The asymptotic posterior normality (APN) of the latent vector in an item response theory model is an important argument in modeling and inference. For a single latent trait, Chang and Stout proved its APN for binary items under general conditions, which generalized Chang for polytomous data and Kornely and Kateri for multivariate latent traits (MLT) and binary items. As MLT and polytomous items are nowadays common in psychometry, an APN-theory covering both simultaneously remains an open and ongoing problem. We generalize the APN-theory accordingly, providing thus a broader foundation for developments relying on APN. We also prove consistency of common estimators for the MLT, extending the according results of Chang and Kornely and Kateri.

Since its conception by Thistlethwaite and Campbell, a regression discontinuity (RD) design has continuously evolved and progressed in various aspects. This paper explores a novel theoretical advancement in fuzzy RD designs by combining them with multiple control groups under one-sided noncompliance. Within this approach, we estimate the average treatment effect on the treated at the cutoff from the fuzzy RD design and construct its bounds derived from multiple control groups. Using the bounds as a sensitivity check, we examine whether the underlying causal or statistical assumptions for the fuzzy RD design are warranted. We verify the effectiveness of our approach via a simulation study and demonstrate its application by studying the effect of extended time accommodations using data from the National Assessment of Educational Progress.

If psychometrics has long concerned itself with validity, reliability, and fairness, then what could psychometrics learn from the cybernetic theories of AI? Through engagement with Burstein’s (2023) Responsible AI Standards, this paper unpacks some paradigmatic differences between psychometrics and cybernetics, points to how recursivity and contingency are both a challenge and opportunity for psychometrics, and how this matters epistemologically, ethically and politically. Following these epistemological differences, the paper raises ethico-political concerns with the promise of the “human-in-the-loop”.

Ensuring fairness is crucial in developing modern algorithms and tests. To address potential biases and discrimination in algorithmic decision making, researchers have drawn insights from the test fairness literature, notably the work on differential algorithmic functioning (DAF) by Suk and Han. Nevertheless, the exploration of intersectionality in fairness investigations, within both test fairness and algorithmic fairness fields, is still relatively new. In this paper, we propose an extension of the DAF framework to include the concept of intersectionality. Similar to DAF, the proposed notion for intersectionality, which we term “interactive DAF,” leverages ideas from test fairness and algorithmic fairness. We also provide methods based on the generalized Mantel–Haenszel test, generalized logistic regression, and regularized group regression to detect DAF, interactive DAF, or other subtypes of DAF. Specifically, we employ regularized group regression with three different penalties and examine their performance via a simulation study. Finally, we demonstrate our intersectional DAF framework in real-world applications on grade retention and conditional cash transfer programs in education.

Longitudinal processes are often associated with each other over time; therefore, it is important to investigate the associations among developmental processes and understand their joint development. The traditional latent growth curve model (LGCM) with a time-varying covariate (TVC) provides a method to estimate the TVC effect on a longitudinal outcome while modeling the outcome’s change. However, it does not allow the TVC to predict variations in the random growth coefficients. We propose decomposing the TVC into initial trait and temporal states using three methods to address this limitation. In each method, the baseline of the TVC is viewed as an initial trait, and the corresponding effects are obtained by regressing random intercepts and slopes on the baseline value. Temporal states are characterized as (a) interval-specific slopes, (b) interval-specific changes, or (c) changes from the baseline at each measurement occasion, depending on the method. We demonstrate our methods through simulations and real-world data analyses, assuming a linear–linear functional form for the longitudinal outcome. The results demonstrate that LGCMs with a decomposed TVC can provide unbiased and precise estimates with target confidence intervals. We also provide OpenMx and Mplus 8 code for these methods with commonly used linear and nonlinear functions.