estimates dichotomous and polytomous response data using
unidimensional and multidimensional latent trait models under the IRT paradigm. Exploratory and confirmatory models can be
estimated with quadrature (EM) or stochastic (MHRM) methods. Confirmatory bifactor and twotier analyses are available for
modeling item testlets. Multiple group analysis and mixed effects designs also are available for detecting differential item functioning
and modeling item and person covariates.

TAM fits unidimensional and multidimensional item response models and also includes multifaceted models,
latent regression models and options for drawing plausible values.

The mirtjml package uses joint maximum likelihood estimation methods for highdimensional item factor analysis facilitated by multicore processing.

PLmixed fits (generalized) linear mixed models (GLMM) with factor structures.

MLCIRTwithin provides a flexible framework for the estimation of discrete twotier IRT models for the analysis of dichotomous and ordinal polytomous item responses.

An implementation of Gibbs sampling algorithm for Bayesian estimation of the Reduced Reparameterized Unified Model is provided by rrum.

For Bayesian estimation of the DINA (deterministic input, noisy and gate) see dina.

IRTShiny provides an interactive shiny application for IRT analysis.

Some additional uni and multidimensional item response models (especially for locally dependent item responses) and
some exploratory methods (DETECT, LSDM, modelbased reliability) are included in sirt.

The pcIRT estimates the multidimensional polytomous Rasch model and the Mueller's continuous rating scale model.

An implementation of the partial credit model with response styles is given in the PCMRS.

Thurstonian IRT models can be fitted with the kcirt package.

MultiLCIRT estimates IRT models under (1) multidimensionality assumption, (2) discreteness of
latent traits, (3) binary and ordinal polytomous items.

Conditional maximum likelihood estimation via the EM algorithm and
informationcriterionbased model selection in binary mixed Rasch models are
implemented in the mRm package and the psychomix package.
The mixRasch package estimates mixture Rasch models, including the
dichotomous Rasch model, the rating scale model, and the partial credit model.

The PP package includes estimation of (MLE, WLE, MAP, EAP, ROBUST) person parameters for the 1,2,3,4PL model and the
GPCM (generalized partial credit model). The parameters are estimated under the assumption that the item parameters are known and fixed.
The package is useful e.g. in the case that items from an item pool/item bank with known item parameters are administered to a new
population of testtakers and an ability estimation for every testtaker is needed.

The equateIRT package computes direct, chain and average (bisector) equating coefficients with
standard errors using Item Response Theory (IRT) methods for dichotomous items. equateMultiple can be used for equating of multiple forms using IRT methods.

kequate implements the kernel method of test equating using the CB, EG, SG, NEAT CE/PSE and NEC designs, supporting gaussian, logistic and uniform
kernels and unsmoothed and presmoothed input data.

The EstCRM package calibrates the parameters for Samejima's
Continuous IRT Model via EM algorithm and Maximum Likelihood. It allows to
compute item fit residual statistics, to draw empirical 3D item category
response curves, to draw theoretical 3D item category response curves, and to
generate data under the CRM for simulation studies.

The difR package contains several traditional methods to detect DIF in dichotomously scored items. Both uniform and nonuniform 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 DIF.

DIFlasso implements a penalty approach to differential item functioning in Rasch models. It can handle settings with multiple (metric) covariates.

GPCMlasso provides a function to detect DIF in generalized partial credit models (GPCM).

DIFtree performs recursive partitioning for simultaneous selection of items and variables that induce DIF in dichotomous or polytomous items.

DIFboost can be used for DIF detection in Rasch models by boosting techniques.

A set of functions to perform differential item and item functioning analyses is implemented
in the DFIT package. It includes functions to use the Monte Carlo item parameter replication (IPR) approach
for obtaining the associated statistical significance tests cutoff points.

The difNLR package uses nonlinear regression to estimate DIF.

The catR package allows for computarized adaptive testing using
IRT methods.

The mirtCAT package provides tools to generate an HTML interface for creating adaptive and nonadaptive educational and psychological tests
using the shiny package. Suitable for applying unidimensional and multidimensional computerized adaptive tests using IRT methodology and
for creating simple questionnaires forms to collect response data directly in R.

xxIRT is implementation of related to IRT and computerbased testing.

The package plRasch computes maximum likelihood estimates and
pseudolikelihood estimates of parameters of Rasch models for polytomous
(or dichotomous) items and multiple (or single) latent traits. Robust
standard errors for the pseudolikelihood estimates are also computed.

