Multidimensional Item Response Theory

Analysis of dichotomous and polytomous response data using unidimensional and multidimensional latent trait models under the Item Response Theory paradigm (Chalmers (2012) ). 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 and test functioning as well as modeling item and person covariates. Finally, latent class models such as the DINA, DINO, multidimensional latent class, and several other discrete latent variable models, including mixture and zero-inflated response models, are supported.

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Multidimensional item response theory in R.


Analysis of dichotomous and polytomous response data using unidimensional and multidimensional latent trait models under the Item Response Theory 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.

Examples and evaluated help files are available on the wiki

Various examples and worked help files have been compiled using the knitr package to generate HTML output, and are available on the package wiki. User contributions are welcome!

Installing from source

It's recommended to use the development version of this package since it is more likely to be up to date than the version on CRAN. To install this package from source:

  1. Obtain recent gcc, g++, and gfortran compilers. Windows users can install the Rtools suite while Mac users will have to download the necessary tools from the Xcode suite and its related command line tools (found within Xcode's Preference Pane under Downloads/Components); most Linux distributions should already have up to date compilers (or if not they can be updated easily). Windows users should include the checkbox option of installing Rtools to their path for easier command line usage.

  2. Install the devtools package (if necessary). In R, paste the following into the console:

  1. Load the devtools package (requires version 1.4+) and install from the Github source code.

Installing from source via git

If the devtools approach does not work on your system, then you can download and install the repository directly.

  1. Obtain recent gcc, g++, and gfortran compilers (see above instructions).

  2. Install the git command line tools.

  3. Open a terminal/command-line tool. The following code will download the repository code to your computer, and install the package directly using R tools (Windows users may also have to add R and git to their path)

git clone

Special Mac OS X Installation Instructions

In some reported cases XCode does not install the appropriate gfortran compilers in the correct location, therefore they have to be installed manually instead. This is accomplished by inputing the following instructions into the terminal:

curl -O
sudo tar fvxz gfortran-4.8.2-darwin13.tar.bz2 -C /


This package is free and open source software, licensed under GPL (>= 3).

Bugs and Questions

Bug reports are always welcome and the preferred way to address these bugs is through the Github 'issues'. Feel free to submit issues or feature requests on the site, and I'll address them ASAP. Also, if you have any questions about the package, or IRT in general, then feel free to create a 'New Topic' in the mirt-package Google group. Cheers!


Changes in mirt 1.30

  • empirical.poly.collapse argument added to itemfit() to plot expected score functions for polytomous items (suggested by Keri Brady)

  • SRMSR now reported in M2() for GGUMs (suggested by Bo on the mirt-package forum)

  • weights argument added to estfun.AllModelClass to allow for the inclusion of survey.weights to calculate the scores

  • DIF() now simplifies the output by default rather than returning lists from anova(). Wald tests are always simplified

  • Where applicable, RMSEA statistics are reported in itemfit() for tests that return suitable X2 and df components

  • Fix negative TLI and CFI values when using the C2 statistic from the M2() function (reported by Jake Kraska and Charlie Iaconangelo)

  • Fix delta method SEs for 'gpcm' itemtype (reported by Lennart Schneider)

Changes in mirt 1.29

  • When lower/upper bounded parameters are included the default optimizer is now 'nlminb' rather than 'L-BFGS-B'. This is mainly due to the instability in the 'L-BFGS-B' algorithm which is prone to converging instantly for unknown reasons

  • mdirt() gains a item.Q list to specify Q-matrices at the item-category level for each item

  • createItem() functions gain an optional argument to the function definitions to allow for list-specified data from functions such as mirt() via a silent mirt(..., customItemsData) argument

  • lattice auto.key default now reports lines rather than points. This is now more consistent when, for example, color theme is changed to black and white in the trellis window

  • Added Differential Response Function (DRF) statistics from upcoming publication (Chalmers, accepted) in a new function entitled DRF(). These are related to compensatory and non-compensatory measures of response bias for DIF, DBF, and DTF available from the SIBTEST framework but for IRT model fitted within the multiple-group estimation framework

  • structure argument added to mdirt() function to allow log-linear models for simplifying the profile probability model computations

  • export internally used traditional2mirt() function to transform a small selection of classical IRT parameterizations into the slope-intercept form

  • fix survey.weights input for multiple group models (reported by Leigh Allison)

  • fix itemtype = "rsm" block restriction when items contain unequal category lengths (reported by Aiden Loe)

  • SIBTEST() computation of beta coefficient changed to match Shealy and Stout's (1993) form of p_k * (Y_R - Y_F) (was previously p_k * (Y_F - Y_R); reported by Craig Wells). As well, Jmin default is increased to 5 to avoid conservative Type I error behavior in longer tests

  • Fix negative chi-square differences in DIF() function due to non-converged sub-models (reported by Daniel McKelvey)

Changes in mirt 1.28

  • M2() function gains a type input to distinguish between the univariate-bivariate collapsed M2* statistic and the bivariate only collapsed C2 statistic (Cai and Monro, 2014). C2 can be useful for polyomous items when there are too few degrees of freedom to compute the fully collapsed M2*

  • multipleGroup() gains the dentype argument to allow for mixture IRT models to be fitted (e.g., dentype = 'mixture-3' fits a three-class mixture model). This also allow modifications such as the zero-inflated IRT model to be fitted

  • technical gains a zeroExtreme logical flag to assign survey weights of 0 to extreme response patterns (FALSE by default). This may be required when Woods' extrapolation-interpolation method is used with empirical histograms to avoid ill defined extrapolated densities

  • fscores(), itemfit(), M2(), and residuals() gain a use_dentype_estimate argument to compute EAP-based scores whenever the latent trait density was estimated (e.g., via empirical histograms)

  • Empirical histograms can now be now scaled to [0,1] using Woods' extrapolation-interpolation method via the input dentype = 'empiricalhist_Woods'. Degrees of freedom updated to reflect this change, and 121 quadrature points are used instead of the previous 199 for better stability

  • Semi-parametric Davidian curve estimation of the shape of the latent trait distribution in unidimensional IRT models was contributed by Oguzhan Ogreden, as well the associated components used within this framework (such as the interpolation-extrapolation method described by Woods, 2006). This estimation method is available through the new dentype input. mirt also now links to the dcurver package to obtain the associated computation functions in the EM algorithm

  • M2(), itemfit(), SIBTEST(), and fscores() gain an na.rm logical to remove rows of missing data

  • fscores() gains a append_response.pattern logical to indicate whether response patterns via the response.pattern input should be appended to the factor score results

  • new dentype argument added to estimation-based functions to specify the density structure of the latent traits (default is 'Gaussian'). This update breaks the previous empiricalhist logical option

  • anova() will accept a single fitted model object and return information related to AIC, BIC, log-likelihood, etc

  • Hannan–Quinn (HQ) Criterion added to anova()

Changes in mirt 1.27

  • Added multidimensional version of sequential response model (e.g., Tutz, 1990). Includes itemtype = 'sequential' for the multidimensional 2PL variant, and itemtype = 'Tutz' for the Rasch variant

  • Printing IRT parameters via coef(mod, IRTpars = TRUE) now computes the delta method for the g and u terms as well. Interpreting these is generally not recommended due to their bounded parameter nature (CIs can be outside the range [0,1]), but are included for posterity

  • createItem() gains a bytecompile flag to indicate whether the internal functions should be byte-compiled before using (default is TRUE)

  • Special GROUP location holder in mirt.model() to index the group-level hyper-parameter terms

  • key2binary() gains a score_missing flag to indicate whether missing values should be scored as 0 or left as NA

  • createItem() gains support for derivType = 'symbolic' and derivType.hss = 'symbolic' to symbolically compute the gradient/Hessian functions (template code-base contributed by Chen-Wei Liu)

