Students' Behavioral and Emotional Participation in Academic Activities in the Mathematics Classroom: A Multilevel Confirmatory Factor Analysis

In this research, the authors raised the issue that prior studies had failed to address the nested structure of data in examining the construct validity of an instrument measuring students' behavioral and emotional participation in academic activities in the classroom. To address this question, the authors illustrated the utility of the multilevel confirmatory factor analysis (MCFA) approach to reexamine the construct validity of this instrument. The sample consisted of 2,041 students in 5th grade from 67 classes in Hong Kong. First, the results justified the requirement of MCFA and indicated that the 4-factor model tested with MCFA provided better fit to the data than that tested with a single-level confirmatory factor analysis (CFA). Second, the study also provided adequate support for a multilevel second-order two-factor model that distinguished engagement from disaffection. Third, the factor structure was invariant across the student level and the classroom level for both the 4-factor model and the second-order two-factor model. Fourth, the results highlighted the presence of ambiguity in differentiating between the dimensions at the classroom level and supported the unidimensionality of the classroom-level construct. Fifth, student engagement was significantly and positively correlated with mathematics test scores, teachers' classroom-management practices, teacher support, and student order in the classroom. Finally, the authors discuss the implications of the study and its limitations and offer suggestions for model selection and explorations for future research.     

Factorial structure of the New Ecological Paradigm scale in two French samples

The principal objective of this research is to test the factorial structure of the New Ecological Paradigm scale on a population of men and women residing in France. The tested model is a second-order factorial model. This factorial structure is evaluated on two separate samples to test the stability of the solution (a first sample of 253 participants, diversified in terms of age and socioprofessional category, and a second sample of 266 students). The results confirm the existence of a second-order factorial structure in which environmental beliefs, measured based on 13 items taken from the New Ecological Paradigm scale, would constitute a homogeneous system of beliefs supported in five distinct dimensions.     

An Assessment of the Quantitative Literacy of Undergraduate Students

Quantitative literacy (QLT) represents an underlying higher-order construct that accounts for a person's willingness to engage in quantitative situations in everyday life. The purpose of this study is to retest the construct validity of a model of quantitative literacy (Wilkins, 2010). In this model, QLT represents a second-order factor that accounts for the interrelationship among three first-order factors: mathematical beliefs, mathematical disposition, and mathematical cognition. Using data from two samples of undergraduate students (n = 186 and n = 184), a series of confirmatory factor analyses were conducted. Results supported the hierarchical three-factor structure and confirmed its factorial invariance across multiple groups of students. Latent QLT scores from the model were used to compare and rank student QLT by gender and class standing.     

城市居民消费结构变动的因子分析

在居民消费结构研究中,应用最广泛的是恩格尔系数和线性支出系统,但在进行消费结构变动分析时,因指标较多且各指标的变化趋势不尽相同,很难看出居民消费在某一方面的变动趋势.多元统计分析中的因子分析法正是解决这一问题的有力工具,文中利用因子分析法和DPS数据处理系统,对泰安城市居民消费结构的变动情况进行了分析.     

Preliminary development of the Brief–California School Climate Survey: dimensionality and measurement invariance across teachers and administrators

A brief 15-item version of the California School Climate Scale (Brief-CSCS) is presented to fill a need for a measure that could be used for periodic monitoring of school personnel's general perception of the climate of their school campus. From a sample of 81,261 California school personnel, random subsamples of 2,400 teachers and 2,400 administrators were used in the analyses. Confirmatory factor analyses supported a model in which general school climate was a second-order latent factor composed of 2 first-order latent traits, organizational supports and relational supports. Measurement invariance of factor loadings for teachers and administrators was found. Additional analyses revealed that administrators held more positive perceptions of school climate than teachers, with this difference increasing from primary through high school. The implications for these findings for educational research and policy reform are outlined.     

An international validation of the engaged teacher scale

The purpose of this study was to test and validate the Engaged Teacher Scale (ETS) in a Turkish context (ETS-TR). In order to test the construct validity of the ETS, data were collected from 388 teachers in two northeast cities of Turkey. First-order confirmatory factor analysis results supported the 16-item and four-factor model of ETS while second-order confirmatory factor analysis suggested that a single factor was also appropriate for representing teacher engagement. Additionally, four multiple linear regression analyses were conducted to provide further validation evidence. Results showed that subscales of the ETS-TR were found to be positively correlated with teacher self-efficacy. Given our evidence of validity and reliability, we recommend researchers interested in measuring the engagement of Turkish teachers to consider using the ETS-TR. The adaptation of ETS into Turkish also provides a measure for use when conducting research examining cultural comparisons between english-speaking and Turkish teachers.     

