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1.
When both model misspecifications and nonnormal data are present, it is unknown how trustworthy various point estimates, standard errors (SEs), and confidence intervals (CIs) are for standardized structural equation modeling parameters. We conducted simulations to evaluate maximum likelihood (ML), conventional robust SE estimator (MLM), Huber–White robust SE estimator (MLR), and the bootstrap (BS). We found (a) ML point estimates can sometimes be quite biased at finite sample sizes if misfit and nonnormality are serious; (b) ML and MLM generally give egregiously biased SEs and CIs regardless of the degree of misfit and nonnormality; (c) MLR and BS provide trustworthy SEs and CIs given medium misfit and nonnormality, but BS is better; and (d) given severe misfit and nonnormality, MLR tends to break down and BS begins to struggle.  相似文献   

2.
The comparative fit index (CFI) is one of the most widely-used fit indices in structural equation modeling (SEM). When applying the CFI to model evaluation, although it is universally recognized that the focus should be the population fit, in practice one often considers only the CFI value within a sample and neglects the uncertainty in point estimation. Confidence interval (CI) methods for CFI appeared only recently, but these methods assume multivariate normality, which often fails to hold in practice. In addition, the current methods are applications of the bootstrap and are thus computationally intensive. To better handle nonnormal data and simplify CI construction, in this paper we propose an analytic CI method for CFI without assuming normality. We then carry out simulation studies to compare the new and current methods at various levels of model misfit and nonnormality. Simulation results verify the effectiveness and advantages of the new method.  相似文献   

3.
Bootstrapping approximate fit indexes in structural equation modeling (SEM) is of great importance because most fit indexes do not have tractable analytic distributions. Model-based bootstrap, which has been proposed to obtain the distribution of the model chi-square statistic under the null hypothesis (Bollen & Stine, 1992), is not theoretically appropriate for obtaining confidence intervals (CIs) for fit indexes because it assumes the null is exactly true. On the other hand, naive bootstrap is not expected to work well for those fit indexes that are based on the chi-square statistic, such as the root mean square error of approximation (RMSEA) and the comparative fit index (CFI), because sample noncentrality is a biased estimate of the population noncentrality. In this article we argue that a recently proposed bootstrap approach due to Yuan, Hayashi, and Yanagihara (YHY; 2007) is ideal for bootstrapping fit indexes that are based on the chi-square. This method transforms the data so that the “parent” population has the population noncentrality parameter equal to the estimated noncentrality in the original sample. We conducted a simulation study to evaluate the performance of the YHY bootstrap and the naive bootstrap for 4 indexes: RMSEA, CFI, goodness-of-fit index (GFI), and standardized root mean square residual (SRMR). We found that for RMSEA and CFI, the CIs under the YHY bootstrap had relatively good coverage rates for all conditions, whereas the CIs under the naive bootstrap had very low coverage rates when the fitted model had large degrees of freedom. However, for GFI and SRMR, the CIs under both bootstrap methods had poor coverage rates in most conditions.  相似文献   

4.
One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.  相似文献   

5.
Fit indexes are an important tool in the evaluation of model fit in structural equation modeling (SEM). Currently, the newest confidence interval (CI) for fit indexes proposed by Zhang and Savalei (2016) is based on the quantiles of a bootstrap sampling distribution at a single level of misspecification. This method, despite a great improvement over naive and model-based bootstrap methods, still suffers from unsatisfactory coverage. In this work, we propose a new method of constructing bootstrap CIs for various fit indexes. This method directly inverts a bootstrap test and produces a CI that involves levels of misspecification that would not be rejected in a bootstrap test. Similar in rationale to a parametric CI of root mean square error of approximation (RMSEA) based on a noncentral χ2 distribution and a profile-likelihood CI of model parameters, this approach is shown to have better performance than the approach of Zhang and Savalei (2016), with more accurate coverage and more efficient widths.  相似文献   