  • createItem() gains a derivType.hss argument to distinguish gradient from Hessian numerical computations

  • mdirt() gains support for createItem() inputs

  • More plotting points added to default plot() and itemplot() generics to create smoother traceline functions

Bug fixes

  • fix simdata() bug for new ggum itemtype

  • fix new grouping syntax specification in mirt.model() when combining START and FIXED (reported by Garron Gianopulos)

  • fix IRTpars = TRUE input when itemtype was Rasch (reported by Benjamin Shear)

Changes in mirt 1.26.3

  • mod2values() and passing pars = 'values' now return data.frame objects without any factor variables (previously the defaults to data.frame() were used, which created factors for all categorical variables by default)

  • Add monopoly itemtype to fit unidimensional monotonic polynomial item response model for polytomous data (see Falk and Cai, 2016)

  • Add ggum itemtype to fit unidimensional/multidimensional graded unfolding model (e.g., Roberts & Laughlin, 1996). Special thanks to David King for providing the necessary C++ derivative functions and starting values

  • Square brackets can now be included in the mirt.model() syntax to indicate group-specific constraints, priors, starting/fixed values, and so on. These are all of the general form "CONSTRAIN [group1, group2] = ..." or "FIXED [group1] = ..."

  • Added delta method for several classical IRT parameterization (via coef(model, IRTpars = TRUE)) when a suitable information matrix was previously estimated

  • numDeriv dependency removed because numerical_deriv() now supports a local Richardson extrapolation type. For best accuracy, this is now used as the default throughout the package

  • createItem() and lagrange() now use Richardson extrapolation as default instead of the less accurate forward/central difference method

  • estfun() function added to extract gradient information directly from fitted objects (contributed by Lennart Schneider)

  • simdata() gains an equal.K argument to redraw data until $K$ categories are populated for a given item

  • Fix initialization of fscores() when using 'MH' plausible value imputations (reported by Charlie Iaconangelo)

  • Various other small bug fixes and performance improvements, fixes for Solaris compatibility, and run a small number of examples during R CMD check

Changes in mirt 1.25

  • mdirt() now supports latent regression covariate predictors. Associated function (e.g., fscores()) also include the latent regression information for discrete models by default

  • SIBTEST() replaced with the asymptotic sampling distribution version of CSIBTEST described by Chalmers (accepted)

  • calcNull set to FALSE by default

  • Sandwich ACOV estimate now uses the Oakes estimate in the computations rather than the intensive Louis form (which require low-level coding of the item-level Hessian terms). Added a new SE.type = 'sandwich.Louis' for the original sandwich VCOV estimate in the previous version of mirt

  • fix latent regression models with QMCEM and MCEM algorithms (reported by Seongho Bae)

  • fscores() gains a max_theta argument to apply upper/lower bounds to iterative searching algorithms (issue reported by Sebastian Born), and a start input to set the starting values as well (primarily useful in mirtCAT to reduce iterations)

  • alabama package optimizer no longer used. Replaced with generic interface from nloptr package to support numerous optimizers with greater control instead. Associated inputs (e.g., alabama_args) replaced as well

  • Export missing S4 methods for external R packages to import

Changes in mirt 1.24

  • MDIFF and MDISC no longer in normal ogive metric (1.702 scaling value removed)

  • added QMC option to residuals() for LD and LDG2 methods. Also globally set the number of QMC points to 5000 throughout the package for consistency

  • info_if_converged and logLik_if_converged added to technical list to indicate whether the information matrix and stochastic log-likelihood should be computed only when the model converges. Default is now TRUE for both

  • added 'MCEM' method for Monte Carlo EM. An associated MCEM_draws function added to the technical list as well to control the number of draws throughout the EM cycles

  • support for information matrix computations for QMCEM method added (e.g., Oakes, crossprod, Louis)

  • globally improve numerical efficiency of QMC methods, including the QMCEM estimator

  • include missing data values in itemfit() for parametric bootstrap methods to replicate missing data pattern

  • ensure that nest-logit models have at least 3 categories (reported by Seongho Bae)

  • convergence set to FALSE if any g > u is found in the 4PL model

  • in verbose console output the log-posterior is printed when priors are included in the EM (previously was only the marginal likelihood)

  • various bug fixes to SIBTEST, particularly for very small sample sizes

Changes in mirt 1.23

  • anova() LRT comparison gains a bounded logical to indicate whether a bounded parameter is being compared, as well as a mix argument to indicate the mixture of chi-squared distributions

  • MH-RM estimation optimizer argument can now be modified to BFGS, L-BFGS-B, and NR instead of the default NR1

  • a distinction between the NR optimizer in the EM and MH-RM applications is included, where the MH-RM now defaults to NR1 to indicate a single Newton-Raphson update that uses an RM filtered Hessian term

  • method = 'SEM' added to perform the stochastic EM algorithm (first two stages of the MH-RM algorithm setup).
    Alternatively, setting technical = list(NCYCLES = NA) when using the MH-RM algorithm now returns the stochastic EM results

  • added multidim_matrix option to iteminfo() to expose computation of information matrices

  • bounded parameter spaces handled better when using the NR optimizer

  • various bug fixes and performance improvements

Changes in mirt 1.22

  • SE.type = 'Oakes' set as the new default when computing standard errors via the ACOV matrix when using the EM algorithm

  • new SE.type = 'Oakes' to compute Oakes' 1999 form of the observed information matrix using central difference approximation. Applicable for all IRT models (including customized IRT types)

  • added support for gpcmIRT and rsm itemtypes for traditional generalized partial credit model and Rasch rating scale model (which may be modified for a generalized rating scale model by freeing the slope parameters)

  • SE.type = 'Fisher' now supports the inclusion of latent distribution hyper-parameters. Officially, all SE-types now provide proper hyper-parameter influence in the information matrices

  • wrapped various output objects as mirt_df, mirt_matrix, and mirt_list class to avoid the need for passing a digits argument for rounding output in the console. Now, returned objects are never rounded, which makes writing Monte Carlo simulation code safer in that rounded results will not appear in the results

  • added Stone's (2000) fit statistics and forthcoming PV-Q1 fit statistics to itemfit()

Bug fixes

  • patched underflow bug in fscores() when EAP estimates were used in extremely long (1000+ item) tests. Error now reported when this happens. Using MAP estimates in these extreme situations is essentially equivalent and now recommended

Changes in mirt 1.21

  • add information about the number of freely estimated parameters to print() generic

  • in plot(), auto.key is only disabled when facet_items = FALSE for dichotomous items. Also, adjusted ordering of plot(mod, type = 'itemscore') to reflect actual item ordering in the data

  • Stretched the theoretical bounds of the y-axis for score-based functions in plot() and itemplot() (e.g., 3PL models will now always stretch to S(theta) = 0)

  • plot(mod, type = 'score') not supports the which.items input to make expected score plots for bundles of items

  • penalized term added to EM algorithm estimation subroutines to help keep the covariance matrix of the latent trait parameters positive definite in the M-step (helps convergence properties of the optimizers, especially 'L-BFGS-B'). To turn this penalized term off use technical = list(keep_vcov_PD = FALSE)

  • added type = 'itemscore' to plot() generic to plot faceted version of the item scoring functions. Particularly useful when investigating DIF with multipleGroup()

  • better support for splines itemtype in multiple-group models

Bug fixes

  • fix problem with 'EAPsum' in fscores() when response.pattern input supplied (reported by Eva de Schipper)

  • plot(mod, type = 'rxx') now uses the latent variance in the computations (reported by Amin Mousavi)

  • fix syntax input when customized IRT models are supplied

Changes in mirt 1.20.1

  • df adjustment for the S_X2 item-fit statistic for models where the latent trait hyper-parameters have been estimated

