The existence of an item pool can bring out the various merits of using item response theory (IRT). This study considered the case where the development of an item pool is in progress. We examined the robustness of four calibration methods in three linking designs using simulated data. The data were generated assuming that a small-sized item pool had already been developed and new items were to be added to that item pool. The results suggested that the item characteristic curve method generally performed well. The performance of the fixed common item parameter calibration method and the concurrent calibration method worsened in one of the linking designs where the number of common items was small. The results also suggested that performance was better when the sample size per form and the number of common items were large.
A Bayesian nonmetric successive categories multidimensional scaling (MDS) method is proposed. The proposed method can be seen as a Bayesian alternative to the maximum likelihood multidimensional successive scaling method proposed by Takane (1981), or as a nonmetric extension of Bayesian metric MDS by Oh and Raftery (2001). The model has a graded-response type measurement model part and a latent metric MDS part. All the parameters are jointly estimated using a Markov chain Monte Carlo (MCMC) estimation technique. Moreover, WinBUGS/OpenBUGS code for the proposed methodology is also given to aid applied researchers. The proposed method is illustrated through the analysis of empirical two-mode three-way similarity data.
On building a model for estimating response propensity score for survey data adjustment, we carried out computer simulations to examine the effects of seven types of variables, each having differing associations with the sample inclusion probability, response probability and study variable, by comparing the respective cases in which the variables are included and excluded by the model. Then the following main results were obtained. The most important variable for the model is the one that is simultaneously associated with the study variable, the sample inclusion probability, and the response probability.The variables which have no association with the study variable should not be included in the response propensity model.These results support the conclusions of Brookhart et al. (2006), who examined propensity score models in their study on estimating treatment effects. Additionally, a small difference was found in comparing the effects of the variable associated with sample inclusion probability and the study variable to those of the variable associated with the response probability and the study variable.
Hierarchical data sets arise when data for units (e.g., students) are nested within various clusters (e.g., classes and schools), and often appear in behavioral research. Estimating statistical power and sample size requirements is one of the fundamental questions in data collection, especially in experimental research where obtaining large samples is sometimes unrealistic. In the present research, we discuss a general procedure for evaluating statistical power to test intervention effects in experimental research with hierarchical data, focusing mainly on a two-way between-subjects design. This approach enables the statistical power of various types of contrasts to be evaluated with respect to main effects and interaction effects by using multiparameter tests based on Wald statistics. Additionally, several numerical examples are presented to show how the statistical power for various contrasts changes with various values of sample size, sizes of intervention effects, intraclass correlation and some data assumptions. Extensions of the proposed method and issues for practical applications are noted in discussion.
In the power transformation (Box & Cox, 1964), parameters are usually estimated under the assumption that the transformed distribution is a normal distribution even though the transformed distribution is a truncated normal distribution. In the present paper, we evaluate the asymptotic influence of the truncation on estimation of the parameters of the power-normal distribution (Goto, Uesaka, & Inoue, 1979), which specifies original observations before the application of power transformation. Then we demonstrate that when the degree of the truncation of the transformed distribution is large, the parameter estimates based on the ordinary estimation method which ignore the truncation might have large bias through the simulation study and the case study.
The wandering ideal point (WIP) model developed by De Soete, Carroll and DeSarbo in 1986 has been used to analyze individual preferences data. Usually the marginal maximum likelihood (MML) method is applied to estimate the subject's ideal points in the WIP model. However, each ideal point estimated by the Bayes expected a posteriori estimation procedure in the MML method is different in nature from that which should be estimated as a mean vector of the multivariate normal distribution each independently assigned to its respective subject point according to the original WIP model. In this paper I take a Bayesian approach to estimate the distribution of each ideal point. Explicitly, the Gibbs sampler, one of the Marcov Chain Monte Carlo methods, is implemented for fitting the WIP model to “pick any/n” type of binary data. Three applications are provided which demonstrate that the method is useful to estimate the distribution of each subject point.