sirt-package: Supplementary Item Response Theory Models

Description

Supplementary item response theory models to complement existing functions in R.

Arguments

RFunction Versions

class.accuracy.rasch__0.03.R, data.prep__1.03.R, detect__0.03.R, dif.logisticregression__0.03.R, dif.variance__0.04.R, dirichlet__0.04.R, eigenvalues.manymatrices__0.03.R, equating.rasch__0.02.R, fit.adisop__2.09.R, fit.gradedresponse__1.05.R, fit.gradedresponse_alg__1.06.R, fit.isop__2.05.R, fit.logistic__2.01.R, fit.logistic_alg__0.04.R, gom.em.alg__5.01.R, gom.em__5.01.R, gom.jml__0.08.R, gom.jml_alg__0.04.R, greenyang.reliability__0.04.R, isop.dich__3.08.R, isop.poly__2.06.R, isop.scoring__1.03.R, isop_alg__0.03.R, latent.regression__1.06.R, lsdm__0.05.R, marginal.truescore.reliability__0.01.R, matrix_functions__0.01.R, matrixfunctions_sirt__0.04.R, mcmc.2pno.ml__3.08.R, mcmc.2pno.ml_alg__3.12.R, mcmc.2pno.ml_output__1.02.R, mcmc.2pno__1.14.R, mcmc.2pno_alg__1.07.R, mcmc.2pnoh__1.02.R, mcmc.2pnoh_alg__0.05.R, mcmc.3pno.testlet__2.03.R, mcmc.3pno.testlet_alg__2.05.R, mcmc.3pno.testlet_output__1.01.R, mcmc.aux__0.02.R, mcmc.list.descriptives__0.03.R, mcmclist2coda__0.01.R, modelfit.cor__2.05.R, monoreg.rowwise__0.03.R, normal2.cw__0.04.R, np.dich__0.09.R, nr.numdiff__0.01.R, pbivnorm2__1.04.R, personfit.stat__0.01.R, personfit__0.03.R, plausible.values.raschtype__2.04.R, plot.isop__1.02.R, plot.mcmc.sirt__0.07.R, prmse.subscores__0.02.R, prob.guttman__1.02.R, qmc.nodes__0.02.R, R2noharm-utility__1.01.R, R2noharm.EAP__0.04.R, R2noharm.jackknife__1.01.R, R2noharm__2.01.R, rasch.copula__0.992.R, rasch.copula2__4.01.R, rasch.jml.biascorr__0.03.R, rasch.jml__3.12.R, rasch.mirtlc__8.01.R, rasch.mirtlc_aux__8.03.R, rasch.mml.npirt__1.02.R, rasch.mml.ramsay__2.03.R, rasch.mml.raschtype__2.16.R, rasch.mml__2.01.R, rasch.mml2__5.04.R, rasch.pairwise__0.11.R, rasch.pml__2.12.R, rasch.pml_aux__1.03.R, rasch.pml2__4.08.R, rasch.pml2_aux__3.17.R, rasch.pml3__5.04.R, rasch.pml3_aux__5.01.R, rasch.prox__1.03.R, rasch.testlet__0.10.R, rasch.va__0.01.R, rm.facets__2.02.R, rm.facets_alg__2.03.R, rm.hrm__7.04.R, rm.hrm_alg__7.06.R, rm_proc__0.01.R, sim.rasch.dep__0.04.R, smirt__5.33.R, smirt_alg_comp__1.05.R, smirt_alg_noncomp__2.12.R, smirt_preproc__0.05.R, stratified.cronbach.alpha__0.02.R, summary.gom.em__0.04.R, summary.isop__0.04.R, summary.mcmc.sirt__1.02.R, summary.R2noharm.jackknife__1.01.R, summary.R2noharm__0.01.R, summary.rasch.copula__1.01.R, summary.rasch.mirtlc__7.03.R, summary.rasch.pml__0.02.R, summary.rm.facets__0.02.R, summary.rm.hrm__0.02.R, summary.smirt__0.04.R, tetrachoric2__0.07.R, wle.rasch__1.03.R, yen.q3__0.04.R, zzz__1.03.R,