  • itemfit() and personfit() properly detect dichotomous Rasch models which have been defined with the constrained slopes approach

  • argument 'fit_stats' now used in itemfit() to replace longer list of logicals (e.g., itemfit(mod, S_X2 = FALSE, X2 = TRUE, infit = FALSE, ...)). Now fit stats are explicitly requested through a character vector input. Default still uses the S_X2 statistic

  • when using 'lnorm' prior lower bound automatically set to 0, and with 'beta' prior the lower and upper bounds are set to [0,1]

  • mdirt() now uses optimizer = 'nlminb' by default

  • revert using default 'penalized version of the BFGS algorithm' instead of L-BFGS-B when box-constraints are used (introduced in version 1.19)

  • Neale & Miller 1997 approximation added to PLCI() (default still computes exact PL CIs)

  • type = 'score' supported for multiple group models in itemplot()

  • added poly2dich function to quickly change polytomous response data to a comparable matrix of dichotomous response data

Changes in mirt 1.19

  • a penalized version of the BFGS algorithm is now used instead of the L-BFGS-B when upper and lower bounds are included (provides more robust estimates)

  • the variances of the orthogonal factors in bfactor() can now be freely estimated. This allows modeling of designs such as the testlet response model (example included in the documentation)

  • new spline itemtype to model B-spline response functions for dichotomous models. Useful for diagnostic purposes after detecting item-misfit. Additional arguments can be passed to the spline_args list input to control the behaviour of the splines for each item. Currently limited to unidimensional models only

  • fscores() gains a plausible.type argument to select between normal approximation PVs or Metropolis-Hastings samples (suggested by Yang Liu)

  • mdirt() has been modified to support DINA, DINO, located latent class, and other diagnostic classification models. Additionally, the customTheta input required to build customized latent class patterns has been changed from the previously cumbersome
    mdirt(..., technical = list(customTheta = Theta)) to simply mdirt(..., customTheta = Theta)

  • simdata() gains a prob.list input to supply a list of matrices with probability values to be sampled from (useful when specialized response functions outside the package are required)

  • simdata() supports 'lca' itemtypes for latent class model generation

  • improved M2 accuracy when latent trait variances are estimated

  • corrected behaviour of M2() when linear constraints are applied (M2 test was previously too conservative when constraints were used). This affects single as well as multiple-group models (reported by Rudolf Debelak)

  • add plausible values for latent class and related models estimated from mdirt()


  • multipleGroup() throws proper error when vertical scaling is not identified correctly due to NAs

  • S-X2 itemfit statistic fix when very rare expected categories appear (reported by Seongho Bae)

Changes in mirt 1.18

  • mdirt() function now includes explicit parameters for the latent class intercepts (in log-form). This implies that correct standard errors can be computed using various methods (e.g., SEM, Richardson, etc)

  • new customGroup() function to define hyper-parameter objects for the latent trait distributions (generally assumed to be Gaussian with a mean and covariance structure)

  • new boot.LR() function to perform a parametric bootstrap likelihood-ratio test between nested models. Useful when testing nested models which contain bounded parameters (e.g., testing a 3PL versus a 2PL model)

  • adjust the lagrange() function to use the full information matrix (was previously only a quasi-lagrange approximation)

  • greatly improved speed in simdata(), consequently changes the default seed


  • fix crash error in mirtmirt() for multidimensional models with lr.random effects (reported by Diah Wihardini)

  • expbeta prior starting values fix by setting to the mean of the prior rather than the mode (reported by Insu Paek)

Changes in mirt 1.17.1

  • itemfit() function reworked so that all statistics have their own input flag (e.g., Zh = TRUE, infit = TRUE, etc). Additionally, only S-X2 is computed by default and X2/G2 (and the associated graphics and tables) are computed using 10 fixed bins

  • added empirical.table argument to return tables of expected/observed values for X2 and G2

  • group.bins and argument added to itemfit() to control the size of the bins and the central tendancy function for X2 and G2 computations

  • 'expbeta' option added to implement a beta prior specifically for the g and u parameters which internally have been transformed to logits (performes the back transformation before computing the values)

  • check whether multiple-group models contain enough data to estimate parameters uniquely when no constraints are applied

  • set the starting values the same when using parprior list or mirt.model() syntax (reported by Insu Paek)

  • empirical_ES() function added for effect size estimates in DIF/DBF/DTF analyses (contributed by Adam Meade)


  • standardized loadings not correct when factor correlations included in confirmatory models (reported by Seongho Bae)

  • MDISC and MDIFF values were missing the 1.702 multiplicitive constant (reported by Yi-Ling Cheng)

  • fix information trace-lines in multiple-group plots (reported by Conal Monaghan)

  • suppress standard errors in exploratory models when rotate != 'none' (suggested by Hao Wu)

  • sequential schemes in DIF() generated the wrong results (reported by Adam Meade)

  • M2() was not properly accounting for latent variance terms (reported by Ismail Cuhadar)

Changes in mirt 1.16

  • enable lr.random input to mixedmirt() for multilevel-IRT models which are not from the Rasch family

  • add common vcov() and logLik() methods

  • latent regression EM models now have standard error computation supporte with the 'complete', 'forward', 'central', and 'Richardson' methods

  • new areainfo() function to compute the area under information curves within specified ranges (suggested by Conal Monaghan)

  • method = 'BL' supported for multiple-group models. As well, SE.type = 'numerical' included to return the observed-data ACOV matrix from the call to optim() (can only be used when the BL method is selected)

  • new SE.type = 'FMHRM' to compute information matrix based on a fixed number of MHRM draws, and an associated technical = list(MHRM_SE_draws) argument has been added to control the number of draws

  • added lagrange (i.e., score) test function for testing whether parameters should be freed in single and multiple group models estimated with the EM algorithm

  • numerical_deriv function made available for simple numerical derivatives, which may be useful when defining fast custom itemtype derivative terms

  • SE.type used to compute the ACOV matrix gained three numerical estimates for the forward difference ('forward'), central difference ('central'), and Richardson extropolation ('Richardson')


  • SE methods based on the Louis (1982) computations no longer contain NA placeholders for the latent trait hyper-parameters

Changes in mirt 1.15


  • added SIBTEST and crossed-SIBTEST procedures with the new function SIBTEST()

  • added empirical_plot function for building empirical plots (with potential smoothing) when conditioning on the total score

  • more low-level elements included in extract.mirt() function

  • added grsmIRT itemtype for classical graded rating scale form (contributed by KwonHyun Kim)

  • added missing analytic Hessian terms when gpcm_mats are used (contributed by Carl Falk)


  • fixed row-removal bug when using technical = list(removeEmptyRows = TRUE) (reported by Aaron Kaat)

Changes in mirt 1.14


  • the structure of the output objects now contains considerably fewer S4 slots, and instead are organized into more structured list elements such as Data, Model, Fit, and so on. Additionally, the information matrix has slot has been removed in favour of providing the asymptotic covariance matrix (a.k.a., the inverse of the information matrix)


  • added extract.mirt() function to allow more convenient extracting of internal elements

  • crossprod SE.type now incorporates latent variable information (replaces NA placeholders)

  • changed the default full.scores = FALSE argument to TRUE in fscores()

  • added profile argument to plot() for mdirt() objects so that profile plots can be generated

  • converge_info option added to fscores() to return convergence information

  • add removeEmptyRows option to technical list


  • return a vector of NAs when WLE estimation has a Fisher information matrix with a determinant of 0 (reported by Christopher Gess)

  • fix df in multiple-group models with crossed between/within constrains (reported by Leah Feuerstahler)

  • compute residuals when responses are sparse, and return NaN when residual could not be computed (reported by Aaron Kaat)

Changes in mirt 1.13

  • adjust plausible values format for multiple group objects

  • simdata() gains a model input to impute data from pre-organized models (useful in conjunction with mirtCAT or to generate datasets from already converged models). Also gains a mins argument to specify what the lowest category should be for each item if model is not supplied (default is 0)

