A Survey of the Social Development of the 10th, 11th,and 12th Grade Pupils in a Small High School

A potential weakness of quantitative methods is the intrusive nature of testing in general, and pretesting specifically. The Solomon four-group design ameliorates this difficulty, but because of statistical issues there are few published examples. W. Braver and Braver (1988) suggested the use of meta-analytic Stouffer's Z to combine the data from all four groups. Sawilowsky and Markman (1990a, 1990b, 1990c, 1990d) and Braver and W. Braver (1990a, 1990b) exchanged differing opinions on this approach. The present study is a Monte Carlo demonstration that the experiment-wise error rate inflates nearly triple nominal alpha. However, when not conducted as conditional tests, traditional procedures are more powerful than this meta-analytic approach, despite the ability of Stouffer's Z to combine all available data into a single statistic.     

Collapsing Categorical Variables and Measurement Invariance

Cross-cultural comparisons of latent variable means demands equivalent loadings and intercepts or thresholds. Although equivalence generally emphasizes items as originally designed, researchers sometimes modify response options in categorical items. For example, substantive research interests drive decisions to reduce the number of item categories. Further, categorical multiple-group confirmatory factor analysis (MG-CFA) methods generally require that the number of indicator categories is equal across groups; however, categories with few observations in at least one group can cause challenges. In the current paper, we examine the impact of collapsing ordinal response categories in MG-CFA. An empirical analysis and a complementary simulation study suggested meaningful impacts on model fit due to collapsing categories. We also found reduced scale reliability, measured as a function of Fisher’s information. Our findings further illustrated artifactual fit improvement, pointing to the possibility of data dredging for improved model-data consistency in challenging invariance contexts with large numbers of groups.     

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes and illustrates key features of Bayesian approaches to model diagnostics and assessing data–model fit of structural equation models, discussing their merits relative to traditional procedures.     

Implications of Parcel-Allocation Variability for Comparing Fit of Item-Solutions and Parcel-Solutions

This article relates a still-popular motivation for using parceling to an unrecognized cost. The still-popular motivation is improvement in fit with respect to the item-solution. The cost is uncertainty in fit due to the selection of one out of many possible item-to-parcel allocations. A theoretical framework establishes the reason for this relationship: The same mechanisms that cause larger item- versus parcel-solution differences in the minimized discrepancy function also cause larger allocation to allocation variability in the parcel-solution's minimized discrepancy function. Study 1 illustrates that these shared causal mechanisms lead to a strong positive association between average item–parcel differences in minimized discrepancy function values and parcel-allocation variability in those values. Study 2 extends these results from discrepancy function values to fit indexes, showing that the association remains positive, but varies in magnitude depending on what quantities other than the discrepancy function are involved in computing the fit index. The important implication for practice is that when item–parcel fit differences are large enough to alter conclusions about model adequacy, parcel-allocation variability tends to be large enough for parcel-solution model adequacy to depend on the particular allocation chosen.     

Comparing the Fit of Item Response Theory and Factor Analysis Models

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be compared. When applied to a binary data set, our experience suggests that IRT and FA models yield similar fits. However, when the data are polytomous ordinal, IRT models yield a better fit because they involve a higher number of parameters. But when fit is assessed using the root mean square error of approximation (RMSEA), similar fits are obtained again. We explain why. These test statistics have little power to distinguish between FA and IRT models; they are unable to detect that linear FA is misspecified when applied to ordinal data generated under an IRT model.     

Expert-Based cognitive models vs theory-based cognitive models: Which cognitive models match students’ cognition on ‘Parallel and Perpendicular Lines’ Better?

The cognitive model is a prominent element for supporting teachers' instructional needs regarding the confusing geometry topic named ‘Parallel and Perpendicular Lines’. Nonetheless, the mismatch between the derived cognitive models and the students’ cognition would threaten the validity of the diagnostic inferences made. While cognitive models could be developed by using different approaches, this study evaluated the model-data fit of the expert-based cognitive models which were developed by conducting expert task analysis and the theory-based cognitive models which were developed by reviewing the available theory. The study was conducted by adopting a cross-sectional research design. A total of 1 069 Grade Four students were selected by using two-stage cluster sampling. The findings indicated that the average model-data fit increased with the abilities of students for both theory-based and expert-based cognitive models on ‘Parallel and Perpendicular Lines’. Nonetheless, the theory-based cognitive models have a better model-data fit compared to the expert-based cognitive models. The findings imply the significance of the available theory of cognition in guiding the development of cognitive models. With satisfactory model-data fit, the theory-based cognitive models could serve as a guide for making diagnostic inferences on students' skill acquisition in the topic of 'Parallel and Perpendicular Lines'.     

试论大学物理实验数据处理法的选取

本文论述了大学物理实验的种类和层面及实验中数据处理的几种方法;重点论述了最小二乘法和线性拟合的原理,并分别用图解法、差分法和用线性拟合法对大学物理实验普朗克常数测定的实例数据进行处理,而后进行比较,提出了应根据实验目的而优选大学物理实验数据处理法.     

谈"切合题旨"的诸多制约因素

"切合题旨"是修辞的第一义.只有把握好了制约它的诸多因素,才能做到"切合题旨".制约"切合题旨"的主要因素有"时间、地点、场合、话题、对象、年龄、性别、身份、职业、修养、思想、性格、好恶、处境、风俗、信仰、方言、语体、风格"等等.     

A Regularized GLS for Structural Equation Modeling

Ill conditioning of covariance and weight matrices used in structural equation modeling (SEM) is a possible source of inadequate performance of SEM statistics in nonasymptotic samples. A maximum a posteriori (MAP) covariance matrix is proposed for weight matrix regularization in normal theory generalized least squares (GLS) estimation. Maximum likelihood (ML), GLS, and regularized GLS test statistics (RGLS and rGLS) are studied by simulation in a 15-variable, 3-factor model with 15 levels of sample size varying from 60 to 100,000. A key result showed that in terms of nominal rejection rates, RGLS outperformed ML at all sample sizes below 500, and GLS at most sample sizes below 500. In larger samples, their performance was equivalent. The second regularization methodology (rGLS) performed well asymptotically, but poorly in small samples. Regularization in SEM deserves further study.