Nonlinear Mixed-Effects Modeling Programs in R

In this software review, we provide a brief overview of four R functions to estimate nonlinear mixed-effects programs: nlme (linear and nonlinear mixed-effects model), nlmer (from the lme4 package, linear mixed-effects models using Eigen and S4), saemix (stochastic approximation expectation maximization), and brms (Bayesian regression models using Stan). We briefly describe the approaches used, provide a sample code, and highlight strengths and weaknesses of each.     

Modeling Randomness in Judging Rating Scales with a Random-Effects Rating Scale Model

This study presents the random-effects rating scale model (RE-RSM) which takes into account randomness in the thresholds over persons by treating them as random-effects and adding a random variable for each threshold in the rating scale model (RSM) ( Andrich, 1978 ). The RE-RSM turns out to be a special case of the multidimensional random coefficients multinomial logit model (MRCMLM) ( Adams, Wilson, & Wang, 1997 ) so that the estimation procedures for the MRCMLM can be directly applied. The results of the simulation indicated that when the data were generated from the RSM, using the RSM and the RE-RSM to fit the data made little difference: both resulting in accurate parameter recovery. When the data were generated from the RE-RSM, using the RE-RSM to fit the data resulted in unbiased estimates, whereas using the RSM resulted in biased estimates, large fit statistics for the thresholds, and inflated test reliability. An empirical example of 10 items with four-point rating scales was illustrated in which four models were compared: the RSM, the RE-RSM, the partial credit model ( Masters, 1982 ), and the constrained random-effects partial credit model. In this real data set, the need for a random-effects formulation becomes clear.     

Generalized Linear Mixed-Effects Modeling Programs in R for Binary Outcomes

We review, examine the performance, and discuss the relative strengths and weaknesses of various R functions for the estimation of generalized linear mixed-effects models (GLMMs) for binary outcomes. The R functions reviewed include glmer in the package lme4, hglm2 in the package hglm, MCMCglmm in the package MCMCglmm, and inla in the package INLA. We illustrate the use of these functions through an empirical example and provide sample code.     

Growth curve analysis of ability means and variances in measures of fluid intelligence of older adults

This article is concerned with an application of growth curve analysis to modeling test performance changes demonstrated by older adults following cognitive training or based on experience with repeatedly presented fluid intelligence measures. Group differences and invariance in change over time in ability means and indices of interindividual differences at the ability level in a 2‐group cognitive intervention study (Baltes, Dittmann‐Kohli, & Kliegl, 1986) are examined using 3 latent curve analysis (Meredith & Tisak, 1990) models. The results indicate (a) group equivalence in the pattern of temporal development of ability variances and (b) training effects in the experimental group that are stronger than the practice/experience effects in the control group, whereby both types of effects are maintained over the 6‐month testing period. The findings provide further suggestive evidence for plasticity in fluid intelligence of elderly adults (cf. Baltes et al., 1986; Raykov, 1995, 1996).     

Testing Expert-Based Versus Student-Based Cognitive Models for a Grade 3 Diagnostic Mathematics Assessment

The purpose of this study was to evaluate the adequacy of three cognitive models, one developed by content experts and two generated from student verbal reports for explaining examinee performance on a grade 3 diagnostic mathematics test. For this study, the items were developed to directly measure the attributes in the cognitive model. The performance of each cognitive model was evaluated by examining its fit to different data samples: verbal report, total, high-, moderate-, and low ability using the Hierarchy Consistency Index (Cui & Leighton, 2009), a model-data fit index. This study utilized cognitive diagnostic assessments developed under the framework of construct-centered test design and analyzed using the Attribute Hierarchy Method (Gierl, Wang, & Zhou, 2008; Leighton, Gierl, & Hunka, 2004). Both the expert-based and the student-based cognitive models provided excellent fit to the verbal report and high ability samples, but moderate to poor fit to the total, moderate and low ability samples. Implications for cognitive model development for cognitive diagnostic assessment are discussed.     

Integration and representation in rats’ serial pattern learning in the T-maze

Rats were exposed to three-trial series consisting of reinforced (R) trials and one nonreinforced (N) trial in a fixed order, RRN and RNR (Experiments 1 and 2) or NRR and RRN (Experiment 3), on extended visually distinct runways in a T-maze. When initially presented with the same sequence on each series in a session (separate presentations) with the same runway on all trials within a series (Experiments 1 and 3), all the rats developed slower running speeds on N than on R trials. When a runway was sometimes changed between the first and next two trials during separate presentations training (Experiment 2) or both sequences were later intermixed within each session in each experiment, only rats exposed to each sequence on a specific runway maintained these serial running patterns. Rats displayed serial running patterns on a test RNN sequence similar to that on the RNR sequence (Experiment 2), as would be predicted by an intertrial association model of serial pattern learning (Capaldi & Molina, 1979), but responded on test RRR and NRN sequences (Experiment 3) as would be predicted by an ordinal-trialtag/intratrial association model (Burns, Wiley, & Payne, 1986). Results from test series of free-choice trials in Experiments 1 and 2 failed to support a prediction of the intratrial association model that these rats would integrate RRN and RNR sequences. Rather than always selecting a baited runway on both the second and the third free-choice trials, the rats only selected a baited runway on the third trial on the basis of their choice on the second trial, as would be predicted by the intertrial association model. Only after experiencing all possible outcome sequences during forced-choice training in Experiment 3 did these rats predominantly select a baited runway on every free-choice trial.     

