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1.
This article discusses replication sampling variance estimation techniques that are often applied in analyses using data from complex sampling designs: jackknife repeated replication, balanced repeated replication, and bootstrapping. These techniques are used with traditional analyses such as regression, but are currently not used with structural equation modeling (SEM) analyses. This article provides an extension of these methods to SEM analyses, including a proposed adjustment to the likelihood ratio test, and presents the results from a simulation study suggesting replication estimates are robust. Finally, a demonstration of the application of these methods using data from the Early Childhood Longitudinal Study is included. Secondary analysts can undertake these more robust methods of sampling variance estimation if they have access to certain SEM software packages and data management packages such as SAS, as shown in the article.  相似文献   

2.
Appropriate model specification is fundamental to unbiased parameter estimates and accurate model interpretations in structural equation modeling. Thus detecting potential model misspecification has drawn the attention of many researchers. This simulation study evaluates the efficacy of the Bayesian approach (the posterior predictive checking, or PPC procedure) under multilevel bifactor model misspecification (i.e., ignoring a specific factor at the within level). The impact of model misspecification on structural coefficients was also examined in terms of bias and power. Results showed that the PPC procedure performed better in detecting multilevel bifactor model misspecification, when the misspecification became more severe and sample size was larger. Structural coefficients were increasingly negatively biased at the within level, as model misspecification became more severe. Model misspecification at the within level affected the between-level structural coefficient estimates more when data dependency was lower and the number of clusters was smaller. Implications for researchers are discussed.  相似文献   

3.
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   

4.
The purpose of this study was to investigate the methods of estimating the reliability of school-level scores using generalizability theory and multilevel models. Two approaches, ‘student within schools’ and ‘students within schools and subject areas,’ were conceptualized and implemented in this study. Four methods resulting from the combination of these two approaches with generalizability theory and multilevel models were compared for both balanced and unbalanced data. The generalizability theory and multilevel models for the ‘students within schools’ approach produced the same variance components and reliability estimates for the balanced data, while failing to do so for the unbalanced data. The different results from the two models can be explained by the fact that they administer different procedures in estimating the variance components used, in turn, to estimate reliability. Among the estimation methods investigated in this study, the generalizability theory model with the ‘students nested within schools crossed with subject areas’ design produced the lowest reliability estimates. Fully nested designs such as (students:schools) or (subject areas:students:schools) would not have any significant impact on reliability estimates of school-level scores. Both methods provide very similar reliability estimates of school-level scores.  相似文献   

5.
Recently, advancements in Bayesian structural equation modeling (SEM), particularly software developments, have allowed researchers to more easily employ it in data analysis. With the potential for greater use, come opportunities to apply Bayesian SEM in a wider array of situations, including for small sample size problems. Effective use of Bayseian estimation hinges on selection of appropriate prior distributions for model parameters. Researchers have suggested that informative priors may be useful with small samples, presuming that the mean of the prior is accurate with respect to the population mean. The purpose of this simulation study was to examine model parameter estimation for the Multiple Indicator Multiple Cause model when an informative prior distribution had an incorrect mean. Results demonstrated that the use of incorrect informative priors with somewhat larger variance than is typical, yields more accurate parameter estimates than do naïve priors, or maximum likelihood estimation. Implications for practice are discussed.  相似文献   

6.
This article compares two statistical approaches for modeling growth across time. The two statistical approaches are the multilevel model (MLM) and latent curve analysis (LCA), which have been proposed to depict change or growth adequately. These two approaches were compared in terms of the estimation of growth profiles represented by the parameters of initial status and the rate of growth. A longitudinal data set obtained from a school‐based substance‐use prevention trial for adolescents was used to illustrate the similarities and differences between the two approaches. The results indicated that the two approaches yielded very compatible results. The parameter estimates associated with regression weights are the same, whereas those associated with variances and covariances are similar. The MLM approach is easier for model specification and is more efficient computationally in yielding results. The LCA approach, however, has the advantage of providing model evaluation, that is, an overall test of goodness of fit, and is more flexible in modeling and hypothesis testing as demonstrated in this study.  相似文献   

7.
This article examined the role of centering in estimating interaction effects in multilevel structural equation models. Interactions are typically represented by product term of 2 variables that are hypothesized to interact. In multilevel structural equation modeling (MSEM), the product term involving Level 1 variables is decomposed into within-cluster and between-cluster random components. The choice of centering affects the decomposition of the product term, and therefore affects the sample variance and covariance associated with the product term used in the maximum likelihood fitting function. The simulation study showed that for an interaction between a Level 1 variable and a Level 2 variable, the product term of uncentered variables or the product term of grand mean centered variables produced unbiased estimates in both Level 1 and Level 2 models. The product term of cluster mean centered variables produced biased estimates in the Level 1 model. For an interaction between 2 Level 1 variables, the product term of cluster mean centered variables produced unbiased estimates in the Level 1 model, whereas the product term of grand mean centered variables produced unbiased estimates for the Level 1 model. Recommendations for researchers who wish to estimate interactions in MSEM are provided.  相似文献   

