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
we only give a brief overview of packages that are closely related to
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):
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.
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
fits unidimensional and multidimensional item response models and also includes multifaceted models,
latent regression models and options for drawing plausible values.
allows for the analysis of 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 bi-factor and two-tier 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.
provides a flexible framework for the estimation of discrete two-tier IRT models for the analysis of dichotomous and ordinal polytomous item responses.
provides an interactive shiny application for IRT analysis.
package provides functions to estimate the Nominal Response Model and the Nested Logit Model. Both are models to examine multiple-choice items
and other polytomous response formats. Some additional uni- and multidimensional item response models (especially for locally dependent item responses) and
some exploratory methods (DETECT, LSDM, model-based reliability) are included in
estimates the multidimensional polytomous Rasch model and the Mueller's continuous rating scale model.
Thurstonian IRT models can be fitted with the
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
information-criterion-based model selection in binary mixed Rasch models are
implemented in the
package and the
package estimates mixture Rasch models, including the
dichotomous Rasch model, the rating scale model, and the partial credit model.
package includes estimation of (MLE, WLE, MAP, EAP, ROBUST) person parameters for the 1,2,3,4-PL 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 test-takers and an ability estimation for every test-taker is needed.
package computes direct, chain and average (bisector) equating coefficients with
standard errors using Item Response Theory (IRT) methods for dichotomous items.
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 pre-smoothed input data.
provides several methods for test equating. Besides of traditional approaches (mean-mean, mean-sigma, Haebara and Stocking-Lord IRT, etc.) it
supports methods such that local equating, kernel equating (using Gaussian, logistic and uniform kernels),
and IRT parameter linking methods based on asymmetric item characteristic functions including functions for obtaining standard errors.
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.
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.
provides a logistic regression framework for
detecting various types of differential item functioning (DIF).
implements a penalty approach to differential item functioning in Rasch models.
It can handle settings with multiple (metric) covariates.
A set of functions to perform Raju, van der Linden and Fleer's (1995) differential item and item functioning analyses is implemented
package. It includes functions to use the Monte Carlo item parameter replication (IPR) approach
for obtaining the associated statistical significance tests cut-off points.
package uses nonlinear regression to estimate DIF.
package allows for computarized adaptive testing using
package provides tools to generate an HTML interface for creating adaptive and non-adaptive 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.
is implementation of related to IRT and computer-based testing.
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.
Explicit calculation (not estimation) of Rasch item parameters (dichotomous and polytomous) by means of a pairwise comparison approach
can be done using the
A multilevel Rasch model can be estimated using the package
with functions for mixed-effects models with crossed or
partially crossed random effects. The
package implements this approach for polytomous models. An infrastructure for
estimating tree-structured item response models of the GLMM family using
is provided in
Nonparametric IRT analysis can be computed by means if the
package. It includes an automated item selection algorithm,
and various checks of model assumptions. In relation to that,
performs the Forward Search for Mokken scale analysis. It detects outliers, it
produces several types of diagnostic plots.
package fits nonparametric item and option
characteristic curves using kernel smoothing. It allows for optimal selection of
the smoothing bandwidth using cross-validation and a variety of exploratory
allows the construction of exact Rasch model
tests by generating random zero-one matrices with given marginals.
Statistical power simulation for testing the Rasch model based on a three-way ANOVA design with mixed classification can be carried out using
package 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.
computes classification accuracy and consistency under Item Response Theory.
Implements total score and latent trait IRT methods as well as total score kernel-smoothed methods.
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.
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
can be used for log-normal response time IRT models.
provides various EM-algorithms IRT models (binary and ordinal responses, along with dynamic and hierarchical models).
implements some item response models for multiple ratings, including the hierarchical rater model and a wrapper function to the commercial FACETS program.
An Rcpp based implementation of a variety of IRT models is provided by the packages
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.
The purpose of the
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.
package can be used to examine classification
accuracy and consistency under IRT models.
provides graphical tools for plotting item-person maps.
includes a collection of shiny applications to demonstrate or to explore fundamental IRT concepts.
Correspondence Analysis (CA), Optimal Scaling:
comprises two parts, one for simple
correspondence analysis and one for multiple and joint correspondence
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.
