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A Positive Trait Item Response Model, Joseph F. Lucke
A Positive Trait Item Response Model, Joseph F. Lucke
Joseph Lucke
All current models from item response theory (IRT) assume the latent trait follows a standard normal distribution. While this assumption is appropriate for traits such as ability or attitude, it creates both conceptual and technical problems traits such as addiction (alcohol, drugs, gambling). The distribution of an addiction trait is better assumed to be anchored at zero (no addiction) and positively skewed. A small change to the usual IRT model yields a class of positive-trait item response models (PTIRMs). I discuss PTIRMs and present one model in detail, including item characteristic curves and item information curves. I present an example …
"Rassling The Hog": The Influence Of Correlated Item Error On Internal Consistency, Classical Reliability, And Congeneric Reliability, Joseph F. Lucke
"Rassling The Hog": The Influence Of Correlated Item Error On Internal Consistency, Classical Reliability, And Congeneric Reliability, Joseph F. Lucke
Joseph Lucke
The properties of internal consistency ($\alpha$), classical reliability ($\rho$), and congeneric reliability ($\omega$) for a composite test with correlated item error were analytically investigated. Possible sources of correlated item error are contextual effects, item bundles, and item models that ignore additional attributes or higher-order attributes. The relation between reliability and internal consistency is determined by the deviance from true-score equivalence. Reliability (classical or congeneric) is internal consistency plus the relative deviance from true-score equivalence. The influence of correlated item error on $\alpha$, $\rho$, and $\omega$ is conveyed strictly through the total item error covariance. As the total item error covariance …