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…

Grouped and right-censored (GRC) counts have been used in a wide range of attitudinal and behavioural surveys yet they cannot be readily analyzed or assessed by conventional statistical models. This study develops a unified regression framework for the design and optimality of GRC counts in surveys. To process infinitely many grouping schemes for…

In every culture and era, education is considered the most fundamental reality and rule that societies prioritize and deem essential. Throughout the process spanning thousands of years, from the emergence of writing to the present day, education has undergone various forms and formats of change. Education has been a continuous guide for shaping,…

Predicting learner performance with precision is critical within educational systems, offering a basis for tailored interventions and instruction. The advent of big data analytics presents an opportunity to employ Machine Learning (ML) techniques to this end. Real-world data availability is often hampered by privacy concerns, prompting a shift…

Interactive learning environments can generate massive learning behavior data and the support of learning behavior big data can ensure the completeness of data analysis and robustness of relationship verification. In this study, learning behaviors are divided into training set and testing set, BP neural network and recurrent Elman network are…

A wide range of machine-learning-based approaches have been developed in the past decade, increasing our ability to accurately model nonlinear and nonadditive response surfaces. This has improved performance for inferential tasks such as estimating average treatment effects in situations where standard parametric models may not fit the data well.…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in…

Over the past few years, academics have undertaken initiatives to bridge the gap between theory and practice in the ever-growing field of business analytics, including implementing real-life student projects in all shapes and forms. Every year since 2015, Manhattan College has invited student teams from across North America and elsewhere in the…

This article revisits the Mincer earnings function and presents comparable estimates of the average monetary returns associated with an additional year of education across different regions worldwide. In contrast to the traditional Ordinary Least Squares (OLS) method commonly employed in the literature, this study applied a cutting-edge approach…

The methodology and mathematical treatment of several classic multivariate methods for the analysis of spectroscopic data is demonstrated in a straightforward way that can be used as a basis for teaching an undergraduate introductory course on chemometric analysis. The multivariate techniques of classical least-squares (CLS), principal component…

This study aims to reveal the main trends and findings of the studies examining the use of learning analytics in distance education. For this purpose, journal articles indexed in the SSCI index in the Web of Science database were reviewed, and a total of 400 journal articles were analysed within the scope of this study. The systematic review…

A method for the least squares regression of one squared variable on a second squared variable when the relationship between the original variables is linear is given. The problem arises in multidimensional scaling algorithms. (Author/JKS)

A globally optimal solution is presented for a class of functions composed of a linear regression function and a penalty function for the sums of squared regression weights. A completing-the-squares approach is used, rather than calculus, because it yields global minimality easily in two of three cases examined. (SLD)

The Gibbs sampling algorithms presented by M. H. Seltzer (1993) are fully generalized to a broad range of settings in which vectors of random regression parameters in the hierarchical model are assumed multivariate normally or multivariate "t" distributed across groups. The use of a fully Bayesian approach is discussed. (SLD)

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. An example is presented to demonstrate potential problems in other approaches to maximum likelihood factor analysis. (Author/JKS)