A GUI (Windows only) that allows the user to construct interactive Biplots is
offered by the package
Homogeneity analysis aka multiple CA and various Gifi extensions can be
by means of the
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
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
fits predictive and symmetric
co-correspondence analysis (CoCA) models to relate one data matrix to
another data matrix.
Apart from several factor analytic methods
performs CA including supplementary row and/or
column points and multiple correspondence analysis (MCA) with
supplementary individuals, supplementary quantitative variables and
supplementary qualitative variables.
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
computes bootstrap confidence regions for CA.
implements a GUI with which users can construct and interact with canonical (non-symmetrical) CA.
SVD based multivariate exploratory methods such as PCA, CA, MCA
(as well as a Hellinger form of CA), generalized PCA are implemented in
The package also allows for supplementary data projection.
implements functions to analyze multiple choice data using dual scaling, whereas
can be used
for constrained dual scaling for detecting response styles.
provides six variants of two-way CA: simple, singly ordered, doubly ordered, non-symmetrical, singly ordered non-symmetrical ca, and doubly ordered non-symmetrical.
provides MCA and ordered MCA via orthogonal polynomials.
Specific and class specific MCA on survey-like data can be fitted using
provides tools for performing an optimal scaling transformation on a data vector.
A general framework of optimal scaling methods is implemented in the
Factor Analysis (FA), Principal Component Analysis (PCA):
Exploratory FA is the package stats as function
(ordinal data) in
estimates the number of latent factors and factor matrix.
scales count and binary data with sparse FA.
implements influential case detection methods for FA and SEM.
includes functions such as
for estimating the
appropriate number of factors/components as well as
for item clustering.
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).
PCA can be fitted with
svd(), preferred) as well as
for compatibility with
S-PLUS). Additional rotation methods for FA based on gradient projection algorithms can be found in the package
GPArotation. The package
produces a non-graphical solution to the Cattell scree test. Some graphical PCA representations
can be found in the
implements Horn's test of principal components/factors.
FA and PCA with supplementary individuals and supplementary quantitative/qualitative variables
can be performed using the
has some options for sampling from
the posterior for ordinal and mixed factor models.
package provides nonlinear PCA (aka categorical PCA) and, by defining sets,
nonlinear canonical correlation analysis (models of the Gifi-family).
fit sparse PCA.
Independent component analysis (ICA) can be computed using
A desired number of robust principal components can be computed with the
implements 2D and 3D biplots of multivariate data based on PCA and diagnostic tools of the quality of the reduction.
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):
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.
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.
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
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 chi-square-derived fit measures for a complex sampling design. It incorporates clustering, stratification, sampling weights, and finite population corrections into a SEM analysis.
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).
A collection of functions for conducting meta-analysis using a structural equation modeling (SEM) approach via OpenMx is provided by
A general implementation of a computational framework for latent variable
models (including structural equation models) is given in
package generalizes the framework to censored and
dichotomous variables via a probit link formulation.
package can be used for partial least-squares estimation.
fits 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. PLS methods with
emphasis on structural equation models with latent variables are given in
which also includes
as a companion package
with approaches of segmentation trees in PLS path modeling.
is a package designed to aid in Monte Carlo simulations
using SEM (for methodological investigations, power analyses and much more).
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).
produces path diagrams and visual analysis for outputs of various SEM packages.
for graphing nonlinear relations among latent variables from structural equation mixture models.
conducts tests of difference in fit for mean and
covariance structure models as in structural equation modeling (SEM).
implements outlier, leverage diagnostics, and case influence for SEM, whereas
provides SEM goodness-of-fit indexes.
fits continuous time SEM using linear stochastic differential equations and
fits distributed-lag SEM.
conducts semi-supervised generalized SEM and
fits piecewise SEM.
implements robust SEM with missing data and auxiliary variables.
performs Regularization on SEM and
implements sparse-aware ML for SEM.
Recursive partitioning (SEM trees, SEM forests) is implemented in
constructs large systems of structural equations using a two-stage penalized least squares approach.
Identifiability of linear SEM can be checked using
conducts SEM via penalized likelihood (latent structure learning).
package implements a wider variety of estimators
for observed-variables models, including nonlinear simultaneous-equations models.
An interface between the EQS software for SEM and R is provided by the
package allows to automate latent variable
model estimation and interpretation using Mplus.