8.
Although methodology articles have increasingly emphasized the need to analyze data from two members of a dyad simultaneously, the most popular method in substantive applications is to examine dyad members separately. This might be due to the underappreciation of the extra information simultaneous modeling strategies can provide. Therefore, the goal of this study was to compare multiple growth curve modeling approaches for longitudinal dyadic data (LDD) in both structural equation modeling and multilevel modeling frameworks. Models separately assessing change over time for distinguishable dyad members are compared to simultaneous models fitted to LDD from both dyad members. Furthermore, we compared the simultaneous default versus dependent approaches (whether dyad pairs’ Level 1 [or unique] residuals are allowed to covary and differ in variance). Results indicated that estimates of variance and covariance components led to conflicting results. We recommend the simultaneous dependent approach for inferring differences in change over time within a dyad.  相似文献   

9.
Multilevel modeling has been utilized for combining single-case experimental design (SCED) data assuming simple level-1 error structures. The purpose of this study is to compare various multilevel analysis approaches for handling potential complexity in the level-1 error structure within SCED data, including approaches assuming simple and complex error structures (heterogeneous, autocorrelation, and both) and those using fit indices to select between alternative error structures. A Monte Carlo study was conducted to empirically validate the suggested multilevel modeling approaches. Results indicate that each approach leads to fixed effect estimates with little to no bias and that inferences for fixed effects were frequently accurate, particularly when a simple homogeneous level-1 error structure or a first-order autoregressive structure was assumed and the inferences were based on the Kenward-Roger method. Practical implications and recommendations are discussed.  相似文献   

10.
We develop a theoretical and empirical basis for the design of teacher professional development studies. We build on previous work by (a) developing estimates of intraclass correlation coefficients for teacher outcomes using two- and three-level data structures, (b) developing estimates of the variance explained by covariates, and (c) modifying the conventional optimal design framework to include differential covariate costs so as to capture the point at which the cost of collecting a covariate overtakes the reduction in variance it supplies. We illustrate the use of these estimates to explore the absolute and relative sensitivity of multilevel designs in teacher professional development studies. The results from these analyses are intended to guide researchers in making more-informed decisions about the tradeoffs and considerations involved in selecting study designs for assessing the impacts of professional development programs.  相似文献   

11.
Abstract

Recently, researchers have used multilevel models for estimating intervention effects in single-case experiments that include replications across participants (e.g., multiple baseline designs) or for combining results across multiple single-case studies. Researchers estimating these multilevel models have primarily relied on restricted maximum likelihood (REML) techniques, but Bayesian approaches have also been suggested. The purpose of this Monte Carlo simulation study was to examine the impact of estimation method (REML versus Bayesian with noninformative priors) on the estimation of treatment effects (relative bias, root mean square error) and on the inferences about those effects (interval coverage) for autocorrelated multiple-baseline data. Simulated conditions varied with regard to the number of participants, series length, and distribution of the variance within and across participants. REML and Bayesian estimation led to estimates of the fixed effects that showed little to no bias but that differentially impacted the inferences about the fixed effects and the estimates of the variances. Implications for applied researchers and methodologists are discussed.  相似文献   

12.
This study introduces three growth modeling techniques: latent growth modeling (LGM), hierarchical linear modeling (HLM), and longitudinal profile analysis via multidimensional scaling (LPAMS). It compares the multilevel growth parameter estimates and potential predictor effects obtained using LGM, HLM, and LPAMS. The purpose of this multilevel growth analysis is to alert applied researchers to selected analytical issues that are required for consideration in decisions to apply one of these three approaches to longitudinal academic achievement studies. The results indicated that there were no significant distinctions on either mean growth parameter estimates or on the effects of potential predictors to growth factors at both the student and school levels. However, the study also produced equivocal findings on the statistical testing of variance and covariance growth parameter estimates. Other practical issues pertaining to the three growth modeling methods are also discussed.  相似文献   

13.
The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying methods of estimation, level-1 and level-2 sample size, outcome prevalence, variance component sizes, and number of predictors using SAS software. Mean estimates of statistical power were influenced primarily by sample sizes at both levels. In addition, confidence interval coverage and width and the likelihood of nonpositive definite random effect covariance matrices were impacted by variance component size and estimation method. The interactions of these and other factors with various model performance outcomes are explored.  相似文献   

14.
The log-odds ratio (ln[OR]) is commonly used to quantify treatments' effects on dichotomous outcomes and then pooled across studies using inverse-variance (1/v) weights. Calculation of the ln[OR]'s variance requires four cell frequencies for two groups crossed with values for dichotomous outcomes. While primary studies report the total sample size (n..), many do not report all four frequencies. Using real data, we demonstrated pooling of ln[OR]s using n.. versus 1/v weights. In a simulation study we compared two weighting approaches under several conditions. Efficiency and Type I error rates for 1/v versus n.. weights used to pool ln[OR] estimates depended on sample size and the percent of studies missing cell frequencies. Results are discussed and guidelines for applied meta-analysts are provided.  相似文献   

