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Psychometrics
Psychometric Models and Methods
Patrick Mair, Yves Rosseel, Kathrin Gruber
2023-12-15

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, we only give a brief overview of packages that are closely related to psychometric methodology.

Contributions are always welcome and encouraged, either via e-mail to the maintainer or by submitting an issue or pull request in the GitHub repository linked above.

Item Response Theory (IRT):

  • The r pkg("eRm", priority = "core") 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 r pkg("ltm", priority = "core") 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.
  • The r pkg("mirt", priority = "core") 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 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.
  • r pkg("TAM", priority = "core") fits unidimensional and multidimensional item response models and also includes multifaceted models, latent regression models and options for drawing plausible values.
  • r pkg("Dire") fits weighted latent variable linear models, estimating score distributions for groups of people, in an IRT framework, following Cohen and Jiang (1999). It can then draw plausible values.
  • r pkg("PLmixed") fits (generalized) linear mixed models (GLMM) with factor structures.
  • r pkg("MLCIRTwithin") provides a flexible framework for the estimation of discrete two-tier IRT models for the analysis of dichotomous and ordinal polytomous item responses.
  • r pkg("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, model-based reliability) are included in r pkg("sirt").
  • The r pkg("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 r pkg("PCMRS").
  • r pkg("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 information-criterion-based model selection in binary mixed Rasch models are implemented in the r pkg("psychomix") package.
  • The r pkg("PP") 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.
  • The r pkg("equateIRT") package computes direct, chain and average (bisector) equating coefficients with standard errors using Item Response Theory (IRT) methods for dichotomous items. r pkg("equateMultiple") can be used for equating of multiple forms using IRT methods.
  • r pkg("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 pre-smoothed input data.
  • The r pkg("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 r pkg("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 r pkg("lordif") provides a logistic regression framework for detecting various types of DIF.
  • r pkg("DIFplus") allows users to implement extensions of the Mantel-Haenszel DIF detection procedures in the presence of multilevel data.
  • r pkg("DIFlasso") implements a penalty approach to differential item functioning in Rasch models. It can handle settings with multiple (metric) covariates.
  • r pkg("GPCMlasso") provides a function to detect DIF in generalized partial credit models (GPCM).
  • r pkg("DIFtree") performs recursive partitioning for simultaneous selection of items and variables that induce DIF in dichotomous or polytomous items.
  • r pkg("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 r pkg("DFIT") package. It includes functions to use the Monte Carlo item parameter replication (IPR) approach for obtaining the associated statistical significance tests cut-off points.
  • The r pkg("difNLR") package uses nonlinear regression to estimate DIF.
  • The r pkg("catR") package allows for computarized adaptive testing using IRT methods.
  • The r pkg("mirtCAT") 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.
  • r pkg ("D3mirt") for identifying, estimating, and plotting descriptive multidimensional item response theory models, restricted to 3D and dichotomous or polytomous data that fit the two-parameter logistic model or the graded response model.
  • r pkg("xxIRT") is implementation of related to IRT and computer-based testing.
  • r pkg("Rirt") estimates the 3-parameter-logistic model, generalized partial credit model, and graded response model.
  • Explicit calculation (not estimation) of Rasch item parameters (dichotomous and polytomous) by means of a pairwise comparison approach can be done using the r pkg("pairwise") package.
  • Multilevel Rasch models can be estimated using r pkg("lme4"), r pkg("nlme"), and r pkg("MCMCglmm") with crossed or partially crossed random effects. r pkg("GLMMRR") adds some flexibility in terms of link functions, whereas r pkg("ordinal") can be used for polytomous models. An infrastructure for estimating tree-structured item response models of the GLMM family using r pkg("lme4") is provided in r pkg("irtrees").
  • Nonparametric IRT analysis can be computed by means if the r pkg("mokken", priority = "core") package. It includes an automated item selection algorithm, and various checks of model assumptions.
  • Nonparametric IRT for nonmonotonic IRFs of proximity data can be fitted using the r pkg("mudfold") package.
  • r pkg("RaschSampler") 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 r pkg("pwrRasch").
  • Tools to assess model fit and identify misfitting items for Rasch models and PCMS are implemented in r pkg("iarm"). It includes item fit statistics, ICCs, item-restscore association, conditional likelihood ratio tests, assessment of measurement error, estimates of the reliability and test targeting.
  • r pkg("cacIRT") 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.
  • The package r pkg("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.
  • The r pkg("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 r pkg("VGAM").
  • r pkg("immer") implements some item response models for multiple ratings, including the hierarchical rater model and a wrapper function to the commercial FACETS program.
  • The r pkg("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.
  • The purpose of the r pkg("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.
  • r pkg("WrightMap") provides graphical tools for plotting item-person maps.
  • r pkg("irtDemo") includes a collection of shiny applications to demonstrate or to explore fundamental IRT concepts. r pkg("ifaTools") is a shiny interface to IRT with r pkg("OpenMx", priority = "core").
  • IRT utility functions described in the Baker/Kim book are included in r pkg("birtr").
  • Convenience functions to use and automate IRT modeling for judgement data are implemented in r pkg("jrt").
  • The r pkg("conquestr") package allows users to call ACER ConQuest from within R.
  • r pkg("TestDesign") implements optimal test design approaches for fixed and adaptive test construction.
  • r pkg("PROsetta") provides functions for performing scale linking between instruments, based on the PROsetta Stone methodology.
  • r pkg("maat") performs simulations for multiple administrations adaptive testing.

