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.     

Exploratory and Confirmatory Factor Analysis of the School Level Environment Questionnaire (SLEQ)

The purpose of the present study was to validate an existing school environment instrument, the School Level Environment Questionnaire (SLEQ). The SLEQ consists of 56 items, with seven items in each of eight scales. One thousand, one hundred and six (1106) teachers in 59 elementary schools in a southwestern USA public school district completed the instrument. An exploratory factor analysis was undertaken for a random sample of half of the completed surveys. Using principal axis factoring with oblique rotation, this analysis suggested that 13 items should be dropped and that the remaining 43 items could best be represented by seven rather than eight factors. A confirmatory factor analysis was run with the other half of the original sample using structural equation modeling. Examination of the fit indices indicated that the model came close to fitting the data, with goodness-of-fit (GOF) coefficients just below recommended levels. A second model was then run with two of the seven factors, with their associated items removed. That left five factors with 35 items. Model fit was improved. A third model was tried, using the same five factors with 35 items but with correlated residuals between some of the items within a factor. This model seemed to fit the data well, with GOF coefficients in recommended ranges. These results led to a refined, more parsimonious version of the SLEQ that was then used in a larger study. Future research is needed to see if this model would fit other samples in different elementary schools and in secondary schools both in the USA and in other countries. This revised version was published online in July 2006 with corrections to the Cover Date.     

Factor Retention in Exploratory Factor Analysis With Missing Data

Determining the number of factors in exploratory factor analysis is arguably the most crucial decision a researcher faces when conducting the analysis. While several simulation studies exist that compare various so-called factor retention criteria under different data conditions, little is known about the impact of missing data on this process. Hence, in this study, we evaluated the performance of different factor retention criteria—the Factor Forest, parallel analysis based on a principal component analysis as well as parallel analysis based on the common factor model and the comparison data approach—in combination with different missing data methods, namely an expectation-maximization algorithm called Amelia, predictive mean matching, and random forest imputation within the multiple imputations by chained equations (MICE) framework as well as pairwise deletion with regard to their accuracy in determining the number of factors when data are missing. Data were simulated for different sample sizes, numbers of factors, numbers of manifest variables (indicators), between-factor correlations, missing data mechanisms and proportions of missing values. In the majority of conditions and for all factor retention criteria except the comparison data approach, the missing data mechanism had little impact on the accuracy and pairwise deletion performed comparably well as the more sophisticated imputation methods. In some conditions, especially small-sample cases and when comparison data were used to determine the number of factors, random forest imputation was preferable to other missing data methods, though. Accordingly, depending on data characteristics and the selected factor retention criterion, choosing an appropriate missing data method is crucial to obtain a valid estimate of the number of factors to extract.     

Exploratory Graph Analysis for Factor Retention: Simulation Results for Continuous and Binary Data

Exploratory graph analysis (EGA) is a commonly applied technique intended to help social scientists discover latent variables. Yet, the results can be influenced by the methodological decisions the researcher makes along the way. In this article, we focus on the choice regarding the number of factors to retain: We compare the performance of the recently developed EGA with various traditional factor retention criteria. We use both continuous and binary data, as evidence regarding the accuracy of such criteria in the latter case is scarce. Simulation results, based on scenarios resulting from varying sample size, communalities from major factors, interfactor correlations, skewness, and correlation measure, show that EGA outperforms the traditional factor retention criteria considered in most cases in terms of bias and accuracy. In addition, we show that factor retention decisions for binary data are preferably made using Pearson, instead of tetrachoric, correlations, which is contradictory to popular belief.     

Reordering and Reflecting Factors for Simulation Studies With Exploratory Factor Analysis

This article describes the REREFACT R package, which provides a postrotation algorithm that reorders or reflects factors for each replication of a simulation study with exploratory factor analysis (EFA). The purpose of REREFACT is to provide a general algorithm written in freely available software, R, dedicated to addressing the possibility that a nonuniform order or sign pattern of the factors could be observed across replications. The algorithm implemented in REREFACT proceeds in 4 steps. Step 1 determines the total number of equivalent forms, I, of the vector of factors, η. Step 2 indexes, i = 1, 2 … I, each equivalent form of η (i.e., ηⁱ) via a unique permutation matrix, P (i.e., Pⁱ). Step 3 determines which ηⁱ each replication follows. Step 4 uses the appropriate Pⁱ to reorder or re-sign parameter estimates within each replication so that all replications uniformly follow the order and sign pattern defined by the population values. Results from two simulation studies provided evidence for the efficacy of the REREFACT to identify and remediate equivalent forms of η in models with EFA only (i.e., Example 1) and in fuller parameterizations of exploratory structural equation modeling (i.e., Example 2). How to use REREFACT is briefly demonstrated prior to the Discussion section by providing annotations for key commands and condensed output using a subset of simulated data from Example 1.     