Multidimensional Scaling (MDS):
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.
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.
and stats provide
functionalities for computing classical MDS using the
function. Sammon mapping
and non-metric MDS
are other relevant functions.
Non-metric MDS can additionally be performed with
provide the function
and some routines can be found in
xgobi. Also, the
implements a function for
Principal coordinate analysis can be computed with
Individual differences in multidimensional scaling can be computed with
allows for the computation of maximum likelihood
difference scaling (MLDS).
implements the DiSTATIS/CovSTATIS 3-way metric MDS approach.
Symbolic MDS for interval-valued dissimilarities (hypersphere and hyperbox model) can be fitted with the
(Self-Organising-Deltoids) provides MDS by gradually reducing the dimensionality of an initial space.
Supervised MDS is implemented in
Classical Test Theory (CTT):
package can be used to perform a variety of tasks and
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
package provides functions to statistically compare two or more alpha coefficients based
on either dependent or independent groups of individuals.
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
Cronbach alpha, kappa coefficients, and intra-class correlation coefficients
(ICC) can be found in the
package. Functions for ICC computation can be also found in the packages
A number of routines for scale construction and reliability analysis useful
for personality and experimental psychology are contained in the
can be used for computing subscores in CTT and IRT.
Knowledge Structure Analysis:
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.
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
Latent Class Analysis (LCA):
LCA with random effects can be performed with the package
randomLCA. In addition, the package
provides the function
lca(). Another package is
for polytomous variable latent class analysis.
LCA can also be fitted using
which optionally allows for the inclusion of concomitant variables and latent class regression.
fits latent class models with covariate effects on underlying and measured variables.
fits latent class discriminant analysis.
clusters variables around latent variables.
fits a variety of Bayesian latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models.
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 Gibbs-Sampling are included in
In addition, the
package allows for Bayesian IRT and roll call analysis.
stands for choice IRT and jointly models the accuracy of cognitive responses and item choices within a Bayesian hierarchical framework.
provides convenience functions and preprogrammed Stan models related to IRT.
can be used for Bayesian 4-PL IRT estimation.
Simulation-based Bayesian inference for IRT latent traits can be performed using
implements Bayesian LCA.
Other Related Packages:
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 Bradley-Terry models).
is a package developed to quickly fit and plot psychometric functions for multiple conditions.
Recursive partitioning based on psychometric models, employing the general
MOB algorithm (from package party) are implemented in
Currently, only Bradley-Terry trees are provided.
Psychometric mixture models based on flexmix infrastructure are provided by
means of the
package (at the moment Rasch mixture models
and Bradley-Terry mixture models).
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.
package contains several IRT and non-IRT based
statistical indices proposed in the literature for detecting answer copying on
Interactive shiny application for analysis of educational tests and their items are provided by the
Coefficients for interrater reliability and agreements can be computed with the
generates design matrices 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
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
eba. The latter allows for the computation of
Psychophysical data can be analyzed with the
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
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
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
Functions for data screening, testing moderation, mediation, and estimating
power are contained in the
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 two-mode networks is made
through Galois derivations between families of the pair of subsets.
package can be used to visualize data as networks.
Social Relations Analyses for round robin designs are implemented in the
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
Fitting and testing multinomial processing tree models, a class of statistical
models for categorical data with latent parameters, can be performed using the
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.The
package provides a
user-friendly way for analysis of multinomial processing tree (MPT) models.
Beta regression for modeling beta-distributed dependent variables, e.g., rates
and proportions, is available in
package provides functions to compare two correlations based on either dependent or independent groups.
package provides a set of tools that implement profile
analysis and cross-validation techniques.
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.
calculates Pearson, Spearman, tetrachoric polychoric, and polyserial correlation coefficients, in weighted or unweighted form.
package fits univariate and multivariate generalizability theory (G-theory) models.
package estimates various cognitive diagnosis models (CDMs) within the generalized deterministic inputs, noisy and gate (G-DINA) model and the sequential G-DINA model framework. It can also be used to conduct Q-matrix 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.
for missing item responses imputation for test and assessment data.
performs latent budget analysis for compositional data (two-way contingency table with an exploratory variable and a response variable)
fits latent variable models for mixed continuous and ordinal responses.