Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to…

Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

Why should our life science colleagues adopt, adapt, and implement fractal thinking into their research and teaching paradigms? While numerous articles and books have been written about the utility, power, and insight that can be gained by using fractal analysis of data and developing fractal models, other than just appreciating the beauty of…

The standard model of particle physics is the most successful theory describing the behavior of matter and energy in the subatomic realm. However, success doesn't mean it is perfect, and a recent measurement of the mass of a particle called the W boson is puzzling, as it disagrees with theoretical predictions and earlier precise measurements. If…

The purpose of this paper is to propose a revision of the well-known Campbellian system for causal research. The revised system, termed the COPS model, applies to both applied and basic research. Five validities are included, where two validities are adopted from the Campbellian system, and the validities are partly hierarchically ordered.…

This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

Online discussion forums are highly valued by instructors due to their affordance for understanding class activities and learning. However, a discussion forum with a great number of posts requires a large amount of time to view, and help requests are easily overlooked. Various machine-learning--based tools have been developed to help instructors…

Federal law requires that state accountability systems include "another academic indicator" for elementary and middle schools in addition to academic achievement. Nearly all states use a measure of student longitudinal growth as their other academic indicator. But how should states decide which growth model to use? The Center for…

The purpose of the study is to form a methodological approach to managing the professional development of employees in order to achieve the maximum effect of the digital transformation of the organisation. The authors analysed the environment for implementing the processes of digitalisation of organisations in Russia, identified existing…

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian…

Before creating and implementing a new program of research, it is necessary to consider a theoretical or conceptual framework to guide this planning process. Considering there are many models and frameworks available in terms of directing the development of research programs (e.g., the program development model, the logic model), researchers want…

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit…

Science labs should promote reasoning that resembles the work that scientists do. However, this is often not the case. We present a lab in which students strive to find out which of two models best describes a physics experiment. The quantification of measurement uncertainties--another topic that is often neglected in high school…