Round about irtoys Round about irtoys Ivailo Partchev 2017-12-15 Package irtoys is a collection of functions related to Item Response Theory (IRT), (Hambleton and Swaminathan 1985), (Embretson and Reise 2000). With a bit of knowledge of R, these can be used in practice and combined into larger programs. The diminutive “toys” in the title was supposed to evoke LEGO stones rather than dolls and teddy bears. As of the time irtoys was published, IRT models could be fit with various programs employing diverse and often arcane syntax. Mastering such a syntax took time, and learning several in order to compare results across programs could be a challenge.
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One of the purposes of irtoys was to offer a simple and unified R interface to some of these programs, just enough to be able to start immediately. Irtoys supports a common and basic subset of the features of three estimation programs: R package ltm (Rizopoulos 2006), Brad Hanson’s freely available program, ICL (Hanson 2002), and the commercially available program, BILOG-MG (Zimowski et al. Basically, the estimation of the 1PL, 2PL, and 3PL models is supported for a single test form of dichotomously scored items. Users with more complex problems could use the syntax generated by irtoys as a starting point in learning one of these programs in depth. Alternatively, they could use some of the R packages that have emerged in the meanwhile, such as mirt (Chalmers 2012), TAM (Kiefer, Robitzsch, and Wu 2016), eRm (Mair and Hatzinger 2007), and others. The functions in irtoys cover a wide range of tasks, including but not limited to ability estimation (maximum likelihood, modal likelihood, EAP, weighted likelihood) or IRT scaling – thanks to Tamaki Hattori, it is probably the only package to offer the Haebara’s method in its entirety, as described in (Haebara 1980). But irtoys is particularly strong in item fit.
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While Bilog-style chi-square statistics are supported in an extremely flexible way, R’s strength in graphics and visualisation has enabled the creation of various plots, and the list is still being extended. Irtoys was arguably the first package to offer non-parametric trace lines similar to those in Ramsay’s TestGraf program (Ramsay 2000), nowadays completely emulated by package KernSmoothIRT (Mazza, Punzo, and McGuire 2014). Version 0.1.0 of irtoys adds several new features:. several new graphical tools to evaluate item fit. the interaction model (Haberman 2007), an important link between Classical Test Theory (CTT) and IRT. alternative links for ICL (in the help screen for irtoys-package).
this vignette Because of the many functions included, this vignette will concentrate on graphical tools for assessing item fit, with special emphasis on new inclusions. Library(irtoys) The package includes a small but real data set of 18 items (multiple-choice, 4 options scored as true or false) and 472 persons. The actual responses are provided as a data frame, Unscored, and the 0/1 scores as Scored. Because not everybody has BILOG-MG, item parameters estimates for the 1PL, 2PL and 3PL models are provided as data sets b1, b2, and b3. The original plot method for item response functions (IRF) makes it easy to compare the trace lines under the 1PL, 2PL, and 3PL models for an arbitrary item. For some items the lines are close, while for others they can be quite different. Plot( irf(b1, items= 3), main= 'IRF for item 3', co= 2) plot( irf(b2, items= 3), co= 3, add= TRUE) plot( irf(b3, items= 3), co= 4, add= TRUE) plot( irf(b1, items= 13), main= 'IRF for item 13', co= 2) plot( irf(b2, items= 13), co= 3, add= TRUE) plot( irf(b3, items= 13), co= 4, add= TRUE) The 1PL is shown in red, the 2PL in green, and the 3PL in blue.
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A new function, irfPlot, tries to show the uncertainty about the lines. The delta method is used to compute the standard error of the item response function from the variance-covariance matrix of the item parameter estimates. Because ICL does not produce the variance-covariance matrix, irfPlot will not display the confidence envelopes when ICL is used to estimate the model. Another thing to note is that variance-covariance matrices produced with Bilog and ltm may differ to a larger extent than the parameter estimates themselves.
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