Fuzzy-set qualitative comparative analysis (fsQCA) has become one of the most prominent methods in the social sciences for capturing causal complexity, especially for scholars with small- and medium-"N" data sets. This research note explores two key assumptions in fsQCA's methodology for testing for necessary and sufficient…

Two articles, Edelsbrunner and, Schneider (2013), and Nokelainen and Silander (2014) comment on Musso, Kyndt, Cascallar, and Dochy (2013). Several relevant issues are raised and some important clarifications are made in response to both commentaries. Predictive systems based on artificial neural networks continue to be the focus of current…

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

In this article, the authors discuss a pedagogical approach that connects the cultural aspects of mathematics with its academic aspects in which they refer to as ethnomodeling. Ethnomodeling is the process of translation and elaboration of problems and questions taken from systems that are part of the daily life of the members of any given…

A PUBMED search for "mathematical models in medicine" shows more than 15,000 articles covering almost every field of medicine. We designed a course with the goal of developing the students' skills in computerized data analysis and mathematical modelling, as well as enhancing their ability to read and interpret mathematical data analysis. The study…

Studies of group differences in intelligence often invite conclusions about groups in general from studies of group differences in selected populations. The same design is used in the study of group differences in other traits as well. Investigators observe samples from two groups (e.g. men and women) in some accessible population, but seek to…

Purpose: The present study was a methodological study designed to reveal the dynamic mechanisms of phonation instability pressure (PIP) using bifurcation analysis. Phonation pressure range (PPR) was also proposed for assessing the pressure range of normal vocal fold vibrations. Method: The authors first introduced the concept of bifurcation on the…

Math modeling is currently at the focus of educational methodologists' attention. However, little is known about the extent to which principles of the math modeling lead to methodological fallacies in educational research. The main purpose of this paper is to explore the nature and principles of math modeling and to examine its application in…

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

A simplified version of successive intervals scaling is described. Scale values for various datasets obtained with simplified successive intervals scaling are approximately linearly related to those obtained with traditional successive intervals scaling and the method of pair comparisons. The ease of use and some cautions in method use are…

This paper outlines two types of discriminant analysis, predictive discriminant analysis (PDA) and descriptive discriminant analysis (DDA). Important differences between PDA and DDA are introduced and discussed using a heuristic data set, specifically indicating the portions of the Statistical Package for the Social Sciences (SPSS) output relevant…

The issue of indeterminacy in factor analysis and the debate between the proposed alternative solution and posterior moment position are explored in an article and 14 commentaries and rebuttals in two rounds. Implications for applied work involving factor analysis are discussed. (SLD)

This paper, in a fashion easy to follow, illustrates the interesting relationship between structural equation modeling and canonical correlation analysis. Although computationally somewhat inconvenient, representing canonical correlation as a structural equation model may provide some information which is not available from conventional canonical…

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

An integrated overview is provided of selected multiple comparison methods, with an emphasis on the sequentially rejective Bonferroni (SRB) test and its modifications. Multiple comparisons of means is a frequently used, and yet confusing, method in educational and psychological research. Seven multiple comparison methods are reviewed: (1) the…