  • number of SEMCYCLES increased from 50 to 100 in the MH-RM algorithm, and RM gain rate changed from c(.15, .65) to c(.1, .75)

  • further improve item fit statistics when using imputations

  • facet plots now try to keep the items in their respective order

  • panel theme for lattice plots changed from default to a lighter blue colour, and legend now automatically placed on the right hand side rather than the top


  • fix for Q3 computations (noticed by Katherine Castellano)

Changes in mirt 1.10

  • when using prior distributions, starting values now automatically set equal to the mode of the prior distribution, and appropriate lower and upper parameter bounds are supplied

  • added NEXPLORE term to mirt.model() to specify exploratory models via the syntax

  • add itemGAM() function to provide a non-linear smoother for better understanding mis-functioning items (and without loosing established precision by reverting to purely non-parametric IRT methods)

  • category scores are now automatically recoded to have spaces of 1, and a message is printed if/when this occurs

  • added MDISC() and MDIFF() functions

  • the inclusion of prior parameter distributions will now report the log-posterior rather than the log-likelihood. Functions such as anova() will also report Bayesian criteria rather than the previous likelihood-based model comparison statistics

  • impute argument in itemfit() and M2() now use plausible values instead of point estimates

  • START syntax element in mirt.model() now supports multiple parameters, and FIXED argument added to declare parameters as 'fixed' at their staring values

  • added LBOUND and UBOUND syntax support in mirt.model()

  • report proper lower and upper bounds in starting values data frame and from mod2values()

  • invariance argument to bfactor() now automatically indexes the second-tier factors to make multiple-group testing with bfactor() easier

  • remove rotate and Target arguments from model objects, and pass these only through axillary functions such as summary(), fscores(), etc

  • model based arguments now can be strings, which are passed to mirt.model(). This is now the preferred method for defining models syntactically, though the previous methods will still work

  • integration range (theta_lim) globally set to c(-6, 6), and number of default quadrature nodes have systematically increased in parameter estimation functions. This will slightly change some numerical results, but provides more consistence throughout the package

  • add theta_lim arguments to various functions

  • better control of QMC grid, and more effective usage for higher dimensions

  • internal code organization now makes it easier to add user defined itemtypes (which can be natively added into the package, if requested)


  • fix conservative imputation standard errors in itemfit() and M2() (reported by Irshad Mujawar)

  • fixed plausible value draws for multidimensional latent regression models (reported by Tongyun Li)

  • don't allow crossprod, Louis, or sandwich information matrices when using custom item types (reported by Charlie Rutgers)

Changes in mirt 1.9

  • when using coef(mod, printSE=TRUE) the g and u parameters are relabeled to logit(g) and logit(u) to represent the internal labels

  • added various facet plots for three dimensional models to plot() generic

  • support optimizer = 'nlminb', and pass optimizer control arguments to a contol list

  • added fixef() function to extract expected values implied by the fixed effect parameters in latent regression models

  • added gpcm_mats argument to estimation functions for specifying a customize scoring pattern for multidimensional generalized partial credit models

  • added custom_theta input to fscores() for including customized integration grids

  • add a suppress argument to residuals() and M2() to suppress local dependence values less than this specific value

  • print a message in DIF() and DTF() when hyper-parameters are not freely estimated in focal groups

  • constraits for hetorogenous item names added to mirt.model() syntax

  • WLE support for multidimensional models added

  • added 'SEcontour' argument to plot() generic

  • use NA's in fscores() when response patterns contain all NA responses (suggested by Tomasz Zoltak)


  • S-X2 in itemfit() now returns appropriate values for multiple-group models

  • multidimensional plausible value imputation fix (reported by KK Sasa)

  • plot(..., type = 'infotrace') for multiple group objects fixed (reported by Danilo Pereira)

Changes in mirt 1.8

  • fscores() nows accepts method = "plausible" to draw a single plausible value set

  • plot() default type is now score, and will accept rotation arguments for exploratory models (default rotation is 'none')

  • imputeMissing() supports a list of plausible values to generate multiple complete datasets

  • new custom_den input to fscores() to use custom prior density functions for Bayesian estimates

  • more optimized version of the 'WLE' estimator in fscores()

  • empirical reliability added when method = 'EAPsum' in fscores()

  • new START argument in mirt.model() for specifying simple starting values one parameter at a time


  • fix carryover print-out error in summary() when confirmatory models were estimated

  • bound contraints not were not included for group hyper-parameters (reported by KK Sasa)

Changes in mirt 1.7


  • improved estimation efficiency when using MH-RM algorithm. As a result, the default seed was changed, therefore results from previous versions will be slightly different

  • objects of class 'ExploratoryClass' and 'ConfirmatoryClass' have been merged into a single class 'SingleGroupClass' with an exploratory logical slot

  • the technical = list(SEtol) criteria for approximating the information matrix was lowered to 1e-4 in mixedmirt() to provide better standard error estiamtes


  • boot.mirt now uses the optimizer used to estimate the model (default previously was EM)

  • mixedmirt now supports interaction effects in random intercepts, including cross-level interactions

  • added averageMI() function to compute multiple imputation averages for the plausible values methodology using Rubin's 1987 method

  • plausible value imputation now available in fscores() using the new plausible.draws numeric input

  • add return.models argument to DIF() to return estimated models with free/constrained parameters

  • latent regression models added to mixedmirt() for non-Rasch models using the new lr.formula input

  • mirt.model() syntax can now define within individual item equality constraints by using more than 1 parameter specification name in the syntax

  • latent regression models added to mirt() function by using the new covdata and formula inputs

  • added confidence envelope plots to PLCI.mirt, and throw warnings when intervals could not be located

  • coef() now accepts a simplify logical, indicating whether the items should be collapsed to a matrix and returned as a list of length 2 (suggested by Michael Friendly)


  • bias correction in variance estimates mixedmirt when random effects are included (reported by KK Sasa)

  • fix missing data imputation bug in itemfit() (reported by KK Sasa)

  • M2 statistic for bifactor/two-tier models was overly conservative

  • better checks for numerical underflow issues

  • use triangle 0's for identifying exploratory IFA models. As such, standard errors/condition numbers for exploratory models can be estimated again

Changes in mirt 1.6.1


  • sirt package added to suggests list. Special thanks to Alexander Robitzsch (author of sirt) for developing useful wrapper functions for mirt such as mirt.wrapper.coef(), tam2mirt(), and
    lavaan2mirt(). As well, many examples in sirt demonstrate the possibility of estimating specialized IRT models with mirt, such as the: Ramsay quotient, latent class, mixed Rasch, located latent class, probabilistic Guttman, nonparametric, discrete graded membership, and multidimensional IRT discrete traits, DINA, and Rasch copula models.