Correspondence Analysis (CA), Optimal Scaling:

  • The package r pkg("ca", priority = "core") 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 r pkg("anacor", priority = "core"), 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 r pkg("Gifi", priority = "core") package, which replaces r pkg("homals"). This package includes various other optimal scaling methods such as Morals (monotone regression), Princals (nonlinear PCA), Homals (multiple correspondence analysis), etc.
  • Simple and multiple correspondence analysis can be performed using corresp() and mca() in package r pkg("MASS").
  • The package r pkg("ade4", priority = "core") 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 r pkg("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 r pkg("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 r pkg("vegan", priority = "core") 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.
  • r pkg("cabootcrs") computes bootstrap confidence regions for CA.
  • r pkg("cncaGUI") 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 r pkg("ExPosition"). The package also allows for supplementary data projection.
  • r pkg("cds") can be used for constrained dual scaling for detecting response styles.
  • r pkg("CAvariants") provides six variants of two-way CA: simple, singly ordered, doubly ordered, non-symmetrical, singly ordered non-symmetrical ca, and doubly ordered non-symmetrical.
  • r pkg("MCAvariants") provides MCA and ordered MCA via orthogonal polynomials.
  • Specific and class specific MCA on survey-like data can be fitted using r pkg("soc.ca").
  • r pkg("optiscale") provides tools for performing an optimal scaling transformation on a data vector.
  • A general framework of optimal scaling methods is implemented in the r pkg("aspect").
  • r pkg("candisc"): Visualizing generalized canonical discriminant and canonical correlation analysis.

Factor Analysis (FA), Principal Component Analysis (PCA):

