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1.
The inclusion of covariates improves the prediction of class memberships in latent class analysis (LCA). Several methods for examining covariate effects have been developed over the past decade; however, researchers have limited to the comparisons of the performance among these methods in cases of the single-level LCA. The present study investigated the performance of three different methods for examining covariate effects in a multilevel setting. We conducted a simulation to compare the performance of the three methods when level-1 and level-2 covariates were simultaneously incorporated into the nonparametric multilevel latent class model to predict latent class membership at each level. The simulation results revealed that the bias-adjusted three-step maximum likelihood method performed equally well as the one-step method when the sample sizes were sufficiently large and the latent classes were distinct from each other. However, the unadjusted three-step method significantly underestimated the level-1 covariate effect in most conditions.

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2.
We compared six common methods in estimating the 2-1-1 (level-2 independent, level-1 mediator, level-1 dependent) multilevel mediation model with a random slope. They were the Bayesian with informative priors, the Bayesian with non-informative priors, the Monte-Carlo, the distribution of the product, the bias-corrected, and the bias-uncorrected parametric percentile residual bootstrap. The Bayesian method with informative priors was superior in relative mean square error (RMSE), power, interval width, and interval imbalance. The prior variance and prior mean were also varied and examined. Decreasing the prior variance increased the power, reduced RMSE and interval width when the prior mean was the true value, but decreasing the prior variance reduced the power when the prior mean was set incorrectly. The influence of misspecification of prior information of the b coefficient on multilevel mediation analysis was greater than that on coefficient a. An illustrate example with the Bayesian multilevel mediation was provided.  相似文献   

3.
This article proposes a novel exploratory approach for assessing how the effects of Level-2 predictors differ across Level-1 units. Multilevel regression mixture models are used to identify latent classes at Level 1 that differ in the effect of 1 or more Level-2 predictors. Monte Carlo simulations are used to demonstrate the approach with different sample sizes and to demonstrate the consequences of constraining 1 of the random effects to 0. An application of the method to evaluate heterogeneity in the effects of classroom practices on students is used to show the types of research questions that can be answered with this method and the issues faced when estimating multilevel regression mixtures.  相似文献   

4.
This article examines the effects of clustering in latent class analysis. A comprehensive simulation study is conducted, which begins by specifying a true multilevel latent class model with varying within- and between-cluster sample sizes, varying latent class proportions, and varying intraclass correlations. These models are then estimated under the assumption of a single-level latent class model. The outcomes of interest are measures of bias in the Bayesian Information Criterion (BIC) and the entropy R 2 statistic relative to accounting for the multilevel structure of the data. The results indicate that the size of the intraclass correlation as well as between- and within-cluster sizes are the most prominent factors in determining the amount of bias in these outcome measures, with increasing intraclass correlations combined with small between-cluster sizes resulting in increased bias. Bias is particularly noticeable in the BIC. In addition, there is evidence that class separation interacts with the size of the intraclass correlations and cluster sizes in producing bias in these measures.  相似文献   

5.
The current simulation study examined the effects of Item Parameter Drift (IPD) occurring in a short scale on parameter estimates in multilevel models where scores from a scale were employed as a time-varying predictor to account for outcome scores. Five factors, including three decisions about IPD, were considered for simulation conditions. It was revealed that IPD occurring in a relatively shorter scale led to a substantial increase in the amount of relative bias in parameter estimates. The bias was more prominent in the estimates of level-2 time-varying predictors relative to those of level-1 time-varying predictors. Regarding the decisions about IPD, keeping items exhibiting IPD was more appropriate than removing them based on the results from relative bias of standard errors of estimates. Based on the findings, it can be concluded that removing items exhibiting IPD may lead to an increase of Type II errors due to the underestimation of parameter estimates and overestimation of standard errors. The applied example showed findings consistent with those in the simulation study.  相似文献   

6.
Abstract

Experiments that involve nested structures may assign treatment conditions either to subgroups (such as classrooms) or individuals within subgroups (such as students). The design of such experiments requires knowledge of the intraclass correlation structure to compute the sample sizes necessary to achieve adequate power to detect the treatment effect. This study provides methods for computing power in three-level block randomized balanced designs (with two levels of nesting) where, for example, students are nested within classrooms and classrooms are nested within schools. The power computations take into account nesting effects at the second (classroom) and at the third (school) level, sample size effects (e.g., number of level-1, level-2, and level-3 units), and covariate effects (e.g., pretreatment measures). The methods are generalizable to quasi-experimental studies that examine group differences on an outcome.  相似文献   