  • exploratory IRT models are no longer rotated by default in coef(), and now requires an explicit rotate argument

  • computation of S_X2 statistic in itemfit now much more stable for polytomous item types

  • support for the plink package now unofficially dropped because it was removed from CRAN

  • data inputs are now required to have category spacing codings exactly equal to 1 (e.g., [0, 1, 2, ...]; patterns such as [0, 2, 3] which are implicitly missing spaces are now invalid)


  • mdirt function added to model discrete latent variables such as latent class analysis for dichotomous and polytomous items. Can be used to model several other discrete IRT models as well, such as the located latent class model, multidimensional IRT with discrete traits, DINA models, etc. See the examples and documentation for details

  • axillary support for DiscreteClass objects added to itemfit(), M2(), fscores(), wald(), and boot.mirt()

  • the S-X2 statistic available in itemfit() has been generalized to include multidimensional models

  • the method 'QMCEM' has been added for quasi-Monte Carlo integration in mirt() and multipleGroup() for estimating higher dimensional models with greater accuracy (suggested by Alexander Robitzsch). Several axillary function such as fscores(), itemfit(), and M2() also now contain an QMC argument (or will accept one through the ... argument) to use the same integration scheme for better accuracy in higher dimensional models

  • nonlinear parameter constraints for EM estimation can be specified by using the Rsolnp and alabama packages by passing optimizer = 'solnp' and optimizer = 'alabama', as well as the relevant package arguments through the solnp_ags and alabama_ags list inputs

  • itemnames argument added to mirt.model() to allow model specifications using raw item names rather than location indicators

  • accelerate argument changed from logical to character vector, now allowing three potential options: 'Ramsay' (default), 'squarem', and 'none' for modifying the EM acceleration approach


  • fixed bug in bfactor() starting values when NAs were specified in the model argument

  • adjust overly optimistic termination criteria in EM algorithm

Changes in mirt 1.5


  • for efficiency, the Hessian is no longer computed in fscores() unless it is required in the returned object

  • estimation with method = 'MHRM' now requires and explicitly SE=TRUE call to compute the information matrix. The matrix is now computed using the ML estimates rather than approximated sequentially after each iteration (very unstable), and therefore a separate stage is performed. This provides much better accuracy in the computations


  • new function to extract a single group object from an objects previously returned by multipleGroup()

  • return the SRMSR statistic in M2() along with the residual matrix (suggested by Dave Flora)

  • accept Etable default input in customPriorFun (suggested by Alexander Robitzsch)

  • vignette files for the package examples are now hosted on Github and can be accessed by following the link mentioned in the vignette location in the index or ?mirt help file

  • E-step is now computed in parallel (if available) following a mirtCluster() definition

  • run no M-step optimizations by passing TOL = NaN. Useful to have the model converge instantly with all parameters exactly equal to the starting values

  • confidence envelope plots in itemplot() generate shaded regions instead of dotted lines, and confidence interval plots added to plot() generic through the MI input

  • passes to fscores() slightly more optimized for upcoming mirtCAT package release

  • method = 'EAPsum' argument to fscores() support for multidimensional models


  • fix forcing all SEs MHRM information matrix computations to be positive

  • imputeMissing() crash fix for multiple-group models

  • fix divide-by-0 bug in the E-step when number of items is large

  • fix crash in EM estimation with SE.type = 'MHRM'

Changes in mirt 1.4


  • calculating the information matrix for exploratory item factor analysis models has been disabled since the rotational indeterminacy of the model results in improper parameter variation

  • changed default theta_lim to c(-6,6) and number of quadrature defaults increased as well

  • @Data slot added for organizing data based arguments. Removed several data slots from estimated objects as a consequence

  • removed 'Freq' column when passing a response.pattern argument to fscores()

  • increase number of Mstep iterations proportionally in quasi-Newton algorithms as the estimation approaches the ML location

  • 'rsm' itemtype removed for now until optimized version is implemented


  • link to mirt vignettes on Github have been registered with the knitr package and are now available through the package index

  • optimizer argument added to estimation function to switch the default optimizer. Multiple optimizers are now available, including the BFGS (EM default), L-BFGS-B, Newton-Raphson, Nelder-Mead, and SANN

  • new survey.weights argument can be passed to parameter estimation functions (i.e., mirt()) to apply so-called stratification/survey-weights during estimation

  • returnList argument added to simdata() to return a list containing the S4 item objects, Theta matrix, and simulated data

  • support custom item type fscores() computations when response.pattern is passed instead of the original data

  • impute option for itemfit() and M2() to estimate statistics via plausible imputation when missing data are present

  • multidimensional ideal-point models added for dichotomous items

  • M2* statistic added for polytomous item types

  • Bock and Lieberman ('BL') method argument added (not recommend for serious use)


  • large bias correction in information matrix and standard errors for models that contain equality constraints (standard errors were too high)

  • drop dimensions fix for nested logit models

Changes in mirt 1.3


  • default SE.type changed to crossprod since it is better at detecting when models are not identified compared to SEM, and is generally much cheaper to compute for larger models

  • M-step optimizer now automatically selected to be 'BFGS' if there are no bounded parameters, and 'L-BFGS-B' otherwise. Some models will have notably different parameter estimates because of this, but should have nearly identical model log-likelihoods

  • better shiny UI which adapts to the itemtype specifically, and allows for classical parameter inputs (special thanks to Jonathan Lehrfeld for providing code that inspired both these changes)

  • scores.only option now set to TRUE in fscores()

  • type = 'score' for plot generics no longer adjusts the categories for expected test scores

  • M-step optimizer in EM now deters out-of-order graded response model intercepts (was a problem if the startvalues were too far from the ML estimate in graded models)


  • return.acov logical added to fscores() to return a list of matrices containing the ACOV theta values used to compute the SEs (suggested by Shiyang Su)

  • printCI logical option to summary() to print confidence intervals for standardized loadings

  • new expected.test() function, which is an extension of expected.item() but for the whole test

  • mirt.model() syntax supports multiple * combinations in COV = for more easily specifying covariation blocks between factors. Also allows variances to be freed by specifying the same factor name, e.g., F*F

  • full.scores.SE logical option for fscores() to return standard errors for each respondent

  • multiple imputation (MI) option in fscores(), useful for obtaining less biased factor score estimates when model parameter variability is large (usually due to smaller sample size)

  • group-level (i.e., means/covariances) equality constrains are now available for the EM algorithm

  • theta_lim input to plot(), itemplot(), and fscores() for modifying range of latent values evaluated


  • personfit() crash for multipleGroup objects since itemtype slot was not filled (reported by Michael Hunter)

  • fix crash in two-tier models when correlations are estimated (reported by David Wu)

  • R 3.1.0 appears to evaluate List objects differently at the c level causing strange behaviour, therefore slower R versions of some internal function (such as mirt:::reloadPars()) will be used until a patch is formed

  • behaviour of mvtnorm::dmvnorm changed as of version 0.9-9999, causing widely different convergence results. Similar versions of older mvtnorm functions are now implemented instead

Changes in mirt 1.2.1


  • fitIndices() replaced with M2() function, and currently limited to only dichotomous items of class 'dich'

  • bfactor() default SE.type set to 'crossprod' rather than 'SEM'

  • generalized partial credit models now display fixed scoring coefs

  • TOL convergence criteria moved outside of the technical input to its own argument

  • restype argument to residuals() changed to type to be more consistent with the package

  • removed fitted() since residuals(model, type = 'exp') gives essentially the same output

  • mixedmirt has SE set to TRUE by default to help construct a more accurate information matrix

  • if not specified, S-EM TOL dropped to 1e-6 in the EM, and SEtol = .001 for each parameter to better approximate the information matrix


  • two new SE.type inputs: 'Louis' and 'sandwich' for computing Louis' 1982 computation of the observed information matrix, and for the sandwich estimate of the covariance matrix

  • logical option for coef() to convert list to a row-stacked data.frame

  • type = 'scorecontour' added to plot() for a contour plot with the expected total scores

  • type = 'infotrace' added to itemplot() to plot trace lines and information on the same plot, and type = 'tracecontour' for a contour plot using trace lines (suggested by Armi Lantano)

  • mirt.model() support for multi-line inputs

  • new type = 'LDG2' input for residuals() to compute local dependence stat based on G2 instead of X2, and type = 'Q3' added as well

  • S-EM computation of the information matrix support for latent parameters, which previously was only effective when estimation item-level parameters. A technical option has also been added to force the information matrix to be symmetric (default is set to TRUE for better numerical stability)

  • new empirical.CI argument in itemfit() used when plotting confidence intervals for dichotomous items (suggested by Okan Bulut)