  • Exploratory FA is the package stats as function factanal() and fa() and fa.poly() (ordinal data) in r pkg("psych", priority = "core").
  • r pkg("BayesFM") for Bayesian EFA.
  • r pkg("esaBcv") estimates the number of latent factors and factor matrix.
  • r pkg("SparseFactorAnalysis") scales count and binary data with sparse FA.
  • r pkg("EFAutilities") computes robust standard errors and factor correlations under a variety of conditions.
  • r pkg("faoutlier") implements influential case detection methods for FA and SEM.
  • The package r pkg("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 S-PLUS). Additional rotation methods for FA based on gradient projection algorithms can be found in the package r pkg("GPArotation"). The package r pkg("nFactors") produces a non-graphical solution to the Cattell scree test. Some graphical PCA representations can be found in the r pkg("psy", priority = "core") package. r pkg("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 r pkg("FactoMineR") package whereas r pkg("MCMCpack") has some options for sampling from the posterior for ordinal and mixed factor models.
  • The r pkg("Gifi") package implements Princals, a PCA version for mixed-scale level input data.
  • r pkg("nsprcomp") and r pkg("elasticnet") fit sparse PCA.
  • Threeway PCA models (Tucker, Parafac/Candecomp) can be fitted using r pkg("PTAk"), r pkg("ThreeWay"), and r pkg("multiway").
  • Independent component analysis (ICA) can be computed using r pkg("fastICA"), r pkg("ica"), and r pkg("eegkit") (designed for EEG data).
  • A desired number of robust principal components can be computed with the r pkg("pcaPP") package.
  • r pkg("bpca") implements 2D and 3D biplots of multivariate data based on PCA and diagnostic tools of the quality of the reduction.
  • r pkg("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 r pkg("lavaan", priority = "core") 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 r pkg("OpenMx", priority = "core") 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 r pkg("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 r pkg("polycor") package.
  • r pkg("tidySEM") provides a tidy workflow for generating, estimating, reporting, and plotting structural equation models using lavaan, OpenMx, or Mplus.
  • r pkg("SEMsens") performs sensitivity analysis for omitted confounders in structural equation models using meta-heuristic optimization methods.
  • r pkg("lslx") fits semi-confirmatory SEM via penalized likelihood with elastic net or minimax concave penalty.
  • The r pkg("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 chi-square-derived fit measures for a complex sampling design. It incorporates clustering, stratification, sampling weights, and finite population corrections into a SEM analysis.
  • The r pkg("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).
  • A collection of functions for conducting meta-analysis using a structural equation modeling (SEM) approach via OpenMx is provided by the r pkg("metaSEM") package.
  • A general implementation of a computational framework for latent variable models (including structural equation models) is given in r pkg("lava").
  • The r pkg("pls") package can be used for partial least-squares estimation. The package r pkg("cSEM") fits structural equation models using composite based approaches (e.g., PLS).
  • r pkg("simsem") is a package designed to aid in Monte Carlo simulations using SEM (for methodological investigations, power analyses and much more).
  • r pkg("Sim.DiffProc") provides a framework for parallelized Monte Carlo simulation-estimation in multidimensional continuous-time models, which have been implemented as SEM.
  • r pkg("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).
  • r pkg("semPlot") produces path diagrams and visual analysis for outputs of various SEM packages.
  • r pkg("plotSEMM") for graphing nonlinear relations among latent variables from structural equation mixture models.
  • r pkg("influence.SEM") implements outlier, leverage diagnostics, and case influence for SEM.
  • r pkg("piecewiseSEM") fits piecewise SEM.
  • r pkg("rsem") implements robust SEM with missing data and auxiliary variables.
  • r pkg("regsem") performs Regularization on SEM.
  • Recursive partitioning (SEM trees, SEM forests) is implemented in r pkg("semtree").
  • r pkg("lsl") conducts SEM via penalized likelihood (latent structure learning).
  • r pkg("MIIVsem") contains functions for estimating structural equation models using instrumental variables.
  • The r pkg("systemfit") package implements a wider variety of estimators for observed-variables models, including nonlinear simultaneous-equations models.
  • r pkg("STARTS") contains functions for estimating the STARTS model.
  • Interfaces between R and other SEM software: r pkg("REQS"), r pkg("MplusAutomation"), and r pkg("lisrelToR").

Multidimensional Scaling (MDS):

  • The r pkg("smacof", priority = "core") package provides many approaches to metric and nonmetric MDS, including extensions for MDS with external constraints, spherical MDS, asymmetric MDS, three-way MDS (INDSCAL/IDIOSCAL), Bentler-Weeks model, unidimensional scaling, Procrustes, inverse MDS.
  • r pkg("smacofx") for flexible MDS analyses including MULTISCALE, Sammon mapping, ALSCAL, local MDS, elastic scaling, Box-Cox MDS, POST-MDS, curvilinear component and distance analysis, etc.
  • r pkg("cops") for cluster optimized prozimity scaling pronouncing the clustered appearance of the configuration.
  • r pkg("stops") provides a collection of methods that fit nonlinear distance transformations in multidimensional scaling (MDS) and trade-off the fit with structure considerations to find optimal parameters also known as structure optimized proximity scaling.
  • r pkg("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.
  • Nonmetric MDS can also be computed with metaMDS() in r pkg("vegan"). Furthermore, r pkg("labdsv") and r pkg("ecodist") provide the function nmds(). Also, the r pkg("ExPosition") implements a function for metric MDS.
  • Principal coordinate analysis can be computed with capscale() in r pkg("vegan"); in r pkg("labdsv") and r pkg("ecodist") using pco() and with dudi.pco() in r pkg("ade4").
  • INDSCAL is also implemented in the r pkg("SensoMineR") package.
  • The package r pkg("MLDS") allows for the computation of maximum likelihood difference scaling (MLDS).
  • r pkg("DistatisR") implements the DiSTATIS/CovSTATIS 3-way metric MDS approach.
  • r pkg("munfold") provides functions for metric unfolding.
  • The r pkg("asymmetry") package implements the slide-vector model for asymmetric MDS.
  • r pkg("semds") fits asymmetric and three-way MDS within an SEM framework.
  • r pkg("cops") performs cluster optimized proximity scaling which refers to MDS methods that aim at pronouncing the clustered appearance of the configuration.