6.
The precision of estimates in many statistical models can be expressed by a confidence interval (CI). CIs based on standard errors (SEs) are common in practice, but likelihood-based CIs are worth consideration. In comparison to SEs, likelihood-based CIs are typically more difficult to estimate, but are more robust to model (re)parameterization. In latent variable models, some parameters might take on values outside of their interpretable range. Therefore, it is desirable to place a bound to keep the parameter interpretable. For likelihood-based CI, a correction is needed when a parameter is bounded. The correction is known (Wu & Neale, 2012), but is difficult to implement in practice. A novel automatic implementation that is simple for an applied researcher to use is introduced. A simulation study demonstrates the accuracy of the correction using a latent growth curve model and the method is illustrated with a multilevel confirmatory factor analysis.  相似文献   

7.
Conventionally, moderated mediation analysis is conducted through adding relevant interaction terms into a mediation model of interest. In this study, we illustrate how to conduct moderated mediation analysis by directly modeling the relation between the indirect effect components including a and b and the moderators, to permit easier specification and interpretation of moderated mediation. With this idea, we introduce a general moderated mediation model that can be used to model many different moderated mediation scenarios including the scenarios described in Preacher, Rucker, and Hayes (2007). Then we discuss how to estimate and test the conditional indirect effects and to test whether a mediation effect is moderated using Bayesian approaches. How to implement the estimation in both BUGS and Mplus is also discussed. Performance of Bayesian methods is evaluated and compared to that of frequentist methods including maximum likelihood (ML) with 1st-order and 2nd-order delta method standard errors and mL with bootstrap (percentile or bias-corrected confidence intervals) via a simulation study. The results show that Bayesian methods with diffuse (vague) priors implemented in both BUGS and Mplus yielded unbiased estimates, higher power than the ML methods with delta method standard errors, and the ML method with bootstrap percentile confidence intervals, and comparable power to the ML method with bootstrap bias-corrected confidence intervals. We also illustrate the application of these methods with the real data example used in Preacher et al. (2007). Advantages and limitations of applying Bayesian methods to moderated mediation analysis are also discussed.  相似文献   

8.
The present study evaluated the multiple imputation method, a procedure that is similar to the one suggested by Li and Lissitz (2004), and compared the performance of this method with that of the bootstrap method and the delta method in obtaining the standard errors for the estimates of the parameter scale transformation coefficients in item response theory (IRT) equating in the context of the common‐item nonequivalent groups design. Two different estimation procedures for the variance‐covariance matrix of the IRT item parameter estimates, which were used in both the delta method and the multiple imputation method, were considered: empirical cross‐product (XPD) and supplemented expectation maximization (SEM). The results of the analyses with simulated and real data indicate that the multiple imputation method generally produced very similar results to the bootstrap method and the delta method in most of the conditions. The differences between the estimated standard errors obtained by the methods using the XPD matrices and the SEM matrices were very small when the sample size was reasonably large. When the sample size was small, the methods using the XPD matrices appeared to yield slight upward bias for the standard errors of the IRT parameter scale transformation coefficients.  相似文献   

9.
Confidence intervals (CIs) for parameters are usually constructed based on the estimated standard errors. These are known as Wald CIs. This article argues that likelihood-based CIs (CIs based on likelihood ratio statistics) are often preferred to Wald CIs. It shows how the likelihood-based CIs and the Wald CIs for many statistics and psychometric indexes can be constructed with the use of phantom variables (Rindskopf, 1984 Rindskopf, D. 1984. Using phantom and imaginary latent variables to parameterize constraints in linear structural models. Psychometrika, 49: 37–47. [Crossref], [Web of Science ®] , [Google Scholar]) in some of the current structural equation modeling (SEM) packages. The procedures to form CIs for the differences in correlation coefficients, squared multiple correlations, indirect effects, coefficient alphas, and reliability estimates are illustrated. A simulation study on the Pearson correlation is used to demonstrate the advantages of the likelihood-based CI over the Wald CI. Issues arising from this SEM approach and extensions of this approach are discussed.  相似文献   

10.
We compare the accuracy of confidence intervals (CIs) and tests of close fit based on the root mean square error of approximation (RMSEA) with those based on the standardized root mean square residual (SRMR). Investigations used normal and nonnormal data with models ranging from p = 10 to 60 observed variables. CIs and tests of close fit based on the SRMR are generally accurate across all conditions (even at p = 60 with nonnormal data). In contrast, CIs and tests of close fit based on the RMSEA are only accurate in small models. In larger models (p ≥ 30), they incorrectly suggest that models do not fit closely, particularly if sample size is less than 500.  相似文献   

