Equating is a family of statistical models and methods used to adjust scores on different test forms so that they can be comparable and used interchangeably. Equated scores are obtained estimating the equating transformation function, which maps the scores on the scale of one test form into their equivalents on the scale of other one. All the…

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs…

The multiple-choice (MC) item format has been widely used in educational assessments across diverse content domains. MC items purportedly allow for collecting richer diagnostic information. The effectiveness and economy of administering MC items may have further contributed to their popularity not just in educational assessment. The MC item format…

Widespread availability of rich educational databases facilitates the use of conditioning strategies to estimate causal effects with nonexperimental data. With dozens, hundreds, or more potential predictors, variable selection can be useful for practical reasons related to communicating results and for statistical reasons related to improving the…

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain…

This article describes the analysis of regression-discontinuity designs (RDDs) using the R packages rdd, rdrobust, and rddtools. We discuss similarities and differences between these packages and provide directions on how to use them effectively. We use real data from the Carolina Abecedarian Project to show how an analysis of an RDD can be…

Unless strong assumptions are made, nonparametric identification of principal causal effects can only be partial and bounds (or sets) for the causal effects are established. In the presence of a secondary outcome, recent results exist to sharpen the bounds that exploit conditional independence assumptions. More general results, though not embedded…

Detection of differential item functioning (DIF) by use of the logistic modeling approach has a long tradition. One big advantage of the approach is that it can be used to investigate nonuniform (NUDIF) as well as uniform DIF (UDIF). The classical approach allows one to detect DIF by distinguishing between multiple groups. We propose an…

If standard two-parameter item response functions are employed in the analysis of a test with some newly constructed items, it can be expected that, for some items, the item response function (IRF) will not fit the data well. This lack of fit can also occur when standard IRFs are fitted to personality or psychopathology items. When investigating…

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

Conventional methods for mediation analysis generate biased results when the mediator--outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator…

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is…

Latent partially ordered sets (posets) can be employed in modeling cognitive functioning, such as in the analysis of neuropsychological (NP) and educational test data. Posets are cognitively diagnostic in the sense that classification states in these models are associated with detailed profiles of cognitive functioning. These profiles allow for…

In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This article introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…