Modeling unidimensional categorization in monkeys

The categorization performance of monkeys on a unidimensional perceptual categorization task was examined with reference to decision bound and exemplar theories of categorization. Three rhesus monkeys were presented with stimuli varying along a single dimension, the displacement of a target light from a fixation point. Left or right saccade responses were probabilistically reinforced according to one of three functions, two of which were nonmonotonic at one end of the stimulus space. The monkeys all showed a monotonic increase in response probability as a function of target light displacement in this region, consistent with decision bound theory. Fits of a single-boundary model (GRT; Ashby & Gott, 1988) and two exemplar models—one using a probabilistic response function (GCM; Nosofsky, 1986), the other using a deterministic response function (DEM; Ashby & Maddox, 1993)—revealed overall support for the decision bound model. The results suggest that monkeys used a perceptual decision boundary to perform the task.     

Structural Equation Modeling Diagnostics Using R Package semdiag and EQS

Yuan and Hayashi (2010) Yuan, K.-H. and Hayashi, K. 2010. Fitting data to model: Structural equation modeling diagnosis using two scatter plots. Psychological Methods, 15: 335–351. [Crossref], [Web of Science ®] , [Google Scholar] introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS syntax, one only needs to supply as few as 2 parameters to generate the 2 plots using the semdiag package. Two examples are provided to illustrate the use of the package. Multiple figures are used to explain the elements of data and model diagnostics. Advice on selecting proper estimation methods following the diagnostics is also given.     

Plasticity in fluid intelligence of older adults: An individual latent growth curve modeling application

This article is concerned with modeling the individual latent growth curves of older adults on measures of fluid intelligence in a 2‐group cognitive intervention study (Baltes, Dittmann‐Kohli, & Kliegl, 1986). Second‐order polynomial growth curves reflecting initial test performance improvement followed by relative stability/drop are fitted to the recorded scores of each participant. Experimental subjects are found to exhibit mean ability growth outperforming that shown by untrained subjects. Both the control and experimental groups, however, demonstrate the same pattern of interrelationships among the individual ability intercepts, linear slopes, and quadratic bend parameters of the growth curves. The results suggest substantial amount of plasticity in fluid intelligence of older adults, and that elders may be capable of considerably improving their performance on repeatedly presented fluid measures by capitalizing on interrelationships between fluid intelligence subabilities.     

semPlot: Unified Visualizations of Structural Equation Models

Structural equation modeling (SEM) has a long history of representing models graphically as path diagrams. This article presents the freely available semPlot package for R, which fills the gap between advanced, but time-consuming, graphical software and the limited graphics produced automatically by SEM software. In addition, semPlot offers more functionality than drawing path diagrams: It can act as a common ground for importing SEM results into R. Any result usable as input to semPlot can also be represented in any of the 3 popular SEM frameworks, as well as translated to input syntax for the R packages sem (Fox, Nie, & Byrnes, 2013) and lavaan (Rosseel, 2012). Special considerations are made in the package for the automatic placement of variables, using 3 novel algorithms that extend the earlier work of Boker, McArdle, and Neale (2002). The article concludes with detailed instructions on these node-placement algorithms.     

An algorithm for 3D shape matching using spherical sectioning

3D shape searching is a problem of current interest in several different fields. Most techniques are developed for a particular domain and used to reduce a shape into a simpler shape representation. The techniques developed for a particular domain will also find application in other domains. We propose a new shape matching method. The SSRD （spherical sectioning railroad diagram） algorithm has the general shape distribution＇s properties and overall features of the original model. The SSRD＇s useful properties are discussed. We show the experimental results for the validity of our method.     

Measuring sports class learning climates: The development of the Sports Class Environment Scale

The development and validation of a new and unique learning climate instrument, the Sports Class Environment Scale (SCES), was the focus of this study. We began with a consolidation of the dimensions and items of the Perceived Motivational Climate in Sport Questionnaire–2 and the Classroom Environment Scale. Field-testing of the SCES involved 204 competitive gymnasts from six metropolitan and four regional competitive gymnastics clubs in Queensland, Australia. Exploratory factor analysis provided a revised SCES with five scales labelled Task Involvement & Improvement, Ego Involvement & Mistakes, Coach–Athlete Communication, Effort, Order & Organisation, and Affiliation. Using scales of the revised SCES as dependent variables, multivariate analyses of variance were conducted to compare club types, genders and competitive levels. Effective measurement of sports class learning climates using the SCES could lead to a greater understanding of effective sports classes, and of coach and athlete behaviours in those classes, and provide a first step in monitoring sports class learning climates.     