Explicit calculation (not estimation) of Rasch item parameters (dichotomous and polytomous) by means of a pairwise comparison approach
can be done using the pairwise package.

Multilevel Rasch models can be estimated using lme4, nlme, and MCMCglmm with crossed or
partially crossed random effects. GLMMRR adds some flexibility in terms of link functions, whereas ordinal can be used for polytomous models. An infrastructure for
estimating treestructured item response models of the GLMM family using lme4 is provided in irtrees.

Nonparametric IRT analysis can be computed by means if the mokken package. It includes an automated item selection algorithm, and various checks of model assumptions. In relation to that, fwdmsa
performs the Forward Search for Mokken scale analysis. It detects outliers, it produces several types of diagnostic plots.

Nonparametric IRT for nonmonotonic IRFs of proximity data can be fitted using the mudfold package.

The RaschSampler allows the construction of exact Rasch model tests by generating random zeroone matrices with given marginals.

Statistical power simulation for testing the Rasch model based on a threeway ANOVA design with mixed classification can be carried out using pwrRasch.

The irtProb package is designed to estimate multidimensional subject parameters (MLE and MAP) such as personal pseudoguessing, 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.

cacIRT computes classification accuracy and consistency under Item Response Theory.
Implements total score and latent trait IRT methods as well as total score kernelsmoothed methods.

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, BILOGMG, and ltm, and a variety of functions useful
with IRT models.

The CDM estimates several cognitive diagnosis models (DINA, DINO, GDINA, RRUM, LCDM, pGDINA, mcDINA), the general diagnostic model (GDM)
and structured latent class analysis (SLCA).

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.

emIRT provides various EMalgorithms IRT models (binary and ordinal responses, along with dynamic and hierarchical models).

immer implements some item response models for multiple ratings, including the hierarchical rater model and a wrapper function to the commercial FACETS program.

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 noncrossing ICCs.

The purpose of the rpf package is to factor out logic and math
common to IRT fitting, diagnostics, and analysis. It is envisioned as core
support code suitable for more specialized IRT packages to build upon.

WrightMap provides graphical tools for plotting itemperson maps.

irtDemo includes a collection of shiny applications to demonstrate or to explore fundamental IRT concepts. ifaTools is a shiny interface to IRT with OpenMx.

IRT utility functions described in the Baker/Kim book are included in birtr.
Correspondence Analysis (CA), Optimal Scaling:

The package ca comprises two parts, one for simple
correspondence analysis and one for multiple and joint correspondence
analysis.

Simple and canonical CA are provided by the package anacor, including confidence ellipsoids. It
allows for different scaling methods such as standard scaling, Benzecri scaling,
centroid scaling, and Goodman scaling.

Homogeneity analysis aka multiple CA and various Gifi extensions can be
computed by means of the Gifi package, which replaces homals. This package includes various other optimal scaling methods such as
Morals (monotone regression), Princals (nonlinear PCA), Overals (nonlinear canonical correlation analysis), etc.

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
cocorrespondence 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
nonmetric multidimensional scaling. The constrained ordination methods
include constrained analysis of proximities, redundancy analysis, and
constrained (canonical) and partially constrained correspondence
analysis.

cabootcrs computes bootstrap confidence regions for CA.

cncaGUI implements a GUI with which users can construct and interact with canonical (nonsymmetrical) CA.

SVD based multivariate exploratory methods such as PCA, CA, MCA
(as well as a Hellinger form of CA), generalized PCA are implemented in ExPosition.
The package also allows for supplementary data projection.

cds can be used for constrained dual scaling for detecting response styles.

CAvariants provides six variants of twoway CA: simple, singly ordered, doubly ordered, nonsymmetrical, singly ordered nonsymmetrical ca, and doubly ordered nonsymmetrical.

MCAvariants provides MCA and ordered MCA via orthogonal polynomials.

Specific and class specific MCA on surveylike data can be fitted using soc.ca.

optiscale provides tools for performing an optimal scaling transformation on a data vector.

A general framework of optimal scaling methods is implemented in the aspect.
Factor Analysis (FA), Principal Component Analysis (PCA):

Exploratory FA is the package stats as function
factanal()
and fa()
and fa.poly()
(ordinal data) in psych.

esaBcv estimates the number of latent factors and factor matrix.

SparseFactorAnalysis scales count and binary data with sparse FA.

EFAutilities computes robust standard errors and factor correlations under a variety of conditions.

faoutlier implements influential case detection methods for FA and SEM.