7.
Analysis of variance is one of the most frequently used statistical analyses in the behavioral, educational, and social sciences, and special attention has been paid to the selection and use of an appropriate effect size measure of association in analysis of variance. This article presents the sample size procedures for precise interval estimation of eta-squared and partial eta-squared in fixed-effects analysis of variance designs. The desired precision of a confidence interval is assessed with respect to (a) the control of expected width and (b) the tolerance probability of interval width within a designated value. In addition, sample size calculations for standardized contrasts of treatment effects and corresponding partial strength of association effect sizes are also considered.  相似文献   

8.
Multilevel modeling has grown in use over the years as a way to deal with the nonindependent nature of observations found in clustered data. However, other alternatives to multilevel modeling are available that can account for observations nested within clusters, including the use of Taylor series linearization for variance estimation, the design effect adjusted standard errors approach, and fixed effects modeling. Using 1,000 replications of 12 conditions with varied Level 1 and Level 2 sample sizes, the author compared parameter estimates, standard errors, and statistical significance using various alternative procedures. Results indicate that several acceptable procedures can be used in lieu of or together with multilevel modeling, depending on the type of research question asked and the number of clusters under investigation. Guidelines for applied researchers are discussed.  相似文献   

9.
This study examined the effects of ignoring multilevel data structures in nonhierarchical covariance modeling using a Monte Carlo simulation. Multilevel sample data were generated with respect to 3 design factors: (a) intraclass correlation, (b) group and member configuration, and (c) the models that underlie the between-group and within-group variance components associated with multilevel data. Covariance models that ignored the multilevel structure were then fit to the data. Results indicated that when variables exhibit minimal levels of intraclass correlation, the chi-square model/data fit statistic, the parameter estimators, and the standard error estimators are relatively unbiased. However, as the level of intraclass correlation increases, the chi-square statistic, the parameters, and their standard errors all exhibit estimation problems. The specific group/member configurations as well as the underlying between-group and within-group model structures further exacerbate the estimation problems encountered in the nonhierarchical analysis of multilevel data.  相似文献   

10.
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.  相似文献   

11.
The present study examines bias in parameter estimates and standard error in cross-classified random effect modeling (CCREM) caused by omitting the random interaction effects of the cross-classified factors, focusing on the effect of a sample size within cells and ratio of a small cell. A Monte Carlo simulation study was conducted to compare the correctly specified and the misspecified CCREM. While there was negligible bias in fixed effects, substantial biases were found in the random effects of the misspecified model depending on the number of samples within a cell and the proportion of small cells. However, in the case of the correctly specified model, no bias occurred. The present study suggests considering the random interaction effects when conducting CCREM to avoid overestimation of variance components and to calculate an accurate value of estimation. The implications of this study are to illuminate the conditions of cross-classification ratio and to provide a meaningful reference for applied researchers using CCREM.  相似文献   

12.
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.  相似文献   

13.
This article summarizes single-subject-design intervention studies that include students with learning disabilities. Effect sizes of 85 studies were analyzed across instructional domains (e.g., reading, mathematics); sample characteristics (e.g., age, intelligence); intervention parameters (e.g., number of instructional sessions, instructional components); and methodological procedures (e.g., internal validity, treatment integrity, sample representation). The major findings were as follows: (a) All domain areas except handwriting yielded effect sizes at or above Cohen's .80 threshold for a substantial finding; (b) instructional components related to drill-repetition-practice-review, segmentation, small interactive groups, and the implementation of cues to use strategies contributed significant variance (15%) to estimates of effect size; (c) strategy instruction (SI) models better predicted effect size estimates than direct instruction (DI) models when the results were qualified by the reported intellectual and reading levels of the participants; (d) high-IQ discrepancy groups yielded lower effect sizes compared to low-IQ discrepancy groups in the domain of reading, whereas the reverse effect occurred when treatment outcomes were not reading measures; and (e) the low-IQ discrepancy groups yielded higher effect sizes for a Combined DI and SI Model when compared to competing models. The results are supportive of the pervasive influence of cognitive strategy and direct instruction models across treatment domains and of the notion that variations in sample definition moderate treatment outcomes.  相似文献   

14.
Multilevel structural equation modeling (ML-SEM) for multilevel mediation is noted for its flexibility over a system of multilevel models (MLMs). Sample size requirements are an overlooked limitation of ML-SEM (100 clusters is recommended). We find that 89% of ML-SEM studies have fewer than 100 clusters and the median number is 44. Furthermore, 75% of ML-SEM studies implement 2–1–1 or 1–1–1 models, which can be equivalently fit with MLMs. MLMs theoretically have lower sample size requirements, although studies have yet to assess small sample performance for multilevel mediation. We conduct a simulation to address this pervasive problem. We find that MLMs have more desirable small sample performance and can be trustworthy with 10 clusters. Importantly, many studies lack the sample size and model complexity to necessitate ML-SEM. Although ML-SEM is undeniably more flexible and uniquely positioned for difficult problems, small samples often can be more effectively and simply addressed with MLMs.  相似文献   

