sirt (version 0.31-20)

sirt-package: Supplementary Item Response Theory Models

Description

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

RFunction Versions

ccov.np__0.06.Rd, class.accuracy.rasch__0.06.Rd, conf.detect__1.06.Rd, data.long__0.03.Rd, data.math__0.04.Rd, data.pisaMath__0.04.Rd, data.pisaPars__0.02.Rd, data.pisaRead__0.03.Rd, data.ratings1__0.02.Rd, data.read__0.05.Rd, data.timss__0.03.Rd, detect.index__0.07.Rd, dif.logistic.regression__0.07.Rd, dif.strata.variance__0.04.Rd, dif.variance__0.05.Rd, dirichlet.mle__0.06.Rd, dirichlet.simul__0.02.Rd, eigenvalues.manymatrices__0.04.Rd, equating.rasch.jackknife__0.07.Rd, equating.rasch__1.07.Rd, expl.detect__1.04.Rd, gom.em__1.09.Rd, gom.jml__0.06.Rd, greenyang.reliability__1.08.Rd, jackknife.rasch.jml__1.07.Rd, latent.regression.em.raschtype__1.11.Rd, lsdm__1.03.Rd, marginal.truescore.reliability__0.04.Rd, modelfit.sirt__0.14.Rd, np.dich__0.08.Rd, pbivnorm2__0.03.Rd, person.parameter.rasch.copula__1.03.Rd, personfit.stat__0.03.Rd, pgenlogis__0.05.Rd, plausible.value.imputation.raschtype__1.05.Rd, plot.np.dich__0.08.Rd, prmse.subscores.scales__0.08.Rd, prob.guttman__1.04.Rd, qmc.nodes__0.03.Rd, rasch.copula__1.20.Rd, rasch.jml.biascorr__0.07.Rd, rasch.jml__1.10.Rd, rasch.mirtlc__2.26.Rd, rasch.mml__3.08.Rd, rasch.pairwise.itemcluster__0.08.Rd, rasch.pairwise__0.09.Rd, rasch.pml__2.23.Rd, rasch.prox__1.04.Rd, rasch.testlet.glmer__0.14.Rd, rasch.va__0.02.Rd, reliability.nonlinearSEM__0.06.Rd, rm.facets__0.10.Rd, rm.hrm__0.08.Rd, sim.qm.ramsay__0.09.Rd, sim.rasch.dep__0.13.Rd, sim.raschtype__0.05.Rd, sirt-package__1.30.Rd, smirt__1.14.Rd, stratified.cronbach.alpha__0.08.Rd, summary.gom__0.06.Rd, summary.lsdm__0.07.Rd, summary.prob.guttman__0.07.Rd, summary.rasch.copula__0.08.Rd, summary.rasch.jml__0.08.Rd, summary.rasch.mirtlc__0.06.Rd, summary.rasch.mml__0.07.Rd, summary.rasch.pairwise__0.06.Rd, summary.rasch.pml__0.07.Rd, summary.rm.facets__0.06.Rd, summary.rm.hrm__0.06.Rd, summary.smirt__0.07.Rd, testlet.yen.q3__0.08.Rd, tetrachoric2__1.03.Rd, wle.rasch.jackknife__1.06.Rd, wle.rasch__1.04.Rd, yen.q3__0.11.Rd,