11.
In psychological research, available data are often insufficient to estimate item factor analysis (IFA) models using traditional estimation methods, such as maximum likelihood (ML) or limited information estimators. Bayesian estimation with common-sense, moderately informative priors can greatly improve efficiency of parameter estimates and stabilize estimation. There are a variety of methods available to evaluate model fit in a Bayesian framework; however, past work investigating Bayesian model fit assessment for IFA models has assumed flat priors, which have no advantage over ML in limited data settings. In this paper, we evaluated the impact of moderately informative priors on ability to detect model misfit for several candidate indices: posterior predictive checks based on the observed score distribution, leave-one-out cross-validation, and widely available information criterion (WAIC). We found that although Bayesian estimation with moderately informative priors is an excellent aid for estimating challenging IFA models, methods for testing model fit in these circumstances are inadequate.  相似文献   

12.
Among the commonly used resampling methods of dealing with small-sample problems, the bootstrap enjoys the widest applications because it often outperforms its counterparts. However, the bootstrap still has limitations when its operations are contemplated. Therefore, the purpose of this study is to examine an alternative, new resampling method (called S-SMART) and compare the statistical performance of it with that of the bootstrap through an application of them to the most advanced modelling technique, SEM, as an example. The evaluation of the statistical performances of S-SMART and the bootstrap with respect to the standard errors of the parameter estimates was conducted through a Monte Carlo simulation study. This work, while potentially benefiting educational and behavioural research, conceivably would also provide methodological support for other research areas, such as bioinformatics, biology, geosciences, astronomy, and ecology, where large samples are hard to obtain.  相似文献   

13.
The validity and reliability of Technological Pedagogical Content Knowledge (TPACK) as a framework to measure the extent to which teachers can teach with technology hinges on the ability to aggregate results across empirical studies. The results of data collected using the survey of pre-service teacher knowledge of teaching with technology (TKTT) were synthesized using confidence intervals (CIs). Mean pre-service teacher TPACK point estimates were characterized by graphing CIs across studies from 2009 until 2011. The results present approximations of TPACK population parameters and implications for researchers and teacher educators.  相似文献   

14.
Functional form misfit is frequently a concern in item response theory (IRT), although the practical implications of misfit are often difficult to evaluate. In this article, we illustrate how seemingly negligible amounts of functional form misfit, when systematic, can be associated with significant distortions of the score metric in vertical scaling contexts. Our analysis uses two‐ and three‐parameter versions of Samejima's logistic positive exponent model (LPE) as a data generating model. Consistent with prior work, we find LPEs generally provide a better comparative fit to real item response data than traditional IRT models (2PL, 3PL). Further, our simulation results illustrate how 2PL‐ or 3PL‐based vertical scaling in the presence of LPE‐induced misspecification leads to an artificial growth deceleration across grades, consistent with that commonly seen in vertical scaling studies. The results raise further concerns about the use of standard IRT models in measuring growth, even apart from the frequently cited concerns of construct shift/multidimensionality across grades.  相似文献   

15.
Background: Advocates for children’s rights have recommended the elimination of all forms of violent discipline given its detrimental effects on children’s development. Yet, little is known about the global prevalence of various forms of discipline, including physical and psychological aggression, as well as alternative forms of non-violent discipline, especially in low- and middle-income countries (LMICs).Objective: This study aims to obtain national, regional, and global prevalence estimates of the percentage and number of 2- to- 4-y-olds in LMICs exposed to these disciplinary practices by their caregivers.Participants and setting: We use data collected between 2010 and 2016 from 107,063 2- to- 4-y-old children living in 49 LMICs as part of the Multiple Indicator Cluster Survey (MICS).Methods: Using the best-fitting model based on cross-validation techniques, we performed predictive modeling to generate country-level prevalence estimates for 131 LMICs in 2013, as well as 95% confidence intervals around these estimates.Results: We estimate that 296.2 million 2- to- 4-y-olds (95% CI 256.9, 300.9) were exposed to non-violent discipline in 2013, which corresponds to 83.9% of the population. Furthermore, 220.4 million (95% CI 138.1, 283.7) and 230.7 million (95% CI 128.4, 300.6) children were exposed to aggressive physical and psychological discipline, respectively, which corresponds to prevalence of 62.5% and 65.4%. We also identify a high heterogeneity in the estimates across and within regions, finding a higher prevalence of both violent disciplinary methods in South Asia and Sub-Saharan Africa.Conclusions: These results suggest the need for new policies and programs to minimize violent discipline around the world.  相似文献   