15.
Cognitive diagnosis models (CDMs) have been developed to evaluate the mastery status of individuals with respect to a set of defined attributes or skills that are measured through testing. When individuals are repeatedly administered a cognitive diagnosis test, a new class of multilevel CDMs is required to assess the changes in their attributes and simultaneously estimate the model parameters from the different measurements. In this study, the most general CDM of the generalized deterministic input, noisy “and” gate (G‐DINA) model was extended to a multilevel higher order CDM by embedding a multilevel structure into higher order latent traits. A series of simulations based on diverse factors was conducted to assess the quality of the parameter estimation. The results demonstrate that the model parameters can be recovered fairly well and attribute mastery can be precisely estimated if the sample size is large and the test is sufficiently long. The range of the location parameters had opposing effects on the recovery of the item and person parameters. Ignoring the multilevel structure in the data by fitting a single‐level G‐DINA model decreased the attribute classification accuracy and the precision of latent trait estimation. The number of measurement occasions had a substantial impact on latent trait estimation. Satisfactory model and person parameter recoveries could be achieved even when assumptions of the measurement invariance of the model parameters over time were violated. A longitudinal basic ability assessment is outlined to demonstrate the application of the new models.  相似文献   

16.
Survival analysis is an advanced statistical method to investigate the occurrence and the timing of an important event such as school access, dropout, and graduation in a longitudinal framework. The aim of our study is to provide practical guidelines for empirical researchers in choosing an appropriate survival analysis model. For this goal, this study chose two major survival analytical models of a discrete-time hazard model and a Cox regression model and compared analytical outcomes considering time metrics, as well as sample sizes and censoring proportions. In the analytical model, the combined specifications of varying factors using two models were adopted to analyse the Educational Longitudinal Study of 2002. We chose the college access of Hispanic English Language Learners to understand the importance of adopting a proper survival model to examine the educational outcome in the educational context. Importantly, we considered the hazard probability for the target event in the model specification which is a fundamental yet often neglected component of survival analysis. We recommended discrete models for the cases with a smaller number of time points, larger time metrics, larger sample size, and smaller proportions of censored observations.  相似文献   

17.
讨论了在不完全数据下的响应变量的估计精度,当不可忽略缺失下,样本的响应有缺失数据时,其联合分布是不可识别的.现证明了估计的精度与工具变量的相关性,当工具变量独立于目标变量时,目标变量估计的方差趋于无穷大.  相似文献   

18.
Abstract

This paper and the accompanying tool are intended to complement existing supports for conducting power analysis tools by offering a tool based on the framework of Minimum Detectable Effect Sizes (MDES) formulae that can be used in determining sample size requirements and in estimating minimum detectable effect sizes for a range of individual- and group-random assignment design studies and for common quasi-experimental design studies. The paper and accompanying tool cover computation of minimum detectable effect sizes under the following study designs: individual random assignment designs, hierarchical random assignment designs (2-4 levels), block random assignment designs (2-4 levels), regression discontinuity designs (6 types), and short interrupted time-series designs. In each case, the discussion and accompanying tool consider the key factors associated with statistical power and minimum detectable effect sizes, including the level at which treatment occurs and the statistical models (e.g., fixed effect and random effect) used in the analysis. The tool also includes a module that estimates for one and two level random assignment design studies the minimum sample sizes required in order for studies to attain user-defined minimum detectable effect sizes.  相似文献   

19.
Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear how their sample size requirements and recommendations transfer to the DSEM framework. This article presents the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8. Three features are varied in the simulations: complexity of the model, number of subjects, and number of time points per subject. Samples with many subjects and few time points are shown to perform substantially better than samples with few subjects and many time points.  相似文献   

20.
To what extent can teacher–student dyadic interactions modify the hierarchy of student performances within a single class? To answer this insufficiently researched question, the authors conducted two parallel studies involving 33 Grade 5 classes in France (759 students) and 15 Grade 5 classes in Luxembourg (243 students). Interactions were observed during whole-class lessons. Posttest scores were analyzed using multilevel models controlling for five level-1 variables and two level-2 variables. The authors did not find any effect of dyadic interactions on relative student performance in mathematics or in language (French or German), in France or in Luxembourg. This result is interpreted in terms of both the public character of dyadic interactions in whole-class settings and the class management functions of these interactions.  相似文献   

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