<em>Rcpp</em> Function Versions

rm.arraymult__0.03.cpp, rm.probraterfct__0.02.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__0.06.Rd, class.accuracy.rasch__0.06.Rd, conf.detect__1.06.Rd, data.long__0.03.Rd, data.math__0.04.Rd, data.pisaMath__0.04.Rd, data.pisaPars__0.02.Rd, data.pisaRead__0.03.Rd, data.ratings1__0.02.Rd, data.read__0.05.Rd, data.timss__0.03.Rd, detect.index__0.07.Rd, dif.logistic.regression__0.07.Rd, dif.strata.variance__0.04.Rd, dif.variance__0.05.Rd, dirichlet.mle__0.06.Rd, dirichlet.simul__0.02.Rd, eigenvalues.manymatrices__0.04.Rd, equating.rasch.jackknife__0.07.Rd, equating.rasch__1.07.Rd, expl.detect__1.04.Rd, gom.em__1.09.Rd, gom.jml__0.06.Rd, greenyang.reliability__1.08.Rd, jackknife.rasch.jml__1.07.Rd, latent.regression.em.raschtype__1.11.Rd, lsdm__1.03.Rd, marginal.truescore.reliability__0.04.Rd, modelfit.sirt__0.14.Rd, np.dich__0.08.Rd, pbivnorm2__0.03.Rd, person.parameter.rasch.copula__1.03.Rd, personfit.stat__0.03.Rd, pgenlogis__0.05.Rd, plausible.value.imputation.raschtype__1.05.Rd, plot.np.dich__0.08.Rd, prmse.subscores.scales__0.08.Rd, prob.guttman__1.04.Rd, qmc.nodes__0.03.Rd, rasch.copula__1.20.Rd, rasch.jml.biascorr__0.07.Rd, rasch.jml__1.10.Rd, rasch.mirtlc__2.26.Rd, rasch.mml__3.08.Rd, rasch.pairwise.itemcluster__0.08.Rd, rasch.pairwise__0.09.Rd, rasch.pml__2.23.Rd, rasch.prox__1.04.Rd, rasch.testlet.glmer__0.14.Rd, rasch.va__0.02.Rd, reliability.nonlinearSEM__0.06.Rd, rm.facets__0.10.Rd, rm.hrm__0.08.Rd, sim.qm.ramsay__0.09.Rd, sim.rasch.dep__0.13.Rd, sim.raschtype__0.05.Rd, sirt-package__1.31.Rd, smirt__1.14.Rd, stratified.cronbach.alpha__0.08.Rd, summary.gom__0.06.Rd, summary.lsdm__0.07.Rd, summary.prob.guttman__0.07.Rd, summary.rasch.copula__0.08.Rd, summary.rasch.jml__0.08.Rd, summary.rasch.mirtlc__0.06.Rd, summary.rasch.mml__0.07.Rd, summary.rasch.pairwise__0.06.Rd, summary.rasch.pml__0.07.Rd, summary.rm.facets__0.06.Rd, summary.rm.hrm__0.06.Rd, summary.smirt__0.07.Rd, testlet.yen.q3__0.08.Rd, tetrachoric2__1.03.Rd, wle.rasch.jackknife__1.06.Rd, wle.rasch__1.04.Rd, yen.q3__0.11.Rd,

Details

ll{ Package: sirt Type: Package Version: 0.31 Publication Year: 2013 License: GPL (>= 2) URL: https://sites.google.com/site/alexanderrobitzsch/software } This package enables the estimation of following models:

%% M-dim generalized item response model
• 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 injackknife.rasch.jmlandrasch.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. %% 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. %% 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. Green, S.B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167. 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. 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. 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. Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450. Zwinderman, A. H. (1995). Pairwise parameter estimation in Rasch models. Applied Psychological Measurement, 19, 369-375.

See Also

For estimating multidimensional models for polytomous item resonses see the mirt and TAM (https://sites.google.com/site/irttam1/) packages. For dichotomous data,the free NOHARM software (http://noharm.niagararesearch.ca/nh4cldl.html) is a reliable alternative, see the R2NOHARM package (https://sites.google.com/site/alexanderrobitzsch/software) for running NOHARM from within R. For conditional maximum likelihood estimation see the eRm package. For pairwise estimation likelihood methods (also known as composite likelihood methods) see pln or lavaan. The estimation of cognitive diagnostic models is possible using the CDM package. For the multidimensional latent class IRT model see the MultiLCIRT package which also allows for polytomous item responses. Latent class analysis can be carried out with poLCA and randomLCA packages.