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.

PCA can be fitted with
prcomp()
(based on svd()
, preferred) as well as
princomp()
(based on eigen()
for compatibility with
SPLUS). Additional rotation methods for FA based on gradient projection algorithms can be found in the package GPArotation. The package
nFactors produces a nongraphical solution to the Cattell scree test. Some graphical PCA representations
can be found in the psy package. paran implements Horn's test of principal components/factors.

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 Gifi package implements Princals, a PCA version for mixedscale level input data.

nsprcomp and elasticnet fit sparse PCA.

Threeway PCA models (Tucker, Parafac/Candecomp) can be fitted using PTAk, ThreeWay, and multiway.

Independent component analysis (ICA) can be computed using fastICA, ica, eegkit (designed for EEG data), and AnalyzeFMRI (designed
for fMRI data).

A desired number of robust principal components can be computed with the pcaPP package.

bpca implements 2D and 3D biplots of multivariate data based on PCA and diagnostic tools of the quality of the reduction.

missMDA provides imputation of incomplete continuous or categorical datasets in principal component analysis (PCA),
multiple correspondence analysis (MCA) model, or multiple factor analysis (MFA) model.
Structural Equation Models (SEM):

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 SatorraBentler 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 OpenMx package allows for the
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.

The sem package fits general (i.e., latentvariable) SEMs by
FIML, and structural equations in observedvariable models by 2SLS. Categorical
variables in SEMs can be accommodated via the polycor package.

lslx fits semiconfirmatory SEM via penalized likelihood with elastic net or minimax concave penalty.

The lavaan.survey package allows for complex survey structural equation modeling (SEM). It fits structural equation models (SEM) including factor analysis, multivariate regression models with latent variables and many other latent variable models while correcting estimates, standard errors, and chisquarederived fit measures for a complex sampling design. It incorporates clustering, stratification, sampling weights, and finite population corrections into a SEM analysis.

The nlsem package fits nonlinear structural equation mixture models using the EM algorithm. Three different approaches are
implemented: LMS (Latent Moderated Structural Equations), SEMM (Structural Equation Mixture Models), and NSEMM (Nonlinear
Structural Equations Mixture Models).

Continuous time structural equation models can be fitted using the ctsem package.

A collection of functions for conducting metaanalysis using a structural equation modeling (SEM) approach via OpenMx is provided by
the metaSEM package.

A general implementation of a computational framework for latent variable models (including structural equation models) is given in lava. The lava.tobit package generalizes the framework to censored and
dichotomous variables via a probit link formulation.

The pls package can be used for partial leastsquares estimation. The package semPLS fits structural equation models using partial
least squares (PLS). The PLS approach is referred to as softmodeling technique requiring no distributional assumptions on the observed data. PLS methods with
emphasis on structural equation models with latent variables are given in plspm which also includes pathmox as a companion package
with approaches of segmentation trees in PLS path modeling.

simsem is a package designed to aid in Monte Carlo simulations using SEM (for methodological investigations, power analyses and much more).

Sim.DiffProc provides a framework for parallelized Monte Carlo simulationestimation in multidimensional continuoustime models, which have been implemented as SEM.

semTools is a package of add on functions that can aid in fitting
SEMs in R (for example one function automates imputing missing data, running
imputed datasets and combining the results from these datasets).

semPlot produces path diagrams and visual analysis for outputs of various SEM packages.

plotSEMM for graphing nonlinear relations among latent variables from structural equation mixture models.

SEMModComp conducts tests of difference in fit for mean and
covariance structure models as in SEM.

semdiag and influence.SEM implements outlier, leverage diagnostics, and case influence for SEM.

gSEM conducts semisupervised generalized SEM and piecewiseSEM fits piecewise SEM.

rsem implements robust SEM with missing data and auxiliary variables.

regsem performs Regularization on SEM and sparseSEM implements sparseaware ML for SEM.

Recursive partitioning (SEM trees, SEM forests) is implemented in semtree.

BigSEM constructs large systems of structural equations using a twostage penalized least squares approach.

lsl conducts SEM via penalized likelihood (latent structure learning).

MIIVsem contains functions for estimating structural equation models using instrumental variables.

The systemfit package implements a wider variety of estimators for observedvariables models, including nonlinear simultaneousequations models.

STARTS contains functions for estimating the STARTS model.