15.
Reliability can be estimated using structural equation modeling (SEM). Two potential problems with this approach are that estimates may be unstable with small sample sizes and biased with misspecified models. A Monte Carlo study was conducted to investigate the quality of SEM estimates of reliability by themselves and relative to coefficient alpha. The SEM approach showed minimal bias when the model was correctly specified if items were relatively well defined by their underlying factor(s). They tended to demonstrate somewhat greater bias when the model was misspecified, particularly underspecified. Overall, SEM estimates were more stable than anticipated. Researchers are more likely to obtain accurate estimates of reliability using SEM by conducting large-sample studies with well-constructed scales and critically assessing model fit.  相似文献   

16.
Oversampling and cluster sampling must be addressed when analyzing complex sample data. This study: (a) compares parameter estimates when applying weights versus not applying weights; (b) examines subset selection issues; (c) compares results when using standard statistical software (SPSS) versus specialized software (AM); and (d) offers recommendations for analyzing complex sample data. Underestimated standard errors and overestimated test statistics were produced when both the oversampled and cluster sample characteristics of the data were ignored. Regarding subset analysis, marked differences were not evident in SPSS results, but the standard errors of the weighted versus unweighted models became more similar as smaller subsets of the data were extracted using AM. Recommendations to researchers are provided including accommodating both oversampling and cluster sampling.  相似文献   

17.
This study used a Monte Carlo approach to investigate the effect of item sampling by item stratification on parameter estimation when applying multiple matrix sampling to achievement data. From the results of this study it was concluded that the item sampling method and sampling plan which is a practical compromise in terms of precision and sample size is one based on item stratification by item discrimination and a sampling plan with a moderate number of subtests. This sampling condition provides reasonable precision of the mean and variance estimates but requires only a moderately sized sample.  相似文献   

18.
The purpose of this article is to examine the use of sample weights in the latent variable modeling context. A sample weight is the inverse of the probability that the unit in question was sampled and is used to obtain unbiased estimates of population parameters when units have unequal probabilities of inclusion in a sample. Although sample weights are discussed at length in survey research literature, virtually no discussion of sample weights can be found in the latent variable modeling literature. This article examines sample weights in latent variable models applied to the case where a simple random sample is drawn from a population containing a mixture of strata. A bootstrap simulation study is used to compare raw and normalized sample weights to conditions where weights are ignored. The results show that ignoring weights can lead to serious bias in latent variable model parameters and that this bias is mitigated by the incorporation of sample weights. Standard errors appear to be underestimated when sample weights are applied. Results on goodness‐of‐fit statistics demonstrate the advantages of utilizing sample weights.  相似文献   

19.
Minor cross-loadings on non-targeted factors are often found in psychological or other instruments. Forcing them to zero in confirmatory factor analyses (CFA) leads to biased estimates and distorted structures. Alternatively, exploratory structural equation modeling (ESEM) and Bayesian structural equation modeling (BSEM) have been proposed. In this research, we compared the performance of the traditional independent-clusters-confirmatory-factor-analysis (ICM-CFA), the nonstandard CFA, ESEM with the Geomin- or Target-rotations, and BSEMs with different cross-loading priors (correct; small- or large-variance priors with zero mean) using simulated data with cross-loadings. Four factors were considered: the number of factors, the size of factor correlations, the cross-loading mean, and the loading variance. Results indicated that ICM-CFA performed the worst. ESEMs were generally superior to CFAs but inferior to BSEM with correct priors that provided the precise estimation. BSEM with large- or small-variance priors performed similarly while the prior mean for cross-loadings was more important than the prior variance.  相似文献   

20.
In the framework of teacher’s approaches to teaching, this study investigates the relationship between student-related variables (i.e., study time, class absence, domain knowledge, and homework completion), students’ approaches to learning, and teachers’ approaches to teaching using structural equation modeling (SEM) with two independent data samples. The participants were 61 biology teachers and their corresponding 1,518 high school students (12th grade). The first sample was used to fit the model, and the second sample was used to analyze the consistency of the data derived from the first sample. Using a two-level SEM analysis, we established whether the effects found at the individual level varied significantly at class level. The students’ approaches to learning were related to the teachers’ approaches to teaching as a function of the hypotheses established in the model, although the effect size was smaller than expected. However, approximately 48 % of the variance of the surface approach and 46 % of the deep approach sat at class level. At the individual level, the results of this study suggest that students’ approaches to learning significantly explain their teachers’ approaches to teaching and, thus, constitute important contextual variables. At the class level, the way students learn appears to be closely associated with class-related variables. Our data stresses the importance of promoting educational opportunities (e.g., school-based courses) for teachers to reflect upon the teaching methodologies used in class.  相似文献   

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