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1.
A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-based F statistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort.  相似文献   

2.
Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have rarely been used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions.  相似文献   

3.
The number line estimation task is widely used to investigate mathematical learning and development. The present meta‐analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.  相似文献   

4.
Mucoepidermoid carcinoma undergoes uniquely vigorous angiogenic and neovascularization processes, possibly due to proliferation of vascular endothelial cells (ECs) induced by mucoepidermoid carcinoma cells (MCCs) in their three-dimensional (3D) microenvironment. To date, no studies have dealt with tumor cells and vascular ECs from the same origin of mucoepidermoid carcinoma using the in vitro 3D microenvironment model. In this context, the current research aims to observe neovascularization with mucoepidermoid carcinoma microvascular ECs (MCMECs) conditioned by the microenvironment in the 3D collagen matrix model. We observed the growth of MCMECs purified by immunomagnetic beads and induced by MCCs, and characteristics of tubule-like structures (TLSs) formed by induced MCMECs or non-induced MCMECs. The assessment parameters involved the growth curve, the length, the outer and inner diameters, and the wall thickness of the TLSs, and the cell cycle. Results showed that MCCs induced formation of the TLSs in the 3D collagen matrix model. A statistically significant difference was noted regarding the count of TLSs between the control group and the induction group on the 4th day of culture (t=5.00, P=0.001). The outer and inner diameters (t 1=5.549, P 1=0.000; t 2=10.663, P 2=0.000) and lengths (t=18.035, P=0.000) of the TLSs in the induction group were statistically significant larger than those in the control group. The TLSs were formed at the earlier time in the induction group compared with the control group. It is concluded that MCCs promote growth and migration of MCMECs, and formation of the TLSs. The 3D collagen matrix model with MCMECs induced by MCCs in the current research may be a favorable choice for research on pro-angiogenic factors in progression of mucoepidermoid carcinoma.  相似文献   

5.
In this article we describe a structural equation modeling (SEM) framework that allows nonnormal skewed distributions for the continuous observed and latent variables. This framework is based on the multivariate restricted skew t distribution. We demonstrate the advantages of skewed SEM over standard SEM modeling and challenge the notion that structural equation models should be based only on sample means and covariances. The skewed continuous distributions are also very useful in finite mixture modeling as they prevent the formation of spurious classes formed purely to compensate for deviations in the distributions from the standard bell curve distribution. This framework is implemented in Mplus Version 7.2.  相似文献   

6.
An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R 2 indexes associated with repeatedly followed measures in longitudinal studies. In addition to facilitating evaluation of local model fit, the approach is helpful for purposes of differentiating between plausible models stipulating different patterns of change over time, and in particular in empirical situations characterized by large samples and high statistical power. The procedure is also applicable in cross-sectional studies, as well as with general structural equation models. The method is illustrated using data from a nationally representative study of older adults.  相似文献   

7.
This study examined the effect of model size on the chi-square test statistics obtained from ordinal factor analysis models. The performance of six robust chi-square test statistics were compared across various conditions, including number of observed variables (p), number of factors, sample size, model (mis)specification, number of categories, and threshold distribution. Results showed that the unweighted least squares (ULS) robust chi-square statistics generally outperform the diagonally weighted least squares (DWLS) robust chi-square statistics. The ULSM estimator performed the best overall. However, when fitting ordinal factor analysis models with a large number of observed variables and small sample size, the ULSM-based chi-square tests may yield empirical variances that are noticeably larger than the theoretical values and inflated Type I error rates. On the other hand, when the number of observed variables is very large, the mean- and variance-corrected chi-square test statistics (e.g., based on ULSMV and WLSMV) could produce empirical variances conspicuously smaller than the theoretical values and Type I error rates lower than the nominal level, and demonstrate lower power rates to reject misspecified models. Recommendations for applied researchers and future empirical studies involving large models are provided.  相似文献   

8.
This study examined the performance of 4 correlation-based fit indexes (marginal and conditional pseudo R 2s; average and conditional concordance correlations) in detecting misspecification in mean structures in growth curve models. Their performance was also compared to that of 4 traditional SEM fit indexes. We found that the marginal pseudo R 2 and average concordance correlation were able to detect misspecification in the marginal mean structure (average change trajectory). The conditional pseudo R 2 and concordance correlation could detect misspecification when it occurred in the conditional mean structure (individual change trajectory) or in both mean structures. Compared to the SEM fit indexes, the correlation-based fit indexes were more robust to sample size but were less robust to data properties such as magnitude of population mean and measurement error. Theoretical and practical implications of the results and directions for future research are discussed.  相似文献   

