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1.
The authors used Johnson's transformation with approximate test statistics to test the homogeneity of simple linear regression slopes when both xij and xij may have nonnormal distributions and there is Type I heteroscedasticity, Type II heteroscedasticity, or complete heteroscedasticity. The test statistic t was first transformed by Johnson's method for each group to correct the nonnormality and to correct the heteroscedasticity; also an approximate test, such as the Welch test or the DeShon-Alexander test, was applied to test the homogeneity of the regression slopes. Computer simulations showed that the proposed technique can control Type I error rate under various circumstances. Finally, the authors provide an example to demonstrate the calculation. 相似文献
2.
The authors performed a Monte Carlo simulation to empirically investigate the robustness and power of 4 methods in testing mean differences for 2 independent groups under conditions in which 2 populations may not demonstrate the same pattern of nonnormality. The approaches considered were the t test, Wilcoxon rank-sum test, Welch-James test with trimmed means and Winsorized variances, and a nonparametric bootstrap test. Results showed that the Wilcoxon rank-sum test and Welch-James test with trimmed means and Winsorized variances were not robust in terms of type I error control when the 2 populations showed different patterns of nonnormality. The nonparametric bootstrap test provided power advantages over the t test. The authors discuss other results from the simulation study and provide recommendations. 相似文献
3.
Keke Lai 《Structural equation modeling》2018,25(4):600-620
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
4.
Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we describe a nonlinear structural equation mixture approach that integrates the strength of parametric approaches (specification of the nonlinear functional relationship) and the flexibility of semiparametric structural equation mixture approaches for approximating the nonnormality of latent predictor variables. In a comparative simulation study, the advantages of the proposed mixture procedure over contemporary approaches [Latent Moderated Structural Equations approach (LMS) and the extended unconstrained approach] are shown for varying degrees of skewness of the latent predictor variables. Whereas the conventional approaches show either biased parameter estimates or standard errors of the nonlinear effects, the proposed mixture approach provides unbiased estimates and standard errors. We present an empirical example from educational research. Guidelines for applications of the approaches and limitations are discussed. 相似文献
5.
Augustin Kelava Christina S. Werner Karin Schermelleh-Engel Helfried Moosbrugger Dieter Zapf Yue Ma 《Structural equation modeling》2013,20(3):465-491
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x 1 2, x 1 x 4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches. A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided. 相似文献
6.
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
7.
We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's maximum likelihood (ML) chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single- and multiple-group form for specifying the model M 10 that is involved in the new test. 相似文献
8.
Wei Zhang 《Structural equation modeling》2013,20(2):301-326
A major issue in the utilization of covariance structure analysis is model fit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indexes, most of which are actually based on or closely related to F 0, a measure of model fit in the population. This study aims to provide a systematic investigation about the performance of 4 available estimators of F 0. [Fcirc]01 is the conventional estimator and is based on noncentral chi-square approximation. [Fcirc]02 is newly proposed and does not assume noncentral chi-square approximation. [Fcirc]03 and [Fcirc]04 are variations of [Fcirc]02. A Monte Carlo simulation study is conducted to examine how these four estimators of F 0 perform across varying model misspecifications, data distributions, model sizes, and sample sizes. The results show that under normality all 4 quantities estimate F 0 equally well, and under nonnormality [Fcirc]02, [Fcirc]03, and [Fcirc]04 outperform [Fcirc]01. Issues related to these findings are discussed. 相似文献
9.
Sandip Sinharay 《教育实用测度》2017,30(4):314-328
Karabatsos compared the power of 36 person-fit statistics using