Interfaces between R and other SEM software: REQS, MplusAutomation, and lisrelToR.
Multidimensional Scaling (MDS):

The smacof package provides many approaches to metric and nonmetric MDS, including extensions for MDS with external constraints, spherical MDS,
asymmetric MDS, threeway MDS (INDSCAL/IDIOSCAL), BentlerWeeks model, unidimensional scaling, Procrustes, inverse MDS.

MASS and stats provide functionalities for computing classical MDS using the
cmdscale()
function. Sammon mapping sammon()
and nonmetric MDS isoMDS()
are other relevant functions.

Nonmetric MDS can also be computed with
metaMDS()
in vegan. Furthermore, labdsv and ecodist provide the function
nmds()
and some routines can be found in xgobi. Also, the ExPosition implements a function for metric MDS.

Principal coordinate analysis can be computed with
capscale()
in vegan; in labdsv and ecodist using pco()
and
with dudi.pco()
in ade4.

INDSCAL is also implemented in the SensoMineR package.

The package MLDS allows for the computation of maximum likelihood difference scaling (MLDS).

DistatisR implements the DiSTATIS/CovSTATIS 3way metric MDS approach.

Symbolic MDS for intervalvalued dissimilarities (hypersphere and hyperbox model) can be fitted with the smds package.

Supervised MDS is implemented in superMDS.

munfold provides functions for metric unfolding.

The asymmetry package implements the slidevector model for asymmetric MDS.

semds fits asymmetric and threeway MDS within an SEM framework.
Classical Test Theory (CTT):

The CTT package can be used to perform a variety of tasks and
analyses
associated with classical test theory: score multiplechoice responses,
perform reliability analyses,
conduct item analyses, and transform scores onto different scales.

Functions for correlation theory, metaanalysis (validity generalization),
reliability, item analysis, interrater reliability, and classical utility are
contained in the psychometric package.

For multilevel model ICC for slope heterogeneity see iccbeta.

An interactive shiny application for CTT is provided by CTTShiny.

The cocron package provides functions to statistically compare two or more alpha coefficients based
on either dependent or independent groups of individuals.

The CMC package calculates and plots the stepbystep
CronbachMesbach 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 intraclass correlation coefficients
(ICC) can be found in the psy package. Functions for ICC computation can be also found in the packages psych, psychometricand ICC.

A number of routines for scale construction and reliability analysis useful
for personality and experimental psychology are contained in the
package psych.

subscore can be used for computing subscores in CTT and IRT.

The quantifying construct validity procedure is implemented in qcv.
Knowledge Structure Analysis:

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.

The kst package contains basic functionality to generate, handle,
and manipulate deterministic knowledge structures based on sets and relations.
Functions for fitting probabilistic knowledge structures are included in the
pks package.
Latent Class Analysis (LCA):

LCA 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.
LCA can also be fitted using flexmix which optionally allows for the inclusion of concomitant variables and latent class regression.

LCAvarsel implements variable selection for LCA.

covLCA fits latent class models with covariate effects on underlying and measured variables.

lcda fits latent class discriminant analysis.

ClustVarLV clusters variables around latent variables.
Paired Comparisons, Rankings, Ratings:

BradleyTerry models for paired comparisons are implemented in the package BradleyTerry2 and in eba. The latter allows for the computation of eliminationbyaspects models.

Recursive partitioning trees for BradleyTerry models are implemented in psychotree.

BTLLasso allows one to include subjectspecific and objectspecific covariates into paired comparison models shrinks the effects using Lasso.

prefmod fits loglinear BradleyTerry models (LLBT) and pattern models for paired comparisons, rankings, and ratings.

PLMIX fits finite mixtures of PlackettLuce models for partial top rankings/orderings within the Bayesian framework.

A variety of unfolding techniques for rankings and ratings are implemented in smacof.
Bayesian Psychometrics:

blavaan fits a variety of Bayesian latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models.

BayesFM computes Bayesian exploratory factor analysis. The number of factors is determined during MCMC sampling.

Bayesian approaches for estimating item and person parameters by means of GibbsSampling are included in MCMCpack.
In addition, the pscl package allows for Bayesian IRT and roll call analysis.

LNIRT is a package for lognormal response time IRT modeling for responses and response times, estimated with MCMC.

edstan provides convenience functions and preprogrammed Stan models related to IRT.

fourPNO can be used for Bayesian 4PL IRT estimation.

Simulationbased Bayesian inference for IRT latent traits can be performed using ltbayes.

