《《The New Psychometrics – Item Response Theory》.pdfVIP

Chapter 8 The “New Psychometrics” – Item Response Theory Classical test theory is concerned with the reliability of a test and assumes that the items within the test are sampled at random from a domain of relevant items. Reliability is seen as a characteristic of the test and of the variance of the trait it measures. Items are treated as random replicates of each other and their characteristics, if examined at all, are expressed as correlations with total test score or as factor loadings on the putative latent variable(s) of interest. Characteristics of their properties are not analyzed in detail. This led Mellenbergh (1996) to the distinction between theories of tests (Lord and Novick, 1968) and a theories of items (Lord, 1952; Rasch, 1960). The so-called “New Psychometrics” (Embretson and Hershberger, 1999; Embretson and Reise, 2000; Van der Linden and Hambleton, 1997) is a theory of how people respond to items and is known as Item Response Theory or IRT . Over the past twenty years there has been explosive growth in programs that can do IRT, and within R there are at least four very powerful packages: eRm (Mair and Hatzinger, 2007), ltm Rizopoulos (2006), lme4 (Doran et al., 2007) and MiscPsycho, (Doran, 2010). Additional packages include mokken (van der Ark, 2010) to do non-metric IRT and plink (Weeks, 2010) to link multiple groups together. More IRT packages are being added all of the time. In the discussion of Coombs’ Theory of Data the measurement of attitudes and abilities (2.9) were seen as examples of comparing an object (an item) to a person. The comparison was said to be one of order (for abilities) or of distance (for attitudes). The basic model was that for ability there is a latent value for each person, θi and a latent difficulty or location1 δj for each item. The probability of a particular person getting a specific ability item correct was