<em>Rcpp</em> Function Versions

interval_index_c__0.01.cpp, mml2_calcpost_v1__0.01.cpp, mml2_raschtype_counts__0.01.cpp, monoreg_rowwise_c__0.02.cpp, rm.arraymult__0.03.cpp, rm.probraterfct__0.02.cpp, rm_calcpost__0.01.cpp, rowcumsums_source__0.02.cpp, rowksmallest_c__0.01.cpp, rowmaxscpp_source__0.01.cpp, smirt_calcpost__0.02.cpp, smirt_calcprob_comp__0.02.cpp, smirt_calcprob_noncomp__0.02.cpp,

<em>Rd</em> Documentation Versions

ccov.np__0.07.Rd, class.accuracy.rasch__0.07.Rd, conf.detect__1.13.Rd, data.big5__0.12.Rd, data.long__0.05.Rd, data.math__0.05.Rd, data.ml__1.02.Rd, data.noharm__0.03.Rd, data.pisaMath__0.05.Rd, data.pisaPars__0.02.Rd, data.pisaRead__0.04.Rd, data.ratings1__0.03.Rd, data.read__1.04.Rd, data.timss__0.04.Rd, detect.index__0.09.Rd, dif.logistic.regression__0.09.Rd, dif.strata.variance__0.05.Rd, dif.variance__0.06.Rd, dirichlet.mle__0.06.Rd, dirichlet.simul__0.03.Rd, eigenvalues.manymatrices__0.04.Rd, equating.rasch.jackknife__0.08.Rd, equating.rasch__1.13.Rd, expl.detect__1.05.Rd, fit.isop__1.06.Rd, gom.em__1.13.Rd, gom.jml__0.09.Rd, greenyang.reliability__1.11.Rd, isop.scoring__1.08.Rd, isop__3.03.Rd, latent.regression.em.raschtype__1.14.Rd, lsdm__1.12.Rd, marginal.truescore.reliability__0.08.Rd, matrixfunctions.sirt__1.03.Rd, mcmc.2pno.ml__0.17.Rd, mcmc.2pno__1.18.Rd, mcmc.2pnoh__0.12.Rd, mcmc.3pno.testlet__0.12.Rd, mcmc.list.descriptives__0.01.Rd, mcmclist2coda__0.04.Rd, modelfit.sirt__0.18.Rd, monoreg.rowwise__0.04.Rd, np.dich__0.09.Rd, pbivnorm2__0.06.Rd, person.parameter.rasch.copula__1.04.Rd, personfit.stat__0.05.Rd, pgenlogis__0.05.Rd, plausible.value.imputation.raschtype__1.10.Rd, plot.mcmc.sirt__0.04.Rd, plot.np.dich__0.10.Rd, prmse.subscores.scales__0.10.Rd, prob.guttman__1.07.Rd, qmc.nodes__0.04.Rd, R2noharm.EAP__0.05.Rd, R2noharm.jackknife__1.06.Rd, R2noharm__1.18.Rd, rasch.copula__1.22.Rd, rasch.jml.biascorr__0.10.Rd, rasch.jml.jackknife1__2.05.Rd, rasch.jml__1.18.Rd, rasch.mirtlc__2.31.Rd, rasch.mml__3.20.Rd, rasch.pairwise.itemcluster__0.10.Rd, rasch.pairwise__0.11.Rd, rasch.pml__2.29.Rd, rasch.prox__1.05.Rd, rasch.testlet.glmer__0.16.Rd, rasch.va__0.03.Rd, reliability.nonlinearSEM__0.07.Rd, rm.facets__0.13.Rd, rm.hrm__0.15.Rd, sim.qm.ramsay__0.12.Rd, sim.rasch.dep__0.13.Rd, sim.raschtype__0.07.Rd, sirt-package__1.46.Rd, smirt__1.30.Rd, stratified.cronbach.alpha__0.08.Rd, summary.mcmc.sirt__0.05.Rd, testlet.yen.q3__0.09.Rd, tetrachoric2__1.04.Rd, wle.rasch.jackknife__1.08.Rd, wle.rasch__1.04.Rd, yen.q3__0.12.Rd,

Details

ll{ Package: sirt Type: Package Version: 0.34 Publication Year: 2013 License: GPL (>= 2) URL: https://sites.google.com/site/alexanderrobitzsch/software } This package enables the estimation of following models:

Multidimensional marginal maximum likelihood estimation (MML) of generalized logistic Rasch type models using the generalized logistic link function (Stukel, 1988) can be conducted withrasch.mml2and the argumentitemtype="raschtype". This model also allows the estimation of the 4PL item response model (Loken & Rulison, 2010). Multiple group estimation, latent regression models and plausible value imputation are supported. %% M-dim noncompensatory and compensatory IRT model
Multidimensional noncompensatory and compensatory item response models for dichotomous item responses (Reckase, 2009) can be estimated with thesmirtfunction and the optionsirtmodel="noncomp"andirtmodel="comp". %% 1-dim Ramsay type model
The unidimensional quotient model (Ramsay, 1989) can be estimated usingrasch.mml2withitemtype="ramsay.qm". %% 1-dim nonparametric IRT models
Unidimensional nonparametric item response models can be estimated employing MML estimation (Rossi, Wang & Ramsay, 2002) by making use ofrasch.mml2withitemtype="npirt". Kernel smoothing for item response function estimation (Ramsay, 1991) is implemented innp.dich. %% 1-dim Copula model
The unidimensional IRT copula model (Braeken, 2011) can be applied for handling local dependencies, seerasch.copula2. %% 1-dim JML
Unidimensional joint maximum likelihood estimation (JML) of the Rasch model is possible with therasch.jmlfunction. Bias correction methods for item parameters are included inrasch.jml.jackknife1andrasch.jml.biascorr. %% M-dim LC Rasch model
The multidimensional latent class Rasch and 2PL model (Bartolucci, 2007) which employs a discrete trait distribution can be estimated withrasch.mirtlc. %% Rater Models
The unidimensional 2PL rater facets model (Lincare, 1994) can be estimated withrm.facets. A hierarchical rater model based on signal detection theory (DeCarlo, Kim & Johnson, 2011) can be conducted withrm.hrm. %% Grade of membership model
The discrete grade of membership model (Erosheva, Fienberg & Joutard, 2007) and the Rasch grade of membership model can be estimated bygom.em. %% MCMC estimation multilevel IRT models
Some hierarchical IRT models and random item models for dichotomous and normally distributed data (van den Noortgate, de Boeck & Meulders, 2003; Fox & Verhagen, 2010) can be estimated withmcmc.2pno.ml. %% 1-dim PCML
Unidimensional pairwise conditional likelihood estimation (PCML; Zwinderman, 1995) is implemented inrasch.pairwiseorrasch.pairwise.itemcluster. %% 1-dim PMML
Unidimensional pairwise marginal likelihood estimation (PMML; Renard, Molenberghs & Geys, 2004) can be conducted usingrasch.pml3. In this function local dependence can be handled by imposing residual error structure or omitting item pairs within a dependent item cluster from the estimation. %% MCMC estimation of some models
Some item response models insirtcan be estimated via Markov Chain Monte Carlo (MCMC) methods. Inmcmc.2pnothe two-parameter normal ogive model can be estimated. A hierarchical version of this model (Janssen, Tuerlinckx, Meulders & de Boeck, 2000) is implemented inmcmc.2pnoh. The 3PNO testlet model (Wainer, Bradlow & Wang, 2007; Glas, 2012) can be estimated withmcmc.3pno.testlet. Some hierarchical IRT models and random item models (van den Noortgate, de Boeck & Meulders, 2003) can be estimated withmcmc.2pno.ml. %% NOHARM
For dichotomous response data, the free NOHARM software (McDonald, 1997) estimates the multidimensional compensatory 3PL model and the functionR2noharmruns NOHARM from withinR. Note that NOHARM must be downloaded fromhttp://noharm.niagararesearch.ca/nh4cldl.htmlat first. %% Nonparametric item response theory
The measurement theoretic founded nonparametric item response models of Scheiblechner (1995, 1999) -- the ISOP and the ADISOP model -- can be estimated withisop.dichorisop.poly. Item scoring within this theory can be conducted withisop.scoring. %% 1-dim Rasch model variational approximation
The Rasch model can be estimated by variational approximation (Rijmen & Vomlel, 2008) usingrasch.va. %% 1-dim Guttman model
The unidimensional probabilistic Guttman model (Proctor, 1970) can be specified withprob.guttman. %% jackknife WLE
A jackknife method for the estimation of standard errors of the weighted likelihood trait estimate (Warm, 1989) is available inwle.rasch.jackknife. %% reliability
Model based reliability for dichotomous data can be calculated by the method of Green and Yang (2009) withgreenyang.reliabilityand the marginal true score method of Dimitrov (2003) using the functionmarginal.truescore.reliability. %% DETECT
Essential unidimensionality can be assessed by the DETECT index (Stout, Habing, Douglas & Kim, 1996), see the functionconf.detect. %% Person Fit
Some person fit statistics in the Rasch model (Meijer & Sijtsma, 2001) are included inpersonfit.stat. %% LSDM
An alternative to the linear logistic test model (LLTM), the so called least squares distance model for cognitive diagnosis (LSDM; Dimitrov, 2007), can be estimated with the functionlsdm.

