Scale Alignment in the Between-Item Multidimensional Partial Credit Model

In between-item multidimensional item response models, it is often desirable to compare individual latent trait estimates across dimensions. These comparisons are only justified if the model dimensions are scaled relative to each other. Traditionally, this scaling is done using approaches such as standardization—fixing the latent mean and standard deviation to 0 and 1 for all dimensions. However, approaches such as standardization do not guarantee that Rasch model properties hold across dimensions. Specifically, for between-item multidimensional Rasch family models, the unique ordering of items holds within dimensions, but not across dimensions. Previously, Feuerstahler and Wilson described the concept of scale alignment, which aims to enforce the unique ordering of items across dimensions by linearly transforming item parameters within dimensions. In this article, we extend the concept of scale alignment to the between-item multidimensional partial credit model and to models fit using incomplete data. We illustrate this method in the context of the Kindergarten Individual Development Survey (KIDS), a multidimensional survey of kindergarten readiness used in the state of Illinois. We also present simulation results that demonstrate the effectiveness of scale alignment in the context of polytomous item response models and missing data.

Validating the teaching, learning, and assessment quality of Malaysian ECCE instrument

<span>Several instruments that measure the teaching, learning, and assessment quality have been developed and published. However, a psychometrically sound instrument to measure teaching, learning, and assessment quality in early childhood care and education that suitable for the Malaysian context needs to be validated. Therefore, this study aimed to validate on teaching, learning, and assessment quality in early childhood care and education instrument, which contains 68 items. The sample comprised 3,498, selected by stratified random sampling from a population of all Malaysian kindergarten teachers. Data were analyzed based on the Polytomous Item Response Theory (IRT) using the Xcalibre software. Samejima's Graded Rating Model (SRGM) was found to be the fit model with the data. Unidimensionality assumption and local independence were tested using the exploratory factor analysis and were fulfilled. The instrument’s reliability was overall very good (α=0.966) and the construct validity was also fairly fulfilled with the value of 58.17% total variance explained. Therefore, this instrument is suggested to be used as fairly to measure the quality of Malaysian early childhood care and education among teachers so that appropriate follow-up actions can be implemented towards the betterment of early childhood education quality.</span>

Disentangling Direct and Indirect Interactions in Polytomous Item Response Theory Models

Measurement is at the core of scientific discovery. However, some quantities, such as economic behavior or intelligence, do not allow for direct measurement. They represent latent constructs that require surrogate measurements. In other scenarios, non-observed quantities can influence the variables of interest. In either case, models with latent variables are needed. Here, we investigate fused latent and graphical models that exhibit continuous latent variables and discrete observed variables. These models are characterized by a decomposition of the pairwise interaction parameter matrix into a group-sparse component of direct interactions and a low-rank component of indirect interactions due to the latent variables. We first investigate when such a decomposition is identifiable. Then, we show that fused latent and graphical models can be recovered consistently from data in the high-dimensional setting. We support our theoretical findings with experiments on synthetic and real-world data from polytomous item response theory studies.