  • printSE argument can now be passed to coef() for printing the standard errors instead of confidence intervals. As a consequence, rawug is automatically set to TRUE (suggested by Olivia Bertelli)

  • second-order test and condition number added to estimated objects when an information matrix is computed

  • tables argument can be passed to residuals() to return all observed and expected tables used in computing the LD statistics


  • using scores.only = TRUE for multipleGroup objects returns the correct person ordering (reported by Mateusz Zoltak)

  • read.mirt() crash fix for multiple group analyses objects (reported by Felix Hansen)

  • updated math for SE.type = 'crossprod'

Changes in mirt 1.1


  • facet_items argument added to plot() to control whether separate plots should be constructed for each item or to merge them onto a single plot

  • three dimensional models supported in itemplot() for types trace, score, info, and SE

  • new DIF() function to quicky calculate common differential item functioning routines, similar to how IRTLRDIF worked. Supports likelihood ratio testings as well as the Wald approach, and includes forward and backword sequential DIF searching methods

  • added a shiny = TRUE option to itemplot() to run the interactive shiny applet. Useful for instructive purposes, as well as understanding how the internal parameters of mirt behave

  • type = 'trace' and type = 'infotrace' support added to plot generic for multiple group objects

  • fscores(..., method = 'EAPsum') returns observed and expected values, along with general fit statistics that are printed to the console and returned as a 'fit' attribute

  • removed multinomial constant in log-likelihood since it has no influence on nested model comparisons

  • SE.type = 'crossprod' and Fisher added for computing the parameter information matrix based on the variance of the Fisher scoring vector and complete Fisher information matrix, respectively

  • customPriorFun input to technical list now available for utilizing user defined prior distribution functions in the EM algorithm

  • empirical histogram estimation now available in mirt() and multipleGroup() for unidimensional models. Additional plot type = 'empiricalhist' also added to the plot() generic

  • re-implement read.mirt() with better consistency checking between the plink package


  • starting values for multipleGroup() now returns proper estimated parameter information from the invariance input argument

  • remove as.integer() in MultipleGroup df slot

  • pass proper item type when using custom pattern calles in fscores()

  • return proper object in personfit when gpcm models used

Changes in mirt 1.0


  • GenRandomPars logical argument now supported in the technical = list() input. This will generate random starting values for freely estimated parameters, and can be helpful to determine if obtained solutions are local minimums

  • seperate free_var and free_cov invariance options available in multipleGroup

  • new CONSTRAIN and CONSTRAINB arguments in mirt.model() syntax for specifying equality constraints explicitly for parameters accross items and groups. Also the PRIOR = ... specification was brought back and uses a similar format as the new CONSTRAIN options

  • plot(..., type = 'trace') now supports polytomous and dichotomous tracelines, and type = 'infotrace' has a better y-axis range

  • removed the '1PL' itemtype since the name was too ambiguous. Still possible to obtain however by applying slope constraints to the 2PL/graded response models

  • plot() contains a which.items argument to specify which items to plot in aggregate type, such as 'infotrace' and 'trace'

  • fitIndicies() will return CFI.M2 and TLI.M2 if the argument calcNull = TRUE is passed. CFI stats also normed to fall between 0 and 1

  • data.frame returned from mod2values() and pars = 'values' now contains a column indicating the internal item class

  • use ginv() from MASS package to improve accuracy in fitIndices() calculation of M2


  • fix error thrown in PLCI.mirt when parameter value is equal to the bound

  • fix the global df values, and restrict G2 statistic when tables are too sparse

Changes in mirt 0.9.0


  • PLCI.mirt() function added for computing profiled likelihood standard errors. Currently only applicable to unidimensional models

  • prior distributions returned in the pars = 'values' data.frame along with the input parameters, and can be edited and returned as well

  • full.scores option for residuals() to compute residuals for each row in the original data

  • bfactor() can include an additional model argument for modeling two-tier structures introduced by Cai (2010), and now supports a 'group' input for multiple group analyses

  • added a general Ramsey (1975) acceleration to EM estimation by default. Can be disable with accelerate = FALSE (and is done so automatically when estimating SEM standard errors)

  • renamed response.vector to response.pattern in fscores(), and now supports matrix input for computing factor scores on larger data sets (suggested by Felix Hansen)

  • logical added to iteminfo() to return either total item information or information from each category

  • mirt.model() supports the so-called Q-matrix input format, along with a matrix input for the covariance terms

  • MH-RM algorithm now accessible by passing mirt(..., method = 'MHRM'), and confmirt() function removed completely. confmirt.model() also renamed to mirt.model()

  • support for polynomial and interaction terms in EM estimation

  • lognormal priors may now be passed to parprior

  • iterative computations in fscores() can now be run in parallel automatically following a mirtCluster() definition

  • mirtCluster() function added to make utilizing parallel cores more convenient. Globally removed the cl argument for multi-core objects

  • updated documentation for data sets by adding relevant examples, and added Bock1997 data set for replicating table 3 in van der Linden, W. J. & Hambleton, R. K. (1997) Handbook of modern item response theory

  • general speed improvements in all functions


  • WLE estimation fixed and now estimates extreme response patterns

  • exploratory starting values no longer crash in datasets with a huge number of NAs, which caused standard deviations to be zero

  • math fix for beta priors

Changes in mirt 0.8.0


  • support for random effect predictors now available in mixedmirt(), along with a randef() function for computing MAP predictions for the random parameters

  • EAPsum support in fscores() for mixed item types

  • for consistency with current IRT software (rather than TESTFACT and POLYFACT), the scaling constant has been set to D = 1 and fixed at this value

  • nominal.highlow option added to specify which categories are the highest and lowest in nominal models. Often provide better numerical stability when utilized. Default is still to use the highest and lowest categories

  • increase number of draws in the Monte Carlo calculation of the log-likelihood from 3000 to 5000

  • when itemtype all equal 'Rasch' or 'rsm' models the latent variance parameter(s) are automatically freed and estimated

  • mixedmirt() more supportive of user defined R formulas, and now includes an internal 'items' argument to create the item design matrix used to estimate the intercepts. More closely mirrors the results from lme4 for Rasch models as well (special thanks to Kevin Joldersma for testing and debugging)

  • drop.zeros option added to extract.item and itemplot to reduce dimensionality of factor structures that contain slopes equal to zero

  • EM tolerance (TOL argument) default dropped to .0001 (originally .001)

  • type = 'score' and type = 'infoSE' added to plot() generic for expected total score and joint test standard error/information

  • custom latent mean and covariance matrix can be passed to fscores() for EAP, MAP, and EAPsum methods. Also applies to personfit() and itemfit() diagnostics

  • scores.only option to fscores() for returning just the estimated factor scores

  • bfactor can include NA values in the model to omit the estimation of specific factors for the corresponding item


  • limiting values in z.outfit and z.infit statistics for small sample sizes (fix suggested by Mike Linacre)

  • missing data gradient bug fix in MH-RM for dichotomous item models

  • global df fix for multidimensional confirmatory models

  • SEM information matrix computed with more accuracy (M-step was not identical to original EM), and fixed when equality constrains are imposed

Changes in mirt 0.7.0


  • new '#PLNRM' models to fit Suh & Bolt (2010) nested logistic models

  • 'large' option added to estimation functions. Useful when the datasets being analysed are very large and organizing the data becomes a computationally burdensome task that should be avoided when fitting new models. Also, overall faster handling of datasets

  • plot(), fitted(), and residuals() generic support added for MultipleGroup objects

  • CFI and X2 model statistics added, and output now includes fit stats w.r.t. both G2 and X2

  • z stats added for itemfit/personfit infit and outfit statistics

  • supplemented EM ('SEM') added for calculating information matrix from EM history. By default the TOL value is dropped to help make the EM iterations longer and more stable. Supports parallel computing

  • added return empirical reliability (returnER) option to fscores()

