Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study

Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihood-based tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n = 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test proved to be a very consistent indicator of classes across all of the models considered.     

Testing Factorial Invariance in Multilevel Data: A Monte Carlo Study

Testing factorial invariance has recently gained more attention in different social science disciplines. Nevertheless, when examining factorial invariance, it is generally assumed that the observations are independent of each other, which might not be always true. In this study, we examined the impact of testing factorial invariance in multilevel data, especially when the dependency issue is not taken into account. We considered a set of design factors, including number of clusters, cluster size, and intraclass correlation (ICC) at different levels. The simulation results showed that the test of factorial invariance became more liberal (or had inflated Type I error rate) in terms of rejecting the null hypothesis of invariance held between groups when the dependency was not considered in the analysis. Additionally, the magnitude of the inflation in the Type I error rate was a function of both ICC and cluster size. Implications of the findings and limitations are discussed.     

Testing the Intervention Effect in Single-Case Experiments: A Monte Carlo Simulation Study

This article reports on a Monte Carlo simulation study, evaluating two approaches for testing the intervention effect in replicated randomized AB designs: two-level hierarchical linear modeling (HLM) and using the additive method to combine randomization test p values (RTcombiP). Four factors were manipulated: mean intervention effect, number of cases included in a study, number of measurement occasions for each case, and between-case variance. Under the simulated conditions, Type I error rate was under control at the nominal 5% level for both HLM and RTcombiP. Furthermore, for both procedures, a larger number of combined cases resulted in higher statistical power, with many realistic conditions reaching statistical power of 80% or higher. Smaller values for the between-case variance resulted in higher power for HLM. A larger number of data points resulted in higher power for RTcombiP.     

The Misspecification of the Covariance Structures in Multilevel Models for Single-Case Data: A Monte Carlo Simulation Study

The impact of misspecifying covariance matrices at the second and third levels of the three-level model is evaluated. Results indicate that ignoring existing covariance has no effect on the treatment effect estimate. In addition, the between-case variance estimates are unbiased when covariance is either modeled or ignored. If the research interest lies in the between-study variance estimate, including at least 30 studies is warranted. Modeling covariance does not result in less biased between-study variance estimates as the between-study covariance estimate is biased. When the research interest lies in the between-case covariance, the model including covariance results in unbiased between-case variance estimates. The three-level model appears to be less appropriate for estimating between-study variance if fewer than 30 studies are included.     

Modeling Causal Error Structures in Longitudinal Panel Data: A Monte Carlo Study

This research was designed to investigate how much more suitable moving average (MA) and autoregressive-moving average (ARMA) models are for longitudinal panel data in which measurement errors correlate than AR, quasi-simplex, and 1-factor models. The conclusions include (a) when testing for a stochastic process hypothesized to occur in a longitudinal data set, testing for other processes is necessary, because incorrect models often fit other processes well enough to be deceiving; (b) when measurement error correlations are flagged to be relatively high in panel data, the fit and propriety of an MA or ARMA model should be considered and compared to the fit and propriety of other models; (c) when an MA model is fit to AR data, measurement error correlations may nonetheless be deceptively high, though fortunately MA model fit indexes are almost always lower than those for an AR model; and (d) the assumption that longitudinal panel data always contain measurement error correlations is patently false. In summary, whenever evaluating longitudinal panel data, the fit, propriety, and parsimony of all 5 models should be considered jointly and compared before a particular model is endorsed as most suitable.     

一维长程相互作用吸附模型的临界点与作用强度之间的Monte Carlo模拟研究

利用动力学Monte Carlo方法对一维长程相互作用吸附模型进行计算机模拟研究, 得出了其临界点λc与作用力程r-1-α中的α在α>1．0时具有指数关系:λc=λc0 Be-α/γ．     

Detecting Violations of Factorial Invariance Using Data-Based Specification Searches: A Monte Carlo Study

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an alternative method for testing factorial invariance and evaluates the performance of the method in specification searches based on the modification index. The results of the study showed that the proposed specification searches performed well when the number of noninvariant variables was relatively small and this performance improved as sample size increased and the size of group differences increased. When the number of noninvariant variables was relatively large, however, the method rarely succeeded in detecting the noninvariant items in the specification searches. Implications of the findings are discussed along with the limitations of the study.     

Factor Analysis with Ordinal Indicators: A Monte Carlo Study Comparing DWLS and ULS Estimation

Factor analysis models with ordinal indicators are often estimated using a 3-stage procedure where the last stage involves obtaining parameter estimates by least squares from the sample polychoric correlations. A simulation study involving 324 conditions (1,000 replications per condition) was performed to compare the performance of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) in the procedure's third stage. Overall, both methods provided accurate and similar results. However, ULS was found to provide more accurate and less variable parameter estimates, as well as more precise standard errors and better coverage rates. Nevertheless, convergence rates for DWLS are higher. Our recommendation is therefore to use ULS, and, in the case of nonconvergence, to use DWLS, as this method might converge when ULS does not.     

CO催化氧化的实验与Monte Carlo模拟

主要对CO在Pt表面催化氧化反应的实验做了具体描述,介绍以ZGB模型为基础的MC模拟方法,得到一系列与实验较接近的模拟结果.在模拟中,重点考察重构表面的诱导相变和反应物的脱附等因素对反应的影响.     