9.
We describe and evaluate a random permutation test of measurement invariance with ordered-categorical data. To calculate a p-value for the observed (?)χ2, an empirical reference distribution is built by repeatedly shuffling the grouping variable, then saving the χ2 from a configural model, or the ?χ2 between configural and scalar-invariance models, fitted to each permuted dataset. The current gold standard in this context is a robust mean- and variance-adjusted ?χ2 test proposed by Satorra (2000), which yields inflated Type I errors, particularly when thresholds are asymmetric, unless samples sizes are quite large (Bandalos, 2014; Sass et al., 2014). In a Monte Carlo simulation, we compare permutation to three implementations of Satorra’s robust χ2 across a variety of conditions evaluating configural and scalar invariance. Results suggest permutation can better control Type I error rates while providing comparable power under conditions that the standard robust test yields inflated errors.  相似文献   

10.
As a cognitive-motivational construct, self-efficacy has been researched extensively and has involved two important lines of inquiries, namely the impact of sources of information on self-efficacy and the predictive effect of self-efficacy on learning outcomes. We proposed and tested the relations between the four major sources of information (enactive performance accomplishments, vicarious experiences, verbal persuasion and emotional and physiological states), self-efficacy and academic achievement for mathematics and science within one conceptual model. Our model was tested with the conjunctive use of longitudinal data and latent growth curve modelling (LGM) procedures. Two hundred and fifty-two (110 girls, 142 boys) upper elementary school children from three government schools participated in this longitudinal study. Likert-scale inventories were administered over four occasions within a one-year period. We measured the four sources of information at T 1, whereas self-efficacy for mathematics and science was measured at T 2–T 4, and academic achievement was measured at T 4 only. SPSS AMOS v18 was used to test a number of a priori multivariate growth curve models. LGM analyses provided moderate evidence in support of our conceptual model, noting different patterns of trajectories for both mathematics and science.  相似文献   

11.
In longitudinal design, investigating interindividual differences of intraindividual changes enables researchers to better understand the potential variety of development and growth. Although latent growth curve mixture models have been widely used, unstructured finite mixture models (uFMMs) are also useful as a preliminary tool and are expected to be more robust in identifying classes under the influence of possible model misspecifications, which are very common in actual practice. In this study, large-scale simulations were performed in which various normal uFMMs and nonnormal uFMMs were fit to evaluate their utility and the performance of each model selection procedure for estimating the number of classes in longitudinal designs. Results show that normal uFMMs assuming invariance of variance–covariance structures among classes perform better on average. Among model selection procedures, the Calinski–Harabasz statistic, which has a nonparametric nature, performed better on average than information criteria, including the Bayesian information criterion.  相似文献   

12.
This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long‐term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.  相似文献   

13.

Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed.

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14.
Widespread adoption of Response to Intervention (RtI) requires large numbers of educators to develop the knowledge and skills necessary to implement the model with fidelity. This study examined relationships between large‐scale professional development on RtI and educators’ perceived skills. Elementary educators (n = 4,283) from 34 pilot and 27 comparison schools in a southeastern state participated. Leadership teams composed of subsets of educators from pilot schools who were responsible for leading RtI implementation participated in 13 days of training across a 3‐year period. Additionally, job‐embedded coaching was provided to pilot school instructional educators. Results from multilevel models indicated that leadership team membership related to increases in educators’ perceptions of RtI skills applied to academics (π = .05; SE = .02; t[6,726] = 2.60; p < .05) and of data display skills (π = .07; SE = .03; t[6,678] = 2.45, p < .05). Educator participation at pilot schools that received job‐embedded coaching related to increases in perceptions of RtI skills applied to academics (β = .07; SE = .02; t[6,726] = 2.77, p < .05). Implications for future research on RtI implementation and the practice of providing large‐scale professional development focused on RtI are discussed.  相似文献   

15.
This study compares the ability of different robust regression estimators to detect and classify outliers. Well-known estimators with high breakdown points were compared using simulated data. Mean success rates （MSR） were computed and used as comparison criteria. The results showed that the least median of squares （LMS） and least trimmed squares （LTS） were the most successful methods for data that included leverage points, masking and swamping effects or critical and concentrated outliers. We recommend using LMS and LTS as diagnostic tools to classify outliers, because they remain robust even when applied to models that are heavily contaminated or that have a complicated structure of outliers.  相似文献   