BayesLCA implements Bayesian LCA.
Other Related Packages:

The psychotools provides an infrastructure for psychometric modeling such as data classes (e.g., for paired comparisons) and basic model
fitting functions (e.g., for Rasch and BradleyTerry models).

quickpsy is a package developed to quickly fit and plot psychometric functions for multiple conditions.

cNORM provides methods for generating regression based continuous norms. The approach does not rely on prior distribution assumptions and is thus nonparametric, but it can be combined with BoxCox power transformations for semiparametrically modelling the data as well.

A system for the management, assessment, and psychometric analysis of data from educational and psychological tests is implemented in dexter, with multistage test calibration in dexterMST.

Psychometric mixture models based on flexmix infrastructure are provided by
means of the psychomix package (at the moment Rasch mixture models
and BradleyTerry mixture models).

The equate package contains functions for nonIRT equating under
both random groups and nonequivalent groups with anchor test designs. Mean,
linear, equipercentile and circlearc 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.

The CopyDetect package contains several IRT and nonIRT based
statistical indices proposed in the literature for detecting answer copying on
multiplechoice examinations.

Interactive shiny application for analysis of educational tests and their items are provided by the ShinyItemAnalysis package.

Coefficients for interrater reliability and agreements can be computed with the irr.

Psychophysical data can be analyzed with the psyphy package.

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.

The modelfree package provides functions for nonparametric
estimation of a psychometric function and for estimation of a derived threshold
and slope, and their standard deviations and confidence intervals.

Confidence intervals for standardized effect sizes: The MBESS
package.

The mediation allows both parametric and nonparametric causal mediation analysis.
It also allows researchers to conduct sensitivity analysis for certain parametric models.

Mediation analysis using natural effect models can be performed using medflex.

Functions for data screening, testing moderation, mediation, and estimating
power are contained in the QuantPsyc package.

The package multiplex is especially designed for social networks with relations at
different levels. In this sense, the program has effective ways to treat multiple networks data
sets with routines that combine algebraic structures like the partially ordered semigroup
with the existing relational bundles found in multiple networks. An algebraic approach for twomode networks is made
through Galois derivations between families of the pair of subsets.

The qgraph package can be used to visualize data as networks.

NetworkToolbox implements network analysis and graph theory measures used in neuroscience, cognitive science, and psychology.
Methods include various filtering methods and approaches such as threshold, dependency, information filtering networks, and efficiencycost optimization.

Social Relations Analyses for round robin designs are implemented in the
TripleR package. It implements all functionality of the SOREMO
software, and provides new functions like the handling of missing values,
significance tests for single groups, or the calculation of the self enhancement
index.

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
treelike graph and represent the cognitive processing steps executed to arrive
at observable response categories.The MPTinR package provides a
userfriendly way for analysis of multinomial processing tree (MPT) models.
The TreeBUGS package provides userfriendly methods to fit Bayesian hierarchical MPT models
(betaMPT and latenttrait MPT) and implements posteriorpredictive checks, summary plots, correlations and regressions for personlevel MPT parameters.

Beta regression for modeling betadistributed dependent variables, e.g., rates
and proportions, is available in betareg.

The cocor package provides functions to compare two correlations based on either dependent or independent groups.

The profileR package provides a set of tools that implement profile analysis and crossvalidation techniques.

The TestScorer package provides a GUI for entering test items and obtaining raw and transformed scores. The results are shown on the console and can be saved to a
tabular text file for further statistical analysis. The user can define his own tests and scoring procedures through a GUI.

wCorr calculates Pearson, Spearman, tetrachoric polychoric, and polyserial correlation coefficients, in weighted or unweighted form.

The gtheory package fits univariate and multivariate generalizability theory (Gtheory) models.

The GDINA package estimates various cognitive diagnosis models (CDMs) within the generalized deterministic inputs, noisy and gate (GDINA) model and the sequential GDINA model framework. It can also be used to conduct Qmatrix validation, item and model fit statistics, model comparison at the test and item level and differential item functioning. A graphical user interface is also provided.

Simulation routines for cognitive diagnostic model DINA and rRUM are implemented in simcdm.

TestDataImputation for missing item responses imputation for test and assessment data.

lba performs latent budget analysis for compositional data (twoway contingency table with an exploratory variable and a response variable)

fuzzyreg implements multiple methods to fit fuzzy linear regression. Models using fuzzy set theory are suitable for analysis of trait data in situations when the model is indefinite, relationships between model variables are vague, sample size is low or measurements are hierarchically structured.

LAM includes some procedures for latent variable modeling with a particular focus on multilevel data.