  • plot() supports individual item information trace lines on the same graph (dichotomous items only) with the option type = 'infotrace'

  • createItem() function available for defining item types that can be passed to estimation functions. This can be used to model items not available in the package (or anywhere for that matter) with the EM or MHRM. Derivatives are computed numerically by default using the numDeriv package for defining item types on the fly

  • Mstep in EM moved to quasi-Newton instead of my home grown MV Newton-Raphson approach. Gives more stability during estimation when the Hessian is ill-conditioned, and will provide an easier front-end for defining user rolled IRT models


  • small bias fix in Hessian and gradients in mirt() implementation causing the likelihood to not always be increasing near maximum

  • fix input to itemplot() when object is a list of model objects

  • fixed implementation of infit and outfit Rasch statistics

  • order of nominal category intercepts were sometimes backwards. Fixed now

  • S_X2 collapsed cells too much and caused negative df

  • response.vector input now supports NA inputs (reported by Neil Rubens)

Changes in mirt 0.6.0


  • S-X2 statistic computed automatically for unidimensional models via itemfit()

  • EAP for sum-scores added to fscores() with method = 'EAPsum'. Works with full.scores option as well

  • improve speed of estimation in multipleGroup() when latent means/variances are estimated

  • multipleGroup(invariance = '') can include item names to specify which items are to be considered invariant across groups. Useful for anchoring and DIF testing

  • type = 'trace' option added to plot() to display all item trace lines on a single graph (dichotomous items only)

  • default estimation method in multipleGroup() switched to 'EM'

  • boot.mirt() function added for computing bootstrapped standard errors with via the boot package (which supports parallel computing as well), as well as a new option SE.type = '' for choosing between Bock and Lieberman or MHRM type information matrix computations

  • indexing items in itemplot, itemfit, and extract.item can be called using either a number or the original item name

  • added probtrace() function for front end users to generate probability trace functions from models

  • plotting item tracelines with only two categories now omits the lowest category (as is more common)

  • parallel option passed to calcLogLik to compute Monte Carlo log-likelihood more quickly. Can also be passed down the call stack from confmirt, multipleGroup, and mixedmirt

  • Confidence envelopes option added to itemplot() for trace lines and information plots

  • lbound and ubound parameter bounds are now available to the user for restricting the parameter estimation space

  • mod2values() function added to convert an estimated mirt model into the appropriate data.frame used to determine parameter estimation characteristics (starting values, group names, etc)

  • added imputeMissing() function to impute missing values given an estimated mirt model. Useful for checking item and person fit diagnostics and obtaining overall model fit statistics

  • allow for Rasch itemtype in multidimensional confirmatory models

  • oblimin the new default exploratory rotation (suggested by Dave Flora)

  • more flexible calculation of M2 statistic in fitIndicies(), with user prompt option if the internal variables grow too large and cause time/RAM problems


  • read.mirt() fixed when objects contain standard errors (didn't properly line up before)

  • mixedmirt() fix when COV argument supplied (reported by Aaron Kaat)

  • fix for multipleGroup when independent groups don't contain all potential response options (reported by Scot McNary)

  • prevent only using 'free_means' and 'free_varcov' in multipleGroup since this would not be identified without further constraints (reported by Ken Beath)

Changes in mirt 0.5.0

  • all dichotomous, graded rating scale, (generalized) partial credit, rating scale, and nominal models have been better optimized

  • wald() will now support information matrices that contain constrained parameters

  • confmirt.model() can accept a string inputs, which may be useful for knitr/sweave documents since the scan() function tends to hang

  • multipleGroup() now has the logical options bfactor = TRUE to use the dimensional reduction algorithm for when the factor pattern is structured like a bifactor model

  • new fitIndices() function added to compute additional model fit statistics such as M2

  • testinfo() function added for test information

  • lower bound parameters under more stringent control during estimation and are bounded to never be higher than .6

  • infit and outfit stats in itemfit() now work for Rasch partial credit and rating scale models

  • Rasch rating scale models can now be estimated with potential rsm.blocks (same as grsm model). "Generalized" rating scale models can also be estimated, though this requires manipulating the starting values directly

  • added AICc and sample size adjusted BIC (SABIC) information statistics

  • new mixedmirt() function for estimating IRT models with person and item level (e.g., LLTM) covariates. Currently only supports fixed effect predictors, but random effect predictors are being developed

  • more structured output when using the anova() generic

Changes in mirt 0.4.2

  • item probability functions now only permit permissible values, and models may converge even when the log-likelihood decreases during estimation. In the EM if the model does not have a strictly increasing log-likelihood then a warning message will be printed

  • infit and outfit statistics are now only applicable to Rasch models (as they should be), and in itemfit/personfit() a 'method' argument has been added to specify which factor score estimates should be used

  • read.mirt() re-added into the package to allow for translating estimated models into a format usable by the plink package

  • test standard error added to plot() generic using type = 'SE', and expected score plot added to itemplot() using type = 'score'

  • weighted likelihood estimation (WLE) factor scores now available (without standard errors)

  • removed the allpars option to coef() generics and only return a named list with the (possibly rotated) item and group coefficients

  • information functions slightly positively biased due to logistic constant adjustment, fixed for all models. Also, information functions are now available for almost all item response models (mcm items missing)

  • constant (D) used in estimating logistic functions can now be modified (default is still 1.702)

  • partcomp models recently broken, fixed now

  • more than one parameter can now be passed to parprior to make specifying identical priors more convenient

Changes in mirt 0.4.1

  • relative efficiency plots added to itemplot(). Works directly for multipleGroup analysis and for comparing different item types (e.g., 1PL vs 2PL) can be wrapped into a named list

  • infit and outfit statistics added to personfit() and itemfit()

  • empirical reliability printed for each dimension when fscores(..., fulldata = FALSE) called

  • better system to specify fixed/free parameters and starting values using pars = 'values'. Should allow for much better simulation based work

  • graded model type rating scale added (Muraki, 1990) with optional estimation 'blocks'. Use itemtype = 'grsm', and the grsm.block option

  • for multipleGroup(), optional input added to change the current freely estimated parameters to values of a previously computed model. This will save needless iterations in the EM and MHRM since these parameters should be much closer to the new ML estimates

  • itemplot() supports multipleGroup objects now

  • analytical derivatives much more stable, although some are not yet optimized

  • estimation bug fix in bfactor(), and slight bias fix in mirt() estimation (introduced in version 0.4.0 when multipleGroup() added)

  • updated documentation and beamer slide show included for some background on MIRT and some of the packages capabilities

  • labels added to coef() when standard errors not computed. Also allpars = TRUE is now the default

  • kernel estimation moved entirely to one method. Much easier to maintain and guarantees consistency across methods (i.e., no more quasi-Newton algorithms used)

Changes in mirt 0.4.0

  • Added itemfit() and personfit() functions for uni and multidimensional models. Within itemfit empirical response curves can also be plotted for unidimensional models

  • Wrapped itemplot() and fscores() into S3 function for better documentation. Also response curve now are all contained in individual plots

  • Added free.start list option for all estimation functions. Allows a quicker way to specify free and fixed parameters

  • Added iteminfo() and extract.item() to calculate the item information and extract desired items

  • Multiple group estimation available with the multipleGroup() function. Uses the EM and MHRM as the estimation engines. The MHRM seems to be faster at two factors+ though and naturally should be more accurate, therefore it is set as the default

  • wald() function added for testing linear constraints. Useful in situations for testing sets of parameters rather than estimating a new model for a likelihood ratio test

  • Methods that use the MHRM can now estimate the nominal, gpcm, mcm, and 4PL models

  • fscores computable for multiple group objects and in general play nicer with missing data (reported by Judith Conijn). Also, using the options full.scores = TRUE has been optimized with Rcpp

  • Oblique rotation bug fix for fscores and coef (reported by Pedro A. Barbetta)

  • Added the item probability equations in the ?mirt documentation for reference

  • General bug fixes as usual that were spawned from all the added features. Overall, stay frosty.