Classical Test Theory (CTT):

  • The r pkg("CTT", priority = "core") 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.
  • For multilevel model ICC for slope heterogeneity see r pkg("iccbeta").
  • An interactive shiny application for CTT is provided by r pkg("CTTShiny").
  • The r pkg("cocron") package provides functions to statistically compare two or more alpha coefficients based on either dependent or independent groups of individuals.
  • The r pkg("betafunctions") package includes an implementation of the so-called "Livingston and Lewis" approach to classification accuracy and consistency.
  • Cronbach alpha, kappa coefficients, and intra-class correlation coefficients (ICC) can be found in the r pkg("psy") package. Functions for ICC computation can be also found in the packages r pkg("psych"), and r pkg("ICC").
  • A number of routines for scale construction and reliability analysis useful for personality and experimental psychology are contained in the package r pkg("psych").
  • r pkg("subscore") can be used for computing subscores in CTT and IRT.
  • The quantifying construct validity procedure is implemented in r pkg("qcv").

Knowledge Structure Analysis:

  • r pkg("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 r pkg("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 r pkg("pks") package.

Latent Class and Profile Analysis:

  • LCA with random effects can be performed with the package r pkg("randomLCA"). In addition, the package r pkg("e1071") provides the function lca(). Another package is r pkg("poLCA") for polytomous variable latent class analysis. LCA can also be fitted using r pkg("flexmix") which optionally allows for the inclusion of concomitant variables and latent class regression.
  • r pkg("LCAvarsel") implements variable selection for LCA.
  • r pkg("tidyLPA") is a user-friendly implementation of latent profile analysis.
  • r pkg("ClustVarLV") clusters variables around latent variables.
  • r pkg("multilevLCA") for single-level and multilevel latent class analysis with covariates.

Paired Comparisons, Rankings, Ratings:

  • Bradley-Terry models for paired comparisons are implemented in the package r pkg("BradleyTerry2") and in r pkg("eba"). The latter allows for the computation of elimination-by-aspects models.
  • Recursive partitioning trees for Bradley-Terry models are implemented in r pkg("psychotree", priority = "core").
  • r pkg("BTLLasso") allows one to include subject-specific and object-specific covariates into paired comparison models shrinks the effects using Lasso.
  • r pkg("prefmod", priority = "core") fits loglinear Bradley-Terry models (LLBT) and pattern models for paired comparisons, rankings, and ratings.
  • r github("jvparidon/lmerMultiMember") can fit the loglinear Bradley-Terry model as a mixed-effects model (GLMM) using lme4.
  • r pkg("pcFactorStan") provides convenience functions and pre-programmed Stan models related to the pairwise comparison factor model.
  • r pkg("PLMIX") fits finite mixtures of Plackett-Luce models for partial top rankings/orderings within the Bayesian framework.
  • A variety of unfolding techniques for rankings and ratings are implemented in r pkg("smacof").
  • Thurstonian IRT models for forced-choice items can be fitted with r pkg("thurstonianIRT").

Network Psychometrics:

  • Estimation of a sparse inverse covariance matrix using a lasso penalty (graphical lasso) can be achieved using r pkg("glasso").
  • r pkg("networktools") includes assorted tools for network analysis (bridge centrality, impact, and goldbricker).
  • Bootstrap methods to assess accuracy and stability of estimated network structures and centrality indices are implemented in r pkg("bootnet").
  • Permutation tests for network comparisons are implemented in r pkg("NetworkComparisonTest").
  • Model-based recursive partitioning for networks: r pkg("networktree").
  • Network structures for multilevel and graphical vector autoregression models can be obtain using r pkg("mlVAR") and r pkg("graphicalVAR").
  • r pkg("mgm") estimates time-varying k-order mixed graphical models.
  • r pkg("EstimateGroupNetwork") can be used to simultaneously estimate networks from different groups or classes via joint graphical lasso.
  • Various implementations for Ising models: r pkg("IsingSampler"), r pkg("IsingFit").
  • r pkg("lvnet") simultaneously estimates factor and network models.
  • Approaches for SEM and Confirmatory Network Analysis are implemented in r pkg("psychonetrics"). This includes multi-group (dynamic) SEM in combination with confirmatory network models from cross-sectional, time-series and panel data.
  • Network models for longitudinal data estimated within an SEM framework: r pkg("gimme").
  • The r pkg("qgraph") package can be used to visualize data as networks.
  • r pkg("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 efficiency-cost optimization.
  • r pkg("NetworkToolbox") implements methods and measures for brain, cognitive, and psychometric network analysis.
  • r pkg("EGAnet") implements the Exploratory Graph Analysis (EGA) framework for dimensionality and psychometric assessment.

