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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.
In the presence of omitted variables or similar validity threats, regression estimates are biased. Unbiased estimates (the causal effects) can be obtained in large samples by fitting instead the Instrumental Variables Regression (IVR) model. The IVR model can be estimated using structural equation modeling (SEM) software or using Econometric estimators such as two-stage least squares (2SLS). We describe 2SLS using SEM terminology, and report a simulation study in which we generated data according to a regression model in the presence of omitted variables and fitted (a) a regression model using ordinary least squares, (b) an IVR model using maximum likelihood (ML) as implemented in SEM software, and (c) an IVR model using 2SLS. Coverage rates of the causal effect using regression methods are always unacceptably low (often 0). When using the IVR model, accurate coverage is obtained across all conditions when N = 500. Even when the IVR model is misspecified, better coverage than regression is generally obtained. Differences between 2SLS and ML are small and favor 2SLS in small samples (N ≤ 100).  相似文献   

3.
Research in covariance structure analysis suggests that nonnormal data will invalidate chi‐square tests and produce erroneous standard errors. However, much remains unknown about the extent to and the conditions under which highly skewed and kurtotic data can affect the parameter estimates, standard errors, and fit indices. Using actual kurtotic and skewed data and varying sample sizes and estimation methods, we found that (a) normal theory maximum likelihood (ML) and generalized least squares estimators were fairly consistent and almost identical, (b) standard errors tended to underestimate the true variation of the estimators, but the problem was not very serious for large samples (n = 1,000) and conservative (99%) confidence intervals, and (c) the adjusted chi‐square tests seemed to yield acceptable results with appropriate sample sizes.  相似文献   

4.
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   

5.
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   

6.
Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the t distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. The analysis of mathematical development data shows that the robust latent basis growth curve model better describes the mathematical growth trajectory than the corresponding normal growth curve model and can reveal the individual differences in mathematical development. Simulation studies further confirm that the robust growth curve models significantly outperform the normal growth curve models for both heavy-tailed t data and normal data with outliers but lose only slight efficiency for normal data. It appears convincing to replace the normal distribution with the t distribution for growth curve analysis. Three information criteria are evaluated for model selection. Online software is also provided for conducting robust analysis discussed in this study.  相似文献   

7.
The author asserts that editors should publicly declare their expectations and expose the rationales for editorial policies to public scrutiny. He argues that editorial policies ought to require effect size reporting, as those at 17 journals now do. He also argues (a) that score reliabilities should be reported; (b) that stepwise methods should not be used; (c) that structure coefficients should be interpreted; and (d) that if used wisely, confidence intervals differ from hypothesis tests in important ways. The use of noncentral t and F distributions to create confidence intervals about effect sizes also is appealing.  相似文献   

8.
In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts’ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts’ prior beliefs on possible intervals of the parameters of the probability distributions is presented. The model integrates experts’ judgments with statistical data to obtain more convincible assessments of software reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda (JM) model using maximum likelihood (ML). Project supported by the National High-Technology Research and Development Program of China (Grant Nos.2006AA01Z187, 2007AA040605)  相似文献   

9.
Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is to use polychoric correlations and fit the models using methods such as unweighted least squares (ULS), maximum likelihood (ML), weighted least squares (WLS), or diagonally weighted least squares (DWLS). In this simulation evaluation we study the behavior of these methods in combination with polychoric correlations when the models are misspecified. We also study the effect of model size and number of categories on the parameter estimates, their standard errors, and the common chi-square measures of fit when the models are both correct and misspecified. When used routinely, these methods give consistent parameter estimates but ULS, ML, and DWLS give incorrect standard errors. Correct standard errors can be obtained for these methods by robustification using an estimate of the asymptotic covariance matrix W of the polychoric correlations. When used in this way the methods are here called RULS, RML, and RDWLS.  相似文献   

10.
The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact traditional marginal maximum likelihood (ML) estimation of IRT model parameters, including sample size, with smaller samples generally being associated with lower parameter estimation accuracy, and inflated standard errors for the estimates. Given this deleterious impact of small samples on IRT model performance, use of these techniques with low-incidence populations, where it might prove to be particularly useful, estimation becomes difficult, especially with more complex models. Recently, a Pairwise estimation method for Rasch model parameters has been suggested for use with missing data, and may also hold promise for parameter estimation with small samples. This simulation study compared item difficulty parameter estimation accuracy of ML with the Pairwise approach to ascertain the benefits of this latter method. The results support the use of the Pairwise method with small samples, particularly for obtaining item location estimates.  相似文献   

