Recently, deep learning has become a pervasive tool in prediction problems for structured and/or unstructured big data in various areas including science and engineering. In particular, deep neural network models (i.e. a basic core model of deep learning) can be viewed as an extension of statistical models by going through the incorporation of…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

Background: Studying causal effects is an important aim in education. Causal relationships indicate how well implements (e.g., interventions) work for the target subjects. A good strategy to get the inference in such relationships is to conduct randomized experiments. However, random assignment is limited in education research, even is discouraged…

Combining observational and experimental data for causal inference can improve treatment effect estimation. However, many observational data sets cannot be released due to data privacy considerations, so one researcher may not have access to both experimental and observational data. Nonetheless, a small amount of risk of disclosing sensitive…

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social,…

Physics education researchers are interested in using the tools of machine learning and natural language processing to make quantitative claims from natural language and text data, such as open-ended responses to survey questions. The aspiration is that this form of machine coding may be more efficient and consistent than human coding, allowing…

The four-parameter logistic (4PL) Item Response Theory (IRT) model has recently been reconsidered in the literature due to the advances in the statistical modeling software and the recent developments in the estimation of the 4PL IRT model parameters. The current simulation study evaluated the performance of expectation-maximization (EM),…

In recent years, the system of student learning and academic emotions has been taken seriously to re-engineer the teaching-learning process at all levels of education. This research paper considers both aspects of assessing the translation of knowledge i.e. qualitative and quantitative. In the current scenario, quantitative and qualitative…

This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent…

Principal component analysis is an important statistical technique for dimension reduction and exploratory data analysis. However, it is not robust to outliers and may obfuscate important data structure such as clustering. We propose a version of principal component analysis based on the robust L2E method. The technique seeks to find the principal…

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of dichotomous items. The algorithms presented, and three competing deterministic algorithms are compared using computer-generated data. (Author/JKS)

Improvements of the Gaussian quadrature in conjunction with the Newton-Raphson iteration technique (TM 000 789) are discussed as effective methods of calculating the bivariate normal correlation coefficient. (CK)

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The method is described in detail and several examples are presented. (Author/JKS)

A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling, and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous…

ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…