Model Misspecification and Invariance Testing Using Confirmatory Factor Analytic Procedures

Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near perfectly fitting models. In the present study, the authors examined procedures for detecting simulated test structure differences across groups under model misspecification conditions. In particular, they manipulated sample size, number of factors, number of indicators per factor, percentage of a lack of invariance, and model misspecification. Model misspecification was introduced at the factor loading level. They evaluated three criteria for detection of invariance, including the chi-square difference test, the difference in comparative fit index values, and the combination of the two. Results indicate that misspecification was associated with elevated Type I error rates in measurement invariance testing.     

A Multidimensional Approach to Understanding College Writing Processes

The aims of this study were to confirm the factor structure of college writing processes as measured by the Inventory of College Composition, and to test for a second-order, deep and surface structure, as suggested in the literature on college learning and writing. Confirmatory factor analysis was used to examine the dimensionality of the model based on the responses of 517 undergraduate students enrolled in general education courses. Results support the construct validity of the original model, as well as binary second-order factors, reflective of the deep and surface processes. Conclusions address the nature of the interrelationships of writing processes, and suggestions for instruction.     

Self-assessment instrument to measure the competencies of Namibian graduates: Testing of validity and reliability

Namibia has been reported to be one of the countries with the highest unemployment rates. In this work, the reliability and validity of the self-assessment instrument used to measure competencies of graduates in Namibia were assessed using exploratory factor analysis (EFA) and second-order confirmatory factor analysis (CFA). The EFA results demonstrated that the twenty indicators can be categorized into five factors, namely, “management and resilience”, “professional and communication”, “teamwork and critical thinking”, “self-control”, and “achievement motive”. The CFA results showed that all of the factors and indicators are highly reliable with good construct validity. Students and graduates could employ this validated self-assessment instrument to assess or diagnose a pattern of strengths and weaknesses in their own competencies and provide themselves with a realistic and objective estimate of their employability, as well as help them increase effectiveness in their workplace.     

Development and validation of two scales to measure elaboration and behaviors associated with stewardship in children

This investigation examines the development of two scales that measure elaboration and behaviors associated with stewardship in children. The scales were developed using confirmatory factor analysis to investigate their construct validity, reliability, and psychometric properties. Results suggest that a second-order factor model structure provides the best fit. This model produced: (1) a stewardship elaboration scale measuring interest and cognitive engagement in stewardship issues, and (2) a stewardship behavior scale measuring in-park, community, and home behaviors. These scales will be useful for evaluating environmental educational programs focused on environmental and park stewardship. The scales may also help researchers assess whether environmental education results in participants elaborating on persuasive messaging, thereby increasing the likelihood that behavioral intentions leading to behavior change will occur.     

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).     

Examining factorial validity and measurement invariance of the Student-Teacher Relationship Scale

The purposes of this study were to (a) test the hypothesized factor structure of the Student-Teacher Relationship Scale (STRS; Pianta, 2001) for 308 African American (AA) and European American (EA) children using confirmatory factor analysis (CFA) and (b) examine the measurement invariance of the factor structure across AA and EA children. CFA of the hypothesized three-factor model with correlated latent factors did not yield an optimal model fit. Parameter estimates obtained from CFA identified items with low factor loadings and R² values, suggesting that content revision is required for those items on the STRS. Deletion of two items from the scale yielded a good model fit, suggesting that the remaining 26 items reliably and validly measure the constructs for the whole sample. Tests for configural invariance, however, revealed that the underlying constructs may differ for AA and EA groups. Subsequent exploratory factor analyses (EFAs) for AA and EA children were carried out to investigate the comparability of the measurement model of the STRS across the groups. The results of EFAs provided evidence suggesting differential factor models of the STRS across AA and EA groups. This study provides implications for construct validity research and substantive research using the STRS given that the STRS is extensively used in intervention and research in early childhood education.     

