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1.
Though the common default maximum likelihood estimator used in structural equation modeling is predicated on the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to utilize distribution-free estimation methods. Fortunately, promising alternatives are being integrated into popular software packages. Bootstrap resampling, which is offered in AMOS (Arbuckle, 1997), is one potential solution for estimating model test statistic p values and parameter standard errors under nonnormal data conditions. This study is an evaluation of the bootstrap method under varied conditions of nonnormality, sample size, model specification, and number of bootstrap samples drawn from the resampling space. Accuracy of the test statistic p values is evaluated in terms of model rejection rates, whereas accuracy of bootstrap standard error estimates takes the form of bias and variability of the standard error estimates themselves.  相似文献   

2.
This study compared diagonal weighted least squares robust estimation techniques available in 2 popular statistical programs: diagonal weighted least squares (DWLS; LISREL version 8.80) and weighted least squares–mean (WLSM) and weighted least squares—mean and variance adjusted (WLSMV; Mplus version 6.11). A 20-item confirmatory factor analysis was estimated using item-level ordered categorical data. Three different nonnormality conditions were applied to 2- to 7-category data with sample sizes of 200, 400, and 800. Convergence problems were seen with nonnormal data when DWLS was used with few categories. Both DWLS and WLSMV produced accurate parameter estimates; however, bias in standard errors of parameter estimates was extreme for select conditions when nonnormal data were present. The robust estimators generally reported acceptable model–data fit, unless few categories were used with nonnormal data at smaller sample sizes; WLSMV yielded better fit than WLSM for most indices.  相似文献   

3.
The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were substantially less precise than those obtained from a correctly specified GMM. Bias and precision became worse as the ratio of the largest to smallest Level-1 residual variances increased, class proportions became more disparate, and the number of class-specific residual variances in the population increased. Although the Level-1 residuals are typically of little substantive interest, these results suggest that researchers should carefully estimate and report these parameters in published GMM applications.  相似文献   

4.
Type I error rate and power for the t test, Wilcoxon-Mann-Whitney (U) test, van der Waerden Normal Scores (NS) test, and Welch-Aspin-Satterthwaite (W) test were compared for two independent random samples drawn from nonnormal distributions. Data with varying degrees of skewness (S) and kurtosis (K) were generated using Fleishman's (1978) power function. Five sample size combinations were used with both equal and unequal variances. For nonnormal data with equal variances, the power of the U test exceeded the power of the t test regardless of sample size. When the sample sizes were equal but the variances were unequal, the t test proved to be the most powerful test. When variances and sample sizes were unequal, the W test became the test of choice because it was the only test that maintained its nominal Type I error rate.  相似文献   

5.
Gibbons and Chakraborti's (1991) interpretation of recent simulation results and their recommendations to researchers are misleading in some respects. The present note emphasizes that the Mann-Whitney test is not a suitable replacement of the Student t test when variances and sample sizes are unequal, irrespective of whether the assumption of normality is satisfied or violated. When both normality and homogeneity of variance are violated together, an effective procedure, not widely known to researchers in education and psychology, is the Fligner-Policello test or, alternatively, the Welch t' test in conjunction with transformation of the original scores to ranks.  相似文献   

6.
Growth mixture modeling (GMM) is a useful statistical method for longitudinal studies because it includes features of both latent growth modeling (LGM) and finite mixture modeling. This Monte Carlo simulation study explored the impact of ignoring 3 types of time series processes (i.e., AR(1), MA(1), and ARMA(1,1)) in GMM and manipulated the separation of the latent classes, the strength of the time series process, and whether the errors conformed to the time series process in 1 or 2 latent classes. The results showed that omitting time series processes resulted in more serious bias in parameter estimation as the distance between classes increased. However, when the class distances were small, ignoring time series processes contributed to the selection of the correct number of classes. When the GMM models correctly specified the time series process, only models with an AR(1) time series process produced unbiased parameter estimates in most conditions. It was also found that among design factors manipulated, the distance between classes prominently affected the identification of the number of classes and parameter estimation.  相似文献   