The Poor Fit of Model Fit for Selecting Number of Factors in Exploratory Factor Analysis for Scale Evaluation

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker–Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework.     

初中生自主性结构的探索性因素分析

采用自编的<初中生自主性发展自陈问卷>,对随机抽取的257名初中生进行问卷调查,运用探索性因素分析得出了初中生自主性的结构.结果表明:(1)初中生自主性的结构包括自我依靠、自我控制和自我主张3个方面.(2)本研究编制的<初中生自主性发展自陈问卷>具有较高的信度与效度.     

On the Exploratory Road to Unraveling Factor Loading Non-invariance: A New Multigroup Rotation Approach

Multigroup exploratory factor analysis (EFA) has gained popularity to address measurement invariance for two reasons. Firstly, repeatedly respecifying confirmatory factor analysis (CFA) models strongly capitalizes on chance and using EFA as a precursor works better. Secondly, the fixed zero loadings of CFA are often too restrictive. In multigroup EFA, factor loading invariance is rejected if the fit decreases significantly when fixing the loadings to be equal across groups. To locate the precise factor loading non-invariances by means of hypothesis testing, the factors’ rotational freedom needs to be resolved per group. In the literature, a solution exists for identifying optimal rotations for one group or invariant loadings across groups. Building on this, we present multigroup factor rotation (MGFR) for identifying loading non-invariances. Specifically, MGFR rotates group-specific loadings both to simple structure and between-group agreement, while disentangling loading differences from differences in the structural model (i.e., factor (co)variances).     

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.     

Exploratory Mediation Analysis via Regularization

Exploratory mediation analysis refers to a class of methods used to identify a set of potential mediators of a process of interest. Despite its exploratory nature, conventional approaches are rooted in confirmatory traditions, and as such have limitations in exploratory contexts. We propose a two-stage approach called exploratory mediation analysis via regularization (XMed) to better address these concerns. We demonstrate that this approach is able to correctly identify mediators more often than conventional approaches and that its estimates are unbiased. Finally, this approach is illustrated through an empirical example examining the relationship between college acceptance and enrollment.     

新建本科院校教学督导影响因素的探索性分析

教学督导工作影响因素由督导成效、督导环境、督导队伍、教师情绪和督导精力五个维度组成．五个维度的累积解释率为67．241％。独立样本T检验结果显示,前四个维度在不同性别方面无显著性差异,在督导精力方面有显著性差异。     

Exploratory Structural Equation Modeling,Integrating CFA and EFA: Application to Students' Evaluations of University Teaching

This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching (SETs). For these data, there is a well established ESEM structure but typical CFA models do not fit the data and substantially inflate correlations among the nine SET factors (median rs = .34 for ESEM, .72 for CFA) in a way that undermines discriminant validity and usefulness as diagnostic feedback. A 13-model taxonomy of ESEM measurement invariance is proposed, showing complete invariance (factor loadings, factor correlations, item uniquenesses, item intercepts, latent means) over multiple groups based on the SETs collected in the first and second halves of a 13-year period. Fully latent ESEM growth models that unconfounded measurement error from communality showed almost no linear or quadratic effects over this 13-year period. Latent multiple indicators multiple causes models showed that relations with background variables (workload/difficulty, class size, prior subject interest, expected grades) were small in size and varied systematically for different ESEM SET factors, supporting their discriminant validity and a construct validity interpretation of the relations. A new approach to higher order ESEM was demonstrated, but was not fully appropriate for these data. Based on ESEM methodology, substantively important questions were addressed that could not be appropriately addressed with a traditional CFA approach.     