References

Bartolucci, F. (2007). A class of multidimensional IRT models for testing unidimensionality and clustering items. Psychometrika, 72, 141-157. Braeken, J. (2011). A boundary mixture approach to violations of conditional independence. Psychometrika, 76, 57-76. DeCarlo, T., Kim, Y., & Johnson, M. S. (2011). A hierarchical rater model for constructed responses, with a signal detection rater model. Journal of Educational Measurement, 48, 333-356. Dimitrov, D. (2003). Marginal true-score measures and reliability for binary items as a function of their IRT parameters. Applied Psychological Measurement, 27, 440-458. Dimitrov, D. M. (2007). Least squares distance method of cognitive validation and analysis for binary items using their item response theory parameters. Applied Psychological Measurement, 31, 367-387. Erosheva, E. A., Fienberg, S. E., & Joutard, C. (2007). Describing disability through individual-level mixture models for multivariate binary data. Annals of Applied Statistics, 1, 502-537. Fox, J.-P., & Verhagen, A.-J. (2010). Random item effects modeling for cross-national survey data. In E. Davidov, P. Schmidt, & J. Billiet (Eds.), Cross-cultural Analysis: Methods and Applications (pp. 467-488), London: Routledge Academic. Glas, C. A. W. (2012). Estimating and testing the extended testlet model. LSAC Research Report Series, RR 12-03. Green, S.B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167. Janssen, R., Tuerlinckx, F., Meulders, M., & de Boeck, P. (2000). A hierarchical IRT model for criterion-referenced measurement. Journal of Educational and Behavioral Statistics, 25, 285-306. Linacre, J. M. (1994). Many-Facet Rasch Measurement. Chicago: MESA Press. Loken, E. & Rulison, K. L. (2010). Estimation of a four-parameter item response theory model. British Journal of Mathematical and Statistical Psychology, 63, 509-525. McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. van der Linden & R. K. Hambleton (1997): Handbook of modern item response theory (pp. 257-269). New York: Springer. Meijer, R. R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25, 107-135. Proctor, C. H. (1970). A probabilistic formulation and statistical analysis for Guttman scaling. Psychometrika, 35, 73-78. Ramsay, J. O. (1989). A comparison of three simple test theory models. Psychometrika, 54, 487-499. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630. Reckase, M.D. (2009). Multidimensional item response theory. New York: Springer. Rijmen, F., & Vomlel, J. (2008). Assessing the performance of variational methods for mixed logistic regression models. Journal of Statistical Computation and Simulation, 78, 765-779. Renard, D., Molenberghs, G., & Geys, H. (2004). A pairwise likelihood approach to estimation in multilevel probit models. Computational Statistics & Data Analysis, 44, 649-667. Rossi, N., Wang, X. & Ramsay, J. O. (2002). Nonparametric item response function estimates with the EM algorithm. Journal of Educational and Behavioral Statistics, 27, 291-317. Scheiblechner, H. (1995). Isotonic ordinal probabilistic models (ISOP). Psychometrika, 60, 281-304. Scheiblechner, H. (1999). Additive conjoint isotonic probabilistic models (ADISOP). Psychometrika, 64, 295-316. Stout, W., Habing, B., Douglas, J., & Kim, H. R. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20, 331-354. Stukel, T. A. (1988). Generalized logistic models. Journal of the American Statistical Association, 83, 426-431. van den Noortgate, W., De Boeck, P., & Meulders, M. (2003). Cross-classification multilevel logistic models in psychometrics. Journal of Educational and Behavioral Statistics, 28, 369-386. Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450. Wainer, H., Bradlow, E. T., & Wang, X. (2007). Testlet response theory and its applications. Cambridge: Cambridge University Press. Zwinderman, A. H. (1995). Pairwise parameter estimation in Rasch models. Applied Psychological Measurement, 19, 369-375.