16.
Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional z test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a simulation was conducted to evaluate these alternative methods in a more complex path model with multiple mediators and indirect paths with 2 and 3 paths. Methods for testing contrasts of 2 effects were evaluated also. The simulation included 1 exogenous independent variable, 3 mediators and 2 outcomes and varied sample size, number of paths in the mediated effects, test used to evaluate effects, effect sizes for each path, and the value of the contrast. Confidence intervals were used to evaluate the power and Type I error rate of each method, and were examined for coverage and bias. The bias-corrected bootstrap had the least biased confidence intervals, greatest power to detect nonzero effects and contrasts, and the most accurate overall Type I error. All tests had less power to detect 3-path effects and more inaccurate Type I error compared to 2-path effects. Confidence intervals were biased for mediated effects, as found in previous studies. Results for contrasts did not vary greatly by test, although resampling approaches had somewhat greater power and might be preferable because of ease of use and flexibility.  相似文献   

17.
To ensure the statistical result validity, model-data fit must be evaluated for each item. In practice, certain actions or treatments are needed for misfit items. If all misfit items are treated, much item information would be lost during calibration. On the other hand, if only severely misfit items are treated, the inclusion of misfit items may invalidate the statistical inferences based on the estimated item response models. Hence, given response data, one has to find a balance between treating too few and too many misfit items. In this article, misfit items are classified into three categories based on the extent of misfit. Accordingly, three different item treatment strategies are proposed in determining which categories of misfit items should be treated. The impact of using different strategies is investigated. The results show that the test information functions obtained under different strategies can be substantially different in some ability ranges.  相似文献   

18.
Several papers have been devoted to the use of structural equation modeling (SEM) software in fitting autoregressive moving average (ARMA) models to a univariate series observed in a single subject. Van Buuren (1997) went beyond specification and examined the nature of the estimates obtained with SEM software. Although the results were mixed, he concluded that these parameter estimates resemble true maximum likelihood (ML) estimates. Molenaar (1999) argued that the negative findings for pure moving average models might be due to the absence of invertibility constraints in Van Buuren's simulation experiment. The aim of this article is to (a) reexamine the nature of SEM estimates of ARMA parameters; (b) replicate Van Buuren's simulation experiment in light of Molenaar's comment; and (c) examine the behavior of the log-likelihood ratio test. We conclude that estimates of ARMA parameters obtained with SEM software are identical to those obtained by univariate stochastic model preliminary estimation, and are not true ML estimates. Still, these estimates, which may be viewed as moment estimates, have the same asymptotic properties as ML estimates for pure autoregressive (AR) processes. For pure moving average (MA) processes, they are biased and less efficient. The estimates from SEM software for mixed processes seem to have the same asymptotic properties as ML estimates. Furthermore, the log-likelihood ratio is reliable for pure AR processes, but this is not the case for pure MA processes. For mixed processes, the behavior of the log-likelihood ratio varies, and in this case these statistics should be handled with caution.  相似文献   

19.
研究了M/G/c排队系统中顾客队长、排队长的置信区间的求解方法.利用Bootstrap原理,给出了正态区间法、枢轴量法和百分位区间法等三种计算方法.实际应用表明,三种方法都得到了较好的结果.以置信区间的长度为评价标准,正态区间法和百分位区间法较优.  相似文献   

20.
The assessment of mediation in dyadic data is an important issue if researchers are to test process models. Using an extended version of the actor–partner interdependence model the estimation and testing of mediation is complex, especially when dyad members are distinguishable (e.g., heterosexual couples). We show how the complexity of the model can be reduced by assuming specific dyadic patterns. Using structural equation modeling, we demonstrate how specific mediating effects and contrasts among effects can be tested by phantom models that permit point and bootstrap interval estimates. We illustrate the assessment of mediation and the strategies to simplify the model using data from heterosexual couples.  相似文献   

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