By Albert Maydeu-Olivares
Modern Psychometrics gains leading edge chapters prepared in 4 sections: try conception, issue research, structural equation modeling, and multivariate research. The part on attempt thought comprises subject matters reminiscent of multidimensional merchandise reaction conception (IRT), the connection among IRT and issue research, estimation and checking out of those types, and simple dimension concerns which are frequently ignored. The issue research part reports the background and improvement of the version, factorial invariance and issue research indeterminacy, and Bayesian inference for issue ratings and parameter estimates. The part on structural equation modeling (SEM) contains the overall algebraic-graphic ideas for latent variable SEM, a survey of goodness of healthy evaluate, SEM resampling tools, a dialogue of the way to check correlations among and inside of self sustaining samples, dynamic issue versions in response to ARMA time sequence types, and multi-level issue research types for non-stop and discrete facts. the ultimate part on multivariate research contains issues equivalent to twin scaling of ordinal facts, version specification and lacking facts difficulties in time sequence types, and a dialogue of the topics that run via all multivariate equipment. This journey de strength via modern psychometrics will entice complex scholars and researchers within the social and behavioral sciences and schooling, in addition to methodologists from different disciplines.
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Extra info for Contemporary Psychometrics: A Festschrift for Roderick P. Mcdonald (Multivariate Applications Books) (Multivariate Applications Series)
In item response theory, precision is measured using the information function. The reciprocal of the information function is the asymptotic variance of the maximum likelihood estimate of ability. This relationship implies that the larger the information function, the smaller is the asymptotic variance and the greater is the measurement precision. Multidimensional information (MINF) serves as one measure of precision. MINF is computed in a manner similar to its unidimensional IRT counterpart except that the direction of the information must also considered.
2. For example, an item's vector defines the direction in the latent space along which the item response surface has its maximum rate of increase, and thus also corresponds to the unique composite of traits for which the item is maximally discriminating. 5. This is also the location in the multidimensional ability space at which the item is most discriminating. In this respect, the latent trait parametrization may be attractive to practitioners accustomed to interpreting unidimensional IRT models, where similar interpretations can be given to the slope and intercept parameters.
Items that are difficult have lower a values and items that are highly discriminating have higher . When the 9 metric is scaled to have a mean of 0 and variance of 1, items with as below 0 are more difficult items and items with above 1 represent items that are highly discriminating. FIG. 1. (a) Latent response propensity as function of latent ability, and corresponding regions of correct response under the normal ogive model, (b) Example item response curve for a normal ogive item. 2. LIMITED- AND FULL-INFORMATION ESTIMATION 31 MULTIDIMENSIONAL ITEM RESPONSE MODELS In a multidimensional model, the examinee/item interaction is modeled by a vector of latent traits, 9 — ( 1, 2, • • •, ).