The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM…

Analyzing and interpreting data is an important science practice that contributes toward the construction of models from data; yet, there is evidence that students may struggle with making meaning of data. The study reported here focused on characterizing students' approaches to analyzing rate and concentration data in the context of method of…

The relevance of research: The relevance of the problem studied is caused by the acceleration of transition of the Russian economy on an innovative way of development, which depends on the vector of innovative sphere of services and, to a large extent, information and communication services, as well as it is caused by the poor drafting of…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…

Schwartz and Martin ("Cogn Instr" 22:129-184, 2004) as well as Kapur ("Instr Sci", this issue, 2012) have found that students can be better prepared to learn about mathematical formulas when they try to invent them in small groups before receiving the canonical formula from a lesson. The purpose of the present research was to investigate how the…

Obtaining representative samples from populations of emerging adults who do not attend college is challenging for researchers. This article introduces respondent-driven sampling (RDS), a method for obtaining representative samples of hard-to-reach but socially interconnected populations. RDS combines a prescribed method for chain referral with a…

Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more…

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…

Multivariate matching in Differential Item Functioning (DIF) analyses may contribute to understand the sources of DIF. In this context, detecting appropriate additional matching variables is a crucial issue. This present article argues that the variables which are correlated with communalities in item difficulties can be used as an additional…

Although the "K"-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The "p"-median model is an especially well-studied clustering problem that requires the selection of "p" objects to serve as…

The notion of multidimensional structure is discussed within the framework of an additive component model of multidimensional scaling, where a configuration is considered to be composed of disjoint subspaces, each one of which reflects variation due to a specific stimulus component. Empirical examples are given. (Author/BW)

Data are often a continuous function of a variable such as time observed over some interval. One or more such functions might be observed for each subject. The extension of classical data analytic techniques to such functions is discussed. (Author/JKS)

A variety of problems associated with the interpretation of traditional canonical correlation are discussed. A response surface approach is developed which allows for investigation of changes in the coefficients while maintaining an optimum canonical correlation value. Also, a discrete or constrained canonical correlation method is presented. (JKS)

This paper explains how a major statistical package (BMDP) can be used to produce partial, semipartial, or bipartial set correlation in terms of a procedure outlined by Karpman (1980). (BW)

A revision of the initialization strategy is suggested for OSMOD, a method of nonlinear principal component analysis for multivariate nominal and/or ordinal data. The revision is effective in diminishing the possibility of obtaining locally optimal solutions with categorical data provided by the original version of OSMOD. (SLD)