CRAN Task View: Psychometric Models and Methods
|Contact:||Patrick.Mair at wu.ac.at|
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
we only give a brief overview of packages that are closely related to
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):
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
includes the multivariate two- and three-parameter logistic models, confirmatory bifactor analysis, polytomous confirmatory and exploratory item response models, and partially-compensatory item response modeling in conjunction with other IRT models.
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.
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.
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).
package allows for computarized adaptive testing using IRT methods.
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
with functions for mixed-effects models with crossed or
partially crossed random effects.
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 plotting tools.
allows the construction of exact Rasch model tests by generating random zero-one matrices with given marginals.
Simple Rasch computations such a simulating data and joint maximum likelihood are included in the
computes classification accuracy and consistency under Item Response Theory. Currently, only works for 3PL IRT models (or 2PL or 1PL) and only for independent cut scores.
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
Two additional IRT packages (for Microsoft Windows only) are available and documented on the JSS site.
computes multilevel IRT models,
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
package allows for Bayesian IRT and roll call analysis.
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):
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
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
Simple and canonical CA are provided by the package
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
Homogeneity analysis aka multiple CA and various Gifi extensions can be computed
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
Other extensions of CA and MCA which also generalize many common IRT
models can be found on the
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
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
a non-graphical solution to the Cattell scree test. Some graphical PCA representations
can be found in the
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 implements a wider variety of estimators
for observed-variables models, including nonlinear simultaneous-equations models.
See also the
package, for partial least-squares estimation,
task view for graphical models and the
task view for other related packages.
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.
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. 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.
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.
conducts tests of difference in fit for mean and covariance structure models as in structural equation modeling (SEM)
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
has some options for sampling from
the posterior for ordinal and mixed factor models.
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
A desired number of robust principal components can be computed with the
includes functions such as
for estimating the
appropriate number of factors/components as well as
for item clustering.
An interface between the EQS software for SEM and R is provided by the
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
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
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).
Classical Test Theory (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
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
A number of routines for scale construction and reliability analysis useful
for personality and experimental psychology are contained in the
Additional measures for reliability and concordance can be computed with the
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).
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.
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.
Latent class analysis with random effects can be performed with the package
In addition, the package
provides the function
lca(). Another package is
for polytomous variable latent class analysis.
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
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
eba. The latter allowes for the computation of elimination-by-aspects models.
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
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.
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
Functions for data screening, testing moderation, mediation, and estimating power are contained in the
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 index.
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.
package provides a user-friendly way for analysis of multinomial processing tree (MPT) models
Functions and example empirical (i.e., fraction subtraction) and artificial data for cognitive diagnosis modeling are provided by the
package fits the multivariate binary probit model.