We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation and prediction. This paper moves one step further toward the statistical inference for binary matrix…

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

A method is proposed for partially analyzing additive ipsative data (PAID). Transforming the PAID according to a developed equation preserves the density of the transformed data, and maximum likelihood estimation can be carried out as usual. Simulation results show that the original structural parameters can be accurately estimated from PAID. (SLD)

A confirmatory approach to assessing test structure using multidimensional item response theory (MIRT) was developed and evaluated. The approach involved adding to the exponent of the MIRT model an item structure matrix that allows the user to specify the ability dimensions measured by an item. Various combinations of item structures were fit to…