11.
Authors who write introductory business statistics texts do not agree on when to use a t distribution and when to use a Z distribution in both the construction of confidence intervals and the use of hypothesis testing. In a survey of textbooks written in the last 15 years, we found the decision rules to be contradictory and, at times, the explanations unclear. This paper is an attempt to clarify the decision rules and to recommend that one consistent rule be chosen to minimize confusion to students, instructors, and practitioners. Using the t distribution whenever σ is unknown, regardless of sample size, seems to provide the best solution both theoretically and practically.  相似文献   

12.
The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ2 test TAGLS and its small-sample variants TYB and TF(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic TAGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics TYB and TF(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed.  相似文献   

13.
In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BCa intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice.  相似文献   

14.
Although population modeling methods are well established, a paucity of literature appears to exist regarding the effect of missing background data on subpopulation achievement estimates. Using simulated data that follows typical large‐scale assessment designs with known parameters and a number of missing conditions, this paper examines the extent to which missing background data impacts subpopulation achievement estimates. In particular, the paper compares achievement estimates under a model with fully observed background data to achievement estimates for a variety of missing background data conditions. The findings suggest that sub‐population differences are preserved under all analyzed conditions while point estimates for subpopulation achievement values are influenced by missing at random conditions. Implications for cross‐population comparisons are discussed.  相似文献   

15.
小样本测量值正态分布的检验与可疑值的取舍   总被引：1，自引：0，他引：1  
当消除了系统误差时，则量值的分布遵正态分布。根据这一基本原理，本文对小样本可疑值的取舍提出了一种新方法。该方法先检验小样本是否遵从正态分布。凡遵从正态分布的小样本，全部则量值都应该保留；对不遵从正态分布的小样本，再用统计量Ｆ进行舍弃，舍弃后的新样本，若遵从正态分布，余下的则量值都应该保留；若不遵从正态分布，还得继续舍弃，如果舍弃的则量值个数较多，仍不遵从正态分布，说明则量过程存在较大的系统误差或样本来自非正态总体。本文最后对小样本可疑值的取舍进行了评价  相似文献   

16.
Bayesian methods have the potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This article compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N ≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N ≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results.  相似文献   

17.
ABSTRACT

The Powerful Tools for Caregivers (PTC) program is designed to help caregivers develop skills to improve their self-efficacy in caregiving. To demonstrate the effectiveness of the PTC program in Boise, Idaho, the program’s pre-survey (n = 277), end-of-program survey (n = 131), and 6-month follow-up post-survey data (n = 100) collected between 2011 and 2017 were analyzed in this study. The end-of-program survey data indicated that caregivers viewed the quality of the program to be excellent and that all of them felt more confident as a caregiver. Factor analysis and reliability testing on the pre-survey data confirmed that seven questions included in the pre- and 6-month follow-up post-survey instruments reliably measured a single factor named as caregiver confidence. A paired samples t-test on 76 complete sets of pre- and 6-month follow-up post-survey data on the seven questions revealed that caregivers improved their confidence in caregiving to a statistically significant level (p < .001, d = 45). Additional paired samples t-tests on each of the seven questions with the Bonferroni correction showed statistically significant improvements in three areas: making tough decisions (p < .001, d = .53), coping with emotions (p < .001, d = .54), and using stress-reducing activities (p < .007, d = .33). Caregivers experienced the greatest improvement in their confidence in making tough decisions. Despite these significant improvements, caregivers still struggled with finding ways to reduce stress and manage their emotions associated with caregiving as shown by the lowest pre- and 6-month follow-up post-survey scores. In addition to the study results, several considerations when synthesizing PTC research results are discussed.  相似文献   

18.
As Bayesian methods continue to grow in accessibility and popularity, more empirical studies are turning to Bayesian methods to model small sample data. Bayesian methods do not rely on asympotics, a property that can be a hindrance when employing frequentist methods in small sample contexts. Although Bayesian methods are better equipped to model data with small sample sizes, estimates are highly sensitive to the specification of the prior distribution. If this aspect is not heeded, Bayesian estimates can actually be worse than frequentist methods, especially if frequentist small sample corrections are utilized. We show with illustrative simulations and applied examples that relying on software defaults or diffuse priors with small samples can yield more biased estimates than frequentist methods. We discuss conditions that need to be met if researchers want to responsibly harness the advantages that Bayesian methods offer for small sample problems as well as leading small sample frequentist methods.  相似文献   

19.
Many students find understanding confidence intervals difficult, especially because of the amalgamation of concepts such as confidence levels, standard error, point estimates and sample sizes. An R Shiny application was created to assist the learning process of confidence intervals using graphics and data from the US National Basketball Association.  相似文献   

20.
Abstract

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the p values corresponding to intervals of fixed width). Thus, multilevel models address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern.  相似文献   

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