16.
In a recent article, Castro-Schilo, Widaman, and Grimm (2013) compared different approaches for relating multitrait–multimethod (MTMM) data to external variables. Castro-Schilo et al. reported that estimated associations with external variables were in part biased when either the correlated traits–correlated uniqueness (CT-CU) or correlated traits–correlated (methods–1) [CT-C(M–1)] models were fit to data generated from the correlated traits–correlated methods (CT-CM) model, whereas the data-generating CT-CM model accurately reproduced these associations. Castro-Schilo et al. argued that the CT-CM model adequately represents the data-generating mechanism in MTMM studies, whereas the CT-CU and CT-C(M–1) models do not fully represent the MTMM structure. In this comment, we question whether the CT-CM model is more plausible as a data-generating model for MTMM data than the CT-C(M–1) model. We show that the CT-C(M–1) model can be formulated as a reparameterization of a basic MTMM true score model that leads to a meaningful and parsimonious representation of MTMM data. We advocate the use confirmatory factor analysis MTMM models in which latent trait, method, and error variables are explicitly and constructively defined based on psychometric theory.  相似文献   

17.
In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge. An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans, LA, April 2002.  相似文献   

18.
This paper investigates whether inferences about school performance based on longitudinal models are consistent when different assessments and metrics are used as the basis for analysis. Using norm-referenced (NRT) and standards-based (SBT) assessment results from panel data of a large heterogeneous school district, we examine inferences based on vertically equated scale scores, normal curve equivalents (NCEs), and nonvertically equated scale scores. The results indicate that the effect of the metric depends upon the evaluation objective. NCEs significantly underestimate absolute individual growth, but NCEs and scale scores yield highly correlated (r >.90) school-level results based on mean initial status and growth estimates. SBT and NRT results are highly correlated for status but only moderately correlated for growth. We also find that as few as 30 students per school provide consistent results and that mobility tends to affect inferences based on status but not growth – irrespective of the assessment or metric used.  相似文献   

19.
Intensive time-series designs for classroom investigations have been under development since 1975. Studies have been conducted to determine their feasibility (Mayer & Lewis, 1979), their potential for monitoring knowledge acquisition (Mayer & Kozlow, 1980), and the potential threat to validity of the frequency of testing inherent in the design (Mayer & Rojas, 1982). This study, an extension of those previous studies, is an attempt to determine the degree of discrimination the design allows in collecting data on achievement. It also serves as a replication of the Mayer and Kozlow study, an attempt to determine design validity for collecting achievement data. The investigator used her eighth-grade earth science students, from a suburban Columbus (Ohio) junior high school. A multiple-group single intervention time-series design (Glass, Willson, & Gottman, 1975) was adapted to the collection of daily data on achievement in the topic of the intervention, a unit on plate tectonics. Single multiple-choice items were randomly assigned to each of three groups of students, identified on the basis of their ranking on a written test of cognitive level (Lawson, 1978). The top third, or those with formal cognitive tendencies, were compared on the basis of knowledge achievement and understanding achievement with the lowest third of the students, or those with concrete cognitive tendencies, to determine if the data collected in the design would discriminate between the two groups. Several studies (Goodstein & Howe, 1978; Lawson & Renner, 1975) indicated that students with formal cognitive tendencies should learn a formal concept such as plate tectonics with greater understanding than should students with concrete cognitive tendencies. Analyses used were a comparison of regression lines in each of the three study stages: baseline, intervention, and follow-up; t-tests of means of days summed across each stage; and a time-series analysis program. Statistically significant differences were found between the two groups both in slopes of regression lines (0.0001) and in t-tests (0.0005) on both knowledge and understanding levels of learning. These differences confirm the discrimination of the intensive time-series design in showing that it can distinguish differences in learning between students with formal cognitive tendencies and those with concrete cognitive tendencies. The time-series analysis model with a trend in the intervention was better than a model with no trend for both groups of students, in that it accounted for a greater amount of variance in the data from both knowledge and understanding levels of learning. This finding adds additional confidence in the validity of the design for obtaining achievement data. When the analysis model with trend was used on data from the group with formal cognitive tendencies, it accounted for a greater degree of variance than the same model applied to the data from the group with concrete cognitive tendencies. This more conservative analysis, therefor, gave results consistent with those from the more usual linear regression techniques and t-tests, further adding to the confidence in the discrimination of the design.  相似文献   

20.
Extensive evidence has suggested mathematical skill in early childhood is a robust predictor of children's later academic skills and eventual labor market outcomes; however, there is substantial heterogeneity in the degree to which different students learn from the same instructional contexts. Using data from N = 12,082 children enrolled in the Early Childhood Longitudinal Study-Kindergarten Cohort, this paper employs a latent piecewise growth curve modeling approach to investigate the role of classroom math instruction and executive function and approaches to learning in the development of mathematical skills in kindergarten, first, and second grade. Findings suggest that overall instructional frequency relates to math development in kindergarten through second, and that this is driven by exposure to advanced content in kindergarten. Further, executive function moderates children's learning in kindergarten, such that children with higher levels of executive function benefit more from instruction than do those with lower levels.  相似文献   

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