Changes in mirt 0.3.1

  • Individual classes now correspond to the type of methods: ExploratoryClass, ConfirmatoryClass, and MultipleGroupClass

  • plot and itemplot now works for confmirt objects

  • mirt can now make use of confmirt.model specified objects and hence be confirmatory as well

  • stochastic estimation of factor scores removed entirely, now only quadrature based methods for all objects. Also, bfactor returned objects now will estimate all the factors scores instead of just the general dimension

  • Standard errors for mirt now automatically calculated (borrowed from running a tweaked MHRM run)

Changes in mirt 0.3.0

  • radically changed the underlying mechanisms for the estimation functions and in doing so have decided that polymirt() was redundant and could be replaced completely by calling confmirt(data, number_of_factors). The reason for the change was to facilitate a wider range or MIRT models and to allow for easier extensions to future multiple group analysis and multilevel modelling

  • new univariate and MV models are available, including the 1-4 parameter logistic generalized partial credit, nominal, and multiple choice models. These are called by specifying a character vector called 'itemtype' of length nitems with the options '2PL','3PL','4PL','graded','gpcm', 'nominal', or 'mcm'; use 'PC2PL' and 'PC3PL' for partially-compensatory items. If itemtype = '1PL' or 'Rasch', then the 1-parameter logistic/1-parameter ordinal or Rasch/partial credit models are estimated for all the data. The default assumes that items are either '2PL' or 'graded', as before.

  • flexible user defined linear equality restrictions may be imposed on all estimation functions, so too can prior parameter distributions, start values, and choice of which parameters to estimate. These all follow these general 2 steps:

    1. Call the function as you would normally would but use, for example, mirt(data, 1, startvalues = 'index') to return the start values as they are indexed
    2. Edit them as you please (without changing the structure), then input them back into the function as mirt(data, 1, startvalues = editedstartvalues).

    This is true for the parprior (MAP priors), constrain (linear equality constraints), and freepars (parameters freely estimated), each with their own little quirk. All inputs are lists with named parameters for easy identification and manipulation. Note that this means that the partial credit model and Rasch models may be calculated as well by modifying either the start values and constraints accordingly (e.g., constrain all slopes to be equal to 1/1.702 and not freely estimated for the classical Rasch model, or all equal but estimated for the 1PL model)

  • number of confmirt.model() options decreased due to the new way to specify item types, startvalues, prior parameter distributions, and constraints

  • plink package has not kept up with item information curves, so I'll implement my own for now. Replaced plink item plots from 'itemplots' function with ones that I rolled

  • package descriptions and documentation updated

  • coef() now prints slightly different output, with the new option 'allpars = TRUE' to display all the item and group parameters, returned as a list

  • simdata() updated to support new item types

  • more accurate standard errors for MAP and ML factor scores, and specific factors in bfactorClass objects can now be estimated for all methods

Changes in mirt 0.2.6-1

  • dropped the ball and had lots of bug fixes this round. Future commits will avoid this problem by utilizing the testthat package to test code extensively before release

  • internal change in confmirt function to move MHRM engine outside the function for better maintenance

  • theta_angle added to mirt and polymirt plots for changing the viewing angle w.r.t theta_1

  • null model no longer calculated when missing data present

  • fixed item slope models estimated in mirt() with associated standard errors

Changes in mirt 0.2.6

  • null model computed, allowing for model statistics such as TLI

  • documentation changes

  • many back end technical details about estimation moved to technical lists

  • support for all GPArotation methods and options, including Target rotations

  • polymirt() uses confmirt() estimation engine

  • 4PL support for mirt() and bfactor(), treating the upper bound as fixed

  • coef() now has a rotate option for returning rotated IRT parameters

Changes in mirt 0.2.5

  • Fixed translation bug in the C++ code from bfactor() causing illegal vector length throw

  • Fixed fscores() bug when using polychotomous items for mirt() and bfactor()

  • pass rotate='rotation' from mirt and polymirt to override default 'varimax' rotation at estimation time (suggested by Niels Waller)

  • RMSEA, G^2, and p set to NaN instead of internal placeholder when there are missing data

  • df adjusted when missing data present

  • oblique rotations return invisible factor correlation matrix

Changes in mirt 0.2.4

  • degrees of freedom correctly adjusted when using noncompensatory items

  • confmirtClass reorganized to work with S4 methods, now work more consistently with methods.

  • fixed G^2 and log-likelihood in logLik() when product terms included

  • bugfix in drawThetas when noncompensatory items used

Changes in mirt 0.2.3

  • bugfixes for fscores, itemplot, and generic functions

  • read.mirt() added for creating a suitable plink object

  • mirt() and bfactor() can now accommodate polychotomous items using an ordinal IRT scheme

  • itemplot() now makes use of the handy plink package plots, giving a good deal of flexibility.

  • Generic plot()'s now use lattice plots extensively

Changes in mirt 0.2.2

  • Ported src code into Rcpp for future tweaking.

  • Added better fitted() function when missing data exist (noticed by Erin Horn)

Changes in mirt 0.2.1

  • ML estimation of factor scores for mirt and bfactor

  • RMSEA statistic added for all fitted models

  • Nonlinear polynomial estimation specification for confmirt models, now with more consistent returned labels

  • Provide better identification criteria for confmirt() (suggested by Hendrik Lohse)

Changes in mirt 0.2.0

  • parameter standard errors added for mirt() (1 factor only) and bfactor() models

  • bfactor() values that are ommited are recoded to NA in summary and coef for better viewing

  • 'technical' added for confmirt function, allowing for various tweaks and varying beta prior weights

  • product relations added for confmirt.model(). Specified by enclosing in brackets and using an asterisk

  • documentation fixes with roxygenize

Changes in mirt 0.1.20

  • allow lower bound beta priors to vary over items (suggested by James Lee)

Changes in mirt 0.1.6

  • bias fix for mirt() function (noticed by Pedro Barbetta)

Reference manual

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1.35.1 by Phil Chalmers, 2 months ago,,!forum/mirt-package

Report a bug at

Browse source code at

Authors: Phil Chalmers [aut, cre] , Joshua Pritikin [ctb] , Alexander Robitzsch [ctb] , Mateusz Zoltak [ctb] , KwonHyun Kim [ctb] , Carl F. Falk [ctb] , Adam Meade [ctb] , Lennart Schneider [ctb] , David King [ctb] , Chen-Wei Liu [ctb] , Ogreden Oguzhan [ctb]

Documentation:   PDF Manual  

Task views: Psychometric Models and Methods, Missing Data

GPL (>= 3) license

Imports GPArotation, gridExtra, Matrix, Rcpp, mgcv, vegan, Deriv, splines, dcurver

Depends on stats, stats4, lattice, methods

Suggests boot, latticeExtra, directlabels, shiny, knitr, markdown, Rsolnp, nloptr, sirt, plink, mirtCAT

Linking to Rcpp, RcppArmadillo

Imported by BifactorIndicesCalculator, DFIT, GPCMlasso, MultBiplotR, PROsetta, ShinyItemAnalysis, airt, ctgdist, difR, equateIRT, faoutlier, irtGUI, irtreliability, jrt, kequate, mstDIF, scDIFtest, shinyIRT.

Depended on by CopyDetect, NominalLogisticBiplot, OrdinalLogisticBiplot, PerFit, lordif, mirtCAT.

Suggested by EGAnet, LSAmitR, TestDesign, dexterMST, flexmet, irtplay, irtrees, merDeriv, nonnest2, psychotools, rpf, sirt.

Enhanced by CDM.

See at CRAN