Measurement Bias Detection Through Factor Analysis

Assessing the correctness of a structural equation model is essential to avoid drawing incorrect conclusions from empirical research. In the past, the chi-square test was recommended for assessing the correctness of the model but this test has been criticized because of its sensitivity to sample size. As a reaction, an abundance of fit indexes have been developed. The result of these developments is that structural equation modeling packages are now producing a large list of fit measures. One would think that this progression has led to a clear understanding of evaluating models with respect to model misspecifications. In this article we question the validity of approaches for model evaluation based on overall goodness-of-fit indexes. The argument against such usage is that they do not provide an adequate indication of the “size” of the model's misspecification. That is, they vary dramatically with the values of incidental parameters that are unrelated with the misspecification in the model. This is illustrated using simple but fundamental models. As an alternative method of model evaluation, we suggest using the expected parameter change in combination with the modification index (MI) and the power of the MI test.     

Maximum Likelihood Dynamic Factor Modeling for Arbitrary N and T Using SEM

This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary T and N by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time series analysis (T large and N = 1) and conventional SEM (N large and T = 1 or small) by integrating both approaches. The resulting combined model offers a variety of new modeling options including a direct test of the ergodicity hypothesis, according to which the factorial structure of an individual observed at many time points is identical to the factorial structure of a group of individuals observed at a single point in time. Third, we illustrate the flexibility of SEM time series modeling by extending the approach to account for complex error structures. We end with a discussion of current limitations and future applications of SEM-based time series modeling for arbitrary T and N.     

积极人格特质问卷PPTQ在中国大学生中的因素结构研究

探索积极人格特质问卷(PPTQ)在中国大学生中的因素结构。采用积极人格特质问卷(Positive Personality Traits Questionnaire)中文版,对648名大学生施测,对其中一半数据使用PASWStatistics18进行探索性因素分析,另一半数据使用AMOS16.0进行验证性因素分析(CFA)。探索性因素分析得出积极自我意象、外向性和文化认同三因素结构。累计解释率为50.457%,验证性因素分析结果显示:χ2/df=2.230,GFI=0.841。AGFI=0.816,CFI=0.822,RMSEA=0.062,中文版三因素结构在中国大学生人群中较为合理。     

A Simulation Study of Polychoric Instrumental Variable Estimation in Structural Equation Models

Data collected from questionnaires are often in ordinal scale. Unweighted least squares (ULS), diagonally weighted least squares (DWLS) and normal-theory maximum likelihood (ML) are commonly used methods to fit structural equation models. Consistency of these estimators demands no structural misspecification. In this article, we conduct a simulation study to compare the equation-by-equation polychoric instrumental variable (PIV) estimation with ULS, DWLS, and ML. Accuracy of PIV for the correctly specified model and robustness of PIV for misspecified models are investigated through a confirmatory factor analysis (CFA) model and a structural equation model with ordinal indicators. The effects of sample size and nonnormality of the underlying continuous variables are also examined. The simulation results show that PIV produces robust factor loading estimates in the CFA model and in structural equation models. PIV also produces robust path coefficient estimates in the model where valid instruments are used. However, robustness highly depends on the validity of instruments.     

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.     

Measurement invariance across information and communication technology development index and gender: The case of the Pearson Test of English Academic reading

The computerization of reading assessments has presented a set of new challenges to test designers. From the vantage point of measurement invariance, test designers must investigate whether the traditionally recognized causes for violating invariance are still a concern in computer-mediated assessments. In addition, it is necessary to understand the technology-related causes of measurement invariance among test-taking populations. In this study, we used the available data (n = 800) from the previous administrations of the Pearson Test of English Academic (PTE Academic) reading, an international test of English comprising 10 test items, to investigate measurement invariance across gender and the Information and Communication Technology Development index (IDI). We conducted a multi-group confirmatory factor analysis (CFA) to assess invariance at four levels: configural, metric, scalar, and structural. Overall, we were able to confirm structural invariance for the PTE Academic, which is a necessary condition for conducting fair assessments. Implications for computer-based education and the assessment of reading are discussed.     

因子分析模型在三产水平研究中的应用

对反映三产水平的19个观测变量建立因子分析模型,以最少因子刻画预期信息量为方向,以方差贡献为尺度,构造了4个具有代表性的公共因子,并通过载荷因子矩阵的旋转予以合理的命名解释,进一步利用公共因子的信息对我国30个省市的三产水平作了综合性评估,结论支持国家大力开发西部的政策倾向。     

影响我国税收收入增长因素的实证分析

当前税收收入与经济发展之间的关系是否协调,值得研究。通过建立回归模型,运用因素分析法、实证研究等方法,分析税收收入与其影响因素之间的关系,便于采取相应对策,以发挥税收促进财政收入和经济发展的作用。