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Full-Text Articles in Physical Sciences and Mathematics
Bayesian Hierarchical Modeling With 3pno Item Response Models, Yanyan Sheng, Todd Christopher Headrick
Bayesian Hierarchical Modeling With 3pno Item Response Models, Yanyan Sheng, Todd Christopher Headrick
Todd Christopher Headrick
Fully Bayesian estimation has been developed for unidimensional IRT models. In this context, prior distributions can be specified in a hierarchical manner so that item hyperparameters are unknown and yet still have their own priors. This type of hierarchical modeling is useful in terms of the three-parameter IRT model as it reduces the difficulty of specifying model hyperparameters that lead to adequate prior distributions. Further, hierarchical modeling ameliorates the noncovergence problem associated with nonhierarchical models when appropriate prior information is not available. As such, a Fortran subroutine is provided to implement a hierarchical modeling procedure associated with the three-parameter normal …
An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
Todd Christopher Headrick
This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of 𝐿-moments and 𝐿-correlations. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that 𝐿-moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of 𝐿-skew, 𝐿-kurtosis, …