7.
In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.  相似文献   

8.
The accuracy of structural model parameter estimates in latent variable mixture modeling was explored with a 3 (sample size) × 3 (exogenous latent mean difference) × 3 (endogenous latent mean difference) × 3 (correlation between factors) × 3 (mixture proportions) factorial design. In addition, the efficacy of several likelihood-based statistics (Akaike's Information Criterion [AIC], Bayesian Information Ctriterion [BIC], the sample-size adjusted BIC [ssBIC], the consistent AIC [CAIC], the Vuong-Lo-Mendell-Rubin adjusted likelihood ratio test [aVLMR]), classification-based statistics (CLC [classification likelihood information criterion], ICL-BIC [integrated classification likelihood], normalized entropy criterion [NEC], entropy), and distributional statistics (multivariate skew and kurtosis test) were examined to determine which statistics best recover the correct number of components. Results indicate that the structural parameters were recovered, but the model fit statistics were not exceedingly accurate. The ssBIC statistic was the most accurate statistic, and the CLC, ICL-BIC, and aVLMR showed limited utility. However, none of these statistics were accurate for small samples (n = 500).  相似文献   

9.
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   

10.
There is a need for effect sizes that are readily interpretable by a broad audience. One index that might fill this need is π, which represents the proportion of scores in one group that exceed the mean of another group. The robustness of estimates of π to violations of normality had not been explored. Using simulated data, three estimates of π (π? direct, r, and rrobust) were studied under varying conditions of sample size, distribution shape, and group mean difference. This study demonstrated that r and rrobust were biased estimates of π when data were nonnormal. We recommend that neither be used in estimating π unless data are normally distributed.  相似文献   

11.
When the multivariate normality assumption is violated in structural equation modeling, a leading remedy involves estimation via normal theory maximum likelihood with robust corrections to standard errors. We propose that this approach might not be best for forming confidence intervals for quantities with sampling distributions that are slow to approach normality, or for functions of model parameters. We implement and study a robust analog to likelihood-based confidence intervals based on inverting the robust chi-square difference test of Satorra (2000). We compare robust standard errors and the robust likelihood-based approach versus resampling methods in confirmatory factor analysis (Studies 1 & 2) and mediation analysis models (Study 3) for both single parameters and functions of model parameters, and under a variety of nonnormal data generation conditions. The percentile bootstrap emerged as the method with the best calibrated coverage rates and should be preferred if resampling is possible, followed by the robust likelihood-based approach.  相似文献   

12.
As useful multivariate techniques, structural equation models have attracted significant attention from various fields. Most existing statistical methods and software for analyzing structural equation models have been developed based on the assumption that the response variables are normally distributed. Several recently developed methods can partially address violations of this assumption, but still encounter difficulties in analyzing highly nonnormal data. Moreover, the presence of missing data is a practical issue in substantive research. Simply ignoring missing data or improperly treating nonignorable missingness as ignorable could seriously distort statistical influence results. The main objective of this article is to develop a Bayesian approach for analyzing transformation structural equation models with highly nonnormal and missing data. Different types of missingness are discussed and selected via the deviance information criterion. The empirical performance of our method is examined via simulation studies. Application to a study concerning people’s job satisfaction, home life, and work attitude is presented.  相似文献   

13.
Treating Likert rating scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, and so forth, it seems nevertheless possible to recover true parameter values if the data stem from a single homogeneous population. It is shown that, in a multigroup context, an analysis of Likert data under the assumption of multivariate normality may distort the factor structure differently across groups. In that case, investigations of measurement invariance (MI), which are necessary for meaningful group comparisons, are problematic. Analyzing subscale scores computed from Likert items does not seem to solve the problem.  相似文献   

