Fitting Logistie IRT Modeis: Small Wonder

Smte-oi-rbe-art ítem response theo,y (IRT) models use logistie functions exclusivcly as their ítem response functions (IREs). Logistie funcííons mee Ihe reqrtírements thai iheir range is che unit iníerval ami íhat they are monotonically increasing. bur they upase a parameter ipace whose dimensions can only be assigned a meíaphoñcal interpretation in the context of cesting. Applications of 1RT models require obtaining ihe set of values itt Ingístie functíon paranieters thai besí fu an empirícal dato set. l-lowever. success in ohtaininsi such set of values does ncc guarantee thai che constructs they represent actually exisí, for the adequacy of a model is nol sustained hy ihe possihility of estimaring parameters. Thís article illustrates bow meehanical adoplion of off-theshelf logistic lunc[ions as IRFs lbr IRT modeis can result in off-the-shelf parameter estímates and tUs to dato. Thc results of a simulation study are presenced, which show that logistie 11ff modeis can tít a set of dato generated by IREs other chan logiscic funccions just as well as they ¡it iogisric dato. even though the response processes and parameter spaces involved in each case are subsíantially dírferení. An explanation of why logistic funetions wnrk os lhey do is ofreced, che íhcorecical and practícal consequences of Iheir behavior are discuised, and a testable altemative lo logistic IRFs is commented cpon. Key ~vúnIs.goodnass ej/ii, paran cier esíimwíou, ile»> nxsponse theory, legisle: models, Jiniie siate poIynrníur: ,nodels, BILGC