Engaging in Science: A Feeling for the Discipline

Most accounts of affect and motivation in the science education literature have discussed them as relevant to, but distinct from, disciplinary pursuits. These include Pintrich’s seminal work on affective and motivational factors in learning science (P. R. Pintrich, 1999, 2003; P. R. Pintrich & E. De Groot, 1990; P. R. Pintrich, R. W. Marx, & R. A. Boyle, 1993). Our purpose here is to build on those ideas, drawing as well on accounts of scientists’ practices (e.g., H. E. Gruber, 1974; E. F. Keller, 1983) and of students’ taking up of disciplinary pursuits (R. A. Engle & F. R. Conant, 2002; R. Lehrer, 2009; M. Scardamalia & C. Bereiter, 1991, 2006) to propose that affect and motivation are inherent in the disciplinary practices of science. Thus, we introduce notions of epistemic affect and epistemic motivation, and we illustrate how these are evident in a case study of a student we have followed from 4th to 7th grade. We consider how this perspective aligns with and contributes to research on interest (e.g., S. Hidi, 2006; S. Hidi, K. A. Renninger, & A. Krapp, 2004; C. Sansone, 2009), and we discuss implications for research and instruction in science education. We argue that part of what should happen in the science class is to cultivate students’ feelings and motivations within the discipline.     

Designing Reflections on Practice: Helping Teachers Apply Cognitive Learning Principles in an SFT — Inquiry-Based Learning Program

The objective of this research into teacher education was to provide teachers with a deeper understanding of the cognitive goals of an inquiry-based learning program — Schools for Thought (SFT), and how these might be fostered using specific classroom activities. The classroom activities the workshops analyzed are derived from cognitive research aimed at fostering constructivist learning environments and include various strategies for facilitating collaborative learning and discussion among students (Bruer, 1993; Brown & Campione, 1994). The study documents 13 workshop sessions with teachers from grade 6,7, and 8. Teachers were asked to videotape segments of classroom activities in each of four phases of the SFT research cycle. The videotapes were edited by the authors and then discussed with teachers focusing on their effectiveness at implementing the cognitive goals for each unit phase. Analysis of these sessions reveal a shift in the focus of teachers' discussion from identifying procedures or the planning sequence of inquiry-based activities, to the usefulness these activities have for fostering specific cognitive and pedagogical goals. However, important differences remain in what researchers and teachers consider important when reflecting on teaching.     

Exploratory Factor Analysis (EFA) Programs in R

We provide a brief overview of two R packages that can conduct exploratory factor analysis (EFA): psych and EFAutilities. After introducing EFA and the exemplar data used in this paper we discuss best practices for EFA. Next, we describe the approaches used in the two packages for EFA. During this explanation, we provide sample code and discuss the usage and results of two empirical datasets. Finally, we highlight the similarities and distinctions of each package on modeling EFA.     

MplusAutomation: An R Package for Facilitating Large-Scale Latent Variable Analyses in Mplus

MplusAutomation is a package for R that facilitates complex latent variable analyses in Mplus involving comparisons among many models and parameters. More specifically, MplusAutomation provides tools to accomplish 3 objectives: to create and manage Mplus syntax for groups of related models; to automate the estimation of many models; and to extract, aggregate, and compare fit statistics, parameter estimates, and ancillary model outputs. We provide an introduction to the package using applied examples including a large-scale simulation study. By reducing the effort required for large-scale studies, a broad goal of MplusAutomation is to support methodological developments in structural equation modeling using Mplus.     

Development of a Meiosis Concept Inventory

We have designed, developed, and validated a 17-question Meiosis Concept Inventory (Meiosis CI) to diagnose student misconceptions on meiosis, which is a fundamental concept in genetics. We targeted large introductory biology and genetics courses and used published methodology for question development, which included the validation of questions by student interviews (n = 28), in-class testing of the questions by students (n = 193), and expert (n = 8) consensus on the correct answers. Our item analysis showed that the questions’ difficulty and discrimination indices were in agreement with published recommended standards and discriminated effectively between high- and low-scoring students. We foresee other institutions using the Meiosis CI as both a diagnostic tool and an instrument to assess teaching effectiveness and student progress, and invite instructors to visit http://q4b.biology.ubc.ca for more information.     

分段线性函数及其应用研究

分段线性连续函数是一类有着广泛应用的连续函数。本文首先证明：对任意的连续函数可用分段线性连续函数去一致逼近和一致收敛。其次,证明可把通过求分段线性连续函数的不动点来得到相应连续函数不动点的近似值。利用matlab程序,实现了在计算机上输出分段线性连续函数的所有不动点。最后,给出以上结论在经济学中的一个应用。