14.
In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2-parameter item response theory (IRT) model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and platykurtic latent variable distributions, 3 methods were compared in Mplus: limited information, full information integrating over a normal distribution, and full information integrating over the known underlying distribution. Interfactor correlation estimates were similar for all 3 estimation methods. For the platykurtic distribution, estimation method made little difference for the item parameter estimates. When the latent variable was negatively skewed, for the most discriminating easy or difficult items, limited-information estimates of both parameters were considerably biased. Full-information estimates obtained by marginalizing over a normal distribution were somewhat biased. Full-information estimates obtained by integrating over the true latent distribution were essentially unbiased. For the a parameters, standard errors were larger for the limited-information estimates when the bias was positive but smaller when the bias was negative. For the d parameters, standard errors were larger for the limited-information estimates of the easiest, most discriminating items. Otherwise, they were generally similar for the limited- and full-information estimates. Sample size did not substantially impact the differences between the estimation methods; limited information did not gain an advantage for smaller samples.  相似文献   

15.
This Monte Carlo study investigated the impacts of measurement noninvariance across groups on major parameter estimates in latent growth modeling when researchers test group differences in initial status and latent growth. The average initial status and latent growth and the group effects on initial status and latent growth were investigated in terms of Type I error and bias. The location and magnitude of noninvariance across groups was related to the location and magnitude of bias and Type I error in the parameter estimates. That is, noninvariance in factor loadings and intercepts was associated with the Type I error inflation and bias in the parameter estimates of the slope factor (or latent growth) and the intercept factor (or initial status), respectively. As noninvariance became large, the degree of Type I error and bias also increased. On the other hand, a correctly specified second-order latent growth model yielded unbiased parameter estimates and correct statistical inferences. Other findings and implications on future studies were discussed.  相似文献   

16.
A multiple testing procedure for examining the assumption of normality that is often made in analyses of incomplete data sets is outlined. The method is concerned with testing normality within each missingness pattern and arriving at an overall statement about normality using the available data. The approach is readily applied in empirical research with missing data using the popular software Mplus, Stata, and R. The procedure can be used to ascertain a main assumption underlying frequent applications of maximum likelihood in incomplete data modeling with continuous outcomes. The discussed approach is illustrated with numerical examples.  相似文献   

17.
在总体分布为指数分布和均匀分布时,由未知参数θ的无偏估计量,通过修正系数法直接构造θ2的无偏估计量.  相似文献   

18.
Growing interest in fully Bayesian item response models begs the question: To what extent can model parameter posterior draws enhance existing practices? One practice that has traditionally relied on model parameter point estimates but may be improved by using posterior draws is the development of a common metric for two independently calibrated test forms. Before parameter estimates from independently calibrated forms can be compared, at least one form's estimates must be adjusted such that both forms share a common metric. Because this adjustment is estimated, there is a propagation of error effect when it is applied. This effect is typically ignored, which leads to overconfidence in the adjusted estimates; yet, when model parameter posterior draws are available, it may be accounted for with a simple sampling strategy. In this paper, it is shown using simulated data that the proposed sampling strategy results in adjusted posteriors with superior coverage properties than those obtained using traditional point‐estimate‐based methods.  相似文献   

19.
Nonparametric and robust statistics (those using trimmed means and Winsorized variances) were compared for their ability to detect treatment effects in the 2-sample case. In particular, 2 specialized tests, tests designed to be sensitive to treatment effects when the distributions of the data are skewed to the right, were compared with 2 nonspecialized nonparametric (Wilcoxon-Mann-Whitney; Mann &; Whitney, 1947; Wilcoxon, 1949) and trimmed (Yuen, 1974) tests for 6 nonnormal distributions that varied according to their measures of. skewness and kurtosis. As expected, the specialized tests provided more power to detect treatment effects, particularly for the nonparametric comparison. However, when distributions were symmetric, the nonspecialized tests were more powerful; therefore, for all the distributions investigated, power differences did not favor the specialized tests. Consequently, the specialized tests are not recommended; researchers would have to know the shapes of the distributions that they work with in order to benefit from specialized tests. In addition, the nonparametric approach resulted in more power than the trimmed-means approach did.  相似文献   

20.
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   

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