C.TEST语言能力的探索性因素分析

本文运用主成分分析法和ML方法对C.TEST进行探索性因素分析。在C.TEST(A—D级)试卷中,提取到了3个公共因素,我们认为C.TEST(A—D级)至少考察到了应试者听的能力、汉字书写能力和图表的识别能力。在C.TEST(E—F级)试卷中,也提取到3个公共因素,我们认为C.TEST(E—F级)至少考察到了应试者听的能力、读的能力和汉语拼音认读能力。这说明C.TEST除了具有较高的信度外,还具有良好的构想效度,即测到了测验设计者想要测到的东西。     

基于因子分析的中国服务贸易影响因素研究

通过对1985—2010年的相关数据进行因子分析,可以得出影响服务贸易的三个因子:国内消费需求、宏观经济现状及预期、货物贸易及人力资本的拉动。在不同时期,三个因子的重要性不同。我国发展服务贸易,应从市场规模和经济结构两方面入手,让其相互促进、相互配合。     

我国本科经济学教学方法的经济学分析

无论是为了满足我国经济发展对经济人才的需要,还是从提高我国经济学研究水平、培养下一代能够处于世界经济学前沿的经济学家出发,都需要提高经济学本科教学水平.在这之中,教学方法选择是一个关键问题.本文在教育学一般原理的基础上,利用经济学分析方法讨论了教学方法选择问题,本文认为,利用实验辅助教学是一种较好的方法,并进一步讨论了如何设计合理的实验.     

Factor structure of the WISC‐V in four standardization age groups: Exploratory and hierarchical factor analyses with the 16 primary and secondary subtests

This study examined the factor structure of the Wechsler Intelligence Scale for Children‐Fifth Edition (WISC‐V) with four standardization sample age groups (6–8, 9–11, 12–14, 15–16 years) using exploratory factor analysis (EFA), multiple factor extraction criteria, and hierarchical EFA not included in the WISC‐V Technical and Interpretation Manual. Factor extraction criteria suggested that one to four factors might be sufficient despite the publisher‐promoted, five‐factor solution. Forced extraction of five factors resulted in only one WISC‐V subtest obtaining a salient pattern coefficient on the fifth factor in all four groups, rendering it inadequate. Evidence did not support the publisher's desire to split Perceptual Reasoning into separate Visual Spatial and Fluid Reasoning dimensions. Results indicated that most WISC‐V subtests were properly associated with the four theoretically oriented first‐order factors resembling the WISC‐IV, the g factor accounted for large portions of total and common variance, and the four first‐order group factors accounted for small portions of total and common variance. Results were consistent with EFA of the WISC‐V total standardization sample.     

A Systematic Evaluation and Comparison Between Exploratory Structural Equation Modeling and Bayesian Structural Equation Modeling

In this study, we contrast two competing approaches, not previously compared, that balance the rigor of CFA/SEM with the flexibility to fit realistically complex data. Exploratory SEM (ESEM) is claimed to provide an optimal compromise between EFA and CFA/SEM. Alternatively, a family of three Bayesian SEMs (BSEMs) replace fixed-zero estimates with informative, small-variance priors for different subsets of parameters: cross-loadings (CL), residual covariances (RC), or CLs and RCs (CLRC). In Study 1, using three simulation studies, results showed that (1) BSEM-CL performed more closely to ESEM; (2) BSEM-CLRC did not provide more accurate model estimation compared with BSEM-CL; (3) BSEM-RC provided unstable estimation; and (4) different specifications of targeted values in ESEM and informative priors in BSEM have significant impacts on model estimation. The real data analysis (Study 2) showed that the differences in estimation between different models were largely consistent with those in Study1 but somewhat smaller.     

浅谈初中化学探究性教学

通过对初中化学探究性教学的探讨,提出了探究性教学的方法,同时提出了探究性教学的模式。     

美国"基于学分的过渡计划"探析

为了提高大学教育机会及学位获得率,美国高中和中等后教育机构制定了"基于学分的过渡计划".这些计划通过促进学生由高中到中等后教育的过渡衔接了高中与中等后教育.本文介绍了美国"基于学分的过渡计划",并分析了其发展的原因及实施对美国教育产生的影响,以期对我国的教育有所借鉴.