Bayesian Psychometrics:

  • r pkg("blavaan", priority = "core") fits a variety of Bayesian latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve models.
  • An analytical framework for latent variables with different Bayesian learning methods, including the partially confirmatory factor analysis and partially confirmatory IRT is implemented in r pkg("LAWBL").
  • Bayesian approaches for estimating item and person parameters by means of Gibbs-Sampling are included in r pkg("MCMCpack"). In addition, the r pkg("pscl") package allows for Bayesian IRT and roll call analysis.
  • r pkg("LNIRT") is a package for log-normal response time IRT modeling for responses and response times, estimated with MCMC.
  • r pkg("edstan") provides convenience functions and preprogrammed Stan models related to IRT.
  • r pkg("fourPNO") can be used for Bayesian 4-PL IRT estimation.
  • Gibbs sampling for Bayesian estimation of (Exploratory) Reduced Reparameterized Unified Models are implemented in r pkg("rrum") and r pkg("errum").
  • For Bayesian estimation of the (exploratory) DINA (deterministic input, noisy and gate) see r pkg("dina") and r pkg("edina").
  • r pkg("slcm") provides an implementation of the exploratory Sparse Latent Class Model (SLCM) for Binary Data.
  • r pkg("ohoegdm") performs a Bayesian estimation of the ordinal exploratory Higher-order General Diagnostic Model (OHOEGDM) for Polytomous Data.
  • Data package containing coded item and q matrices used in various psychometric publications: r pkg("edmdata").
  • r pkg("BayesLCA") implements Bayesian LCA.

Other Related Packages:

  • The r pkg("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 Bradley-Terry models).
  • r pkg("quickpsy") is a package developed to quickly fit and plot psychometric functions for multiple conditions.
  • r pkg("cNORM") provides methods for generating regression based continuous norms. The approach does not rely on prior distribution assumptions and is thus non-parametric, but it can be combined with Box-Cox power transformations for semi-parametrically modelling the data as well.
  • A system for the management, assessment, and psychometric analysis of data from educational and psychological tests is implemented in r pkg("dexter"), with multi-stage test calibration in r pkg("dexterMST"), and a GUI via r pkg("dextergui").
  • Psychometric mixture models based on flexmix infrastructure are provided by means of the r pkg("psychomix") package (at the moment Rasch mixture models and Bradley-Terry mixture models).
  • The r pkg("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.
  • Interactive shiny application for analysis of educational tests and their items are provided by the r pkg("ShinyItemAnalysis") package.
  • Coefficients for interrater reliability and agreements can be computed with the r pkg("irr").
  • Statistical tools for the analysis of psychophysical data are implemented in r pkg("psyphy") and r pkg("MixedPsy").
  • Functions and example datasets for Fechnerian scaling of discrete object sets are provided by r pkg("fechner"). It computes Fechnerian distances among objects representing subjective dissimilarities, and other related information.
  • The r pkg("mediation") allows both parametric and nonparametric causal mediation analysis. It also allows researchers to conduct sensitivity analysis for certain parametric models.
  • Causal mediation analysis using natural effect models can be performed using r pkg("medflex").
  • The package r pkg("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 two-mode networks is made through Galois derivations between families of the pair of subsets.
  • Social Relations Analyses for round robin designs are implemented in the r pkg("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 r pkg("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.The r pkg("MPTinR") package provides a user-friendly way for analysis of multinomial processing tree (MPT) models. The r pkg("TreeBUGS") package provides user-friendly methods to fit Bayesian hierarchical MPT models (beta-MPT and latent-trait MPT) and implements posterior-predictive checks, summary plots, correlations and regressions for person-level MPT parameters.
  • Beta regression for modeling beta-distributed dependent variables, e.g., rates and proportions, is available in r pkg("betareg").
  • The r pkg("cocor") package provides functions to compare two correlations based on either dependent or independent groups.
  • The r pkg("profileR") package provides a set of tools that implement profile analysis and cross-validation techniques.
  • The r pkg("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.
  • r pkg("wCorr") calculates Pearson, Spearman, tetrachoric polychoric, and polyserial correlation coefficients, in weighted or unweighted form.
  • The r pkg("gtheory") package fits univariate and multivariate generalizability theory (G-theory) models.
  • The r pkg("GDINA") 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.
  • Simulation routines for cognitive diagnostic model DINA and rRUM are implemented in r pkg("simcdm").
  • r pkg("TestDataImputation") for missing item responses imputation for test and assessment data.
  • r pkg("LAM") includes some procedures for latent variable modeling with a particular focus on multilevel data.
  • r pkg("psychTools") contains tools to accompany the r pkg("psych") package.
  • r pkg("ata") provides a collection of psychometric methods to process item metadataand use target assessment and measurement blueprint constraints to assemble a test form.
  • r pkg("heplots"): Visualizing hypothesis tests in multivariate linear models with hypothesis error plots.

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