Examining and Controlling for Wording Effect in a Self-Report Measure: A Monte Carlo Simulation Study

Wording effect refers to the systematic method variance caused by positive and negative item wordings on a self-report measure. This Monte Carlo simulation study investigated the impact of ignoring wording effect on the reliability and validity estimates of a self-report measure. Four factors were considered in the simulation design: (a) the number of positively and negatively worded items, (b) the loadings on the trait and the wording effect factors, (c) sample size, and (d) the magnitude of population validity coefficient. The findings suggest that the unidimensional model that ignores the negative wording effect would underestimate the composite reliability and criterion-related validity, but overestimate the homogeneity coefficient. The magnitude of relative bias of the composite reliability was generally small and acceptable, whereas the relative bias for the homogeneity coefficient and criterion-related validity coefficient was negatively correlated with the strength of the general trait factor.     

Sample Size Requirements in Single- and Multiphase Growth Mixture Models: A Monte Carlo Simulation Study

Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the sample sizes required for using these models are investigated under various theoretical and realistic conditions. In particular, the relationship between the sample size requirement and the number of indicator variables is examined, because the number of indicators can be relatively easily controlled by researchers in many multiphase data collection settings such as ecological momentary assessment. The findings not only provide tangible information about required sample sizes under various conditions to help researchers, but they also increase understanding of sample size requirements in single- and multiphase growth mixture models.     

Comparing Multilevel and Classical Confirmatory Factor Analysis Parameterizations of Multirater Data: A Monte Carlo Simulation Study

This simulation study assesses the statistical performance of two mathematically equivalent parameterizations for multitrait–multimethod data with interchangeable raters—a multilevel confirmatory factor analysis (CFA) and a classical CFA parameterization. The sample sizes of targets and raters, the factorial structure of the trait factors, and rater missingness are varied. The classical CFA approach yields a high proportion of improper solutions under conditions with small sample sizes and indicator-specific trait factors. In general, trait factor related parameters are more sensitive to bias than other types of parameters. For multilevel CFAs, there is a drastic bias in fit statistics under conditions with unidimensional trait factors on the between level, where root mean square error of approximation (RMSEA) and χ2 distributions reveal a downward bias, whereas the between standardized root mean square residual is biased upwards. In contrast, RMSEA and χ2 for classical CFA models are severely upwardly biased in conditions with a high number of raters and a small number of targets.     

关于小组讨论形式口语考试的概化研究

小组讨论形式的口语考试既可以提高考试的效率,又能考到总结谈话等面试考试所考不到的谈话管理能力,所以被认为是可以应用在一般教学环境中的有效的口语考试方式。文章利用概化理论对小组讨论形式口语考试的总体信度进行了实证考察,考察结果表明小组讨论形式口语考试有可能被接受的信度。同时,为了最大限度地节省考试的时间和人力等资源,文章研究通过概化理论的D研究在保证考试信度的基础上科学地削减了分项评价项目的个数。     

基于Monte Carlo方法的泊松方程求解

基于Monte Carlo方法的主要原理,求解泊松方程第一边值问题.通过构建随机游动模型,确定统计量,抽样产生随机样本,得到泊松方程解的估计值.并给出了详细的推导步骤和算法流程,证明了统计量均值是泊松方程第一边值问题的解,为该方法在复杂问题中提供一个简单的思路.     

理想气体扩散的Monte Carlo模拟

用Monte Carlo方法模拟了理想气体系统通过一小孔的扩散。模拟直观展现了气体分子通过小孔的扩散过程。模拟结果表明,一旦经过扩散达到平衡,系统将不会再回到最初的分布,这说明扩散过程是一个不可逆过程;在扩散过程中,系统的混乱程度不断增大。气体扩散快慢与初始分子数以及小孔的尺寸有关。初始分子数越多小尺寸越大,扩散过程进行的就越快。模拟结果与菲克定律一致。     

掺杂法提高聚合物电导率的蒙特卡洛法讨论

掺杂法提高聚合物电导的机理是考虑导电填充物和高聚物所构成的不均匀体系中，导电颗粒间会形成链式组织或聚集体组织而提高导电性能，在此过程中导电颗粒有相互作用。本是采用蒙特卡洛法对掺杂高分子材料的电导特性作了研究，研究结果与实验符合较好，并得出存在剧变特征的所谓绝缘体－金属相变特性的计算结果。     

A Monte Carlo Study of Recovery of Weak Factor Loadings in Confirmatory Factor Analysis

The recovery of weak factors has been extensively studied in the context of exploratory factor analysis. This article presents the results of a Monte Carlo simulation study of recovery of weak factor loadings in confirmatory factor analysis under conditions of estimation method (maximum likelihood vs. unweighted least squares), sample size, loading size, factor correlation, and model specification (correct vs. incorrect). The effects of these variables on goodness of fit and convergence are also examined. Results show that recovery of weak factor loadings, goodness of fit, and convergence are improved when factors are correlated and models are correctly specified. Additionally, unweighted least squares produces more convergent solutions and successfully recovers the weak factor loadings in some instances where maximum likelihood fails. The implications of these findings are discussed and compared to previous research.     

蒙特卡洛模拟指导量本利分析的案例探究

概率型量本利分析是企业当前常用的分析方法,分析所得的结果可以从不同角度反应企业生产、销售、采购、加工等方面的经济状况。为了保证概率型量本利分析的有序进行,在分析时采用蒙特卡洛模拟辅助研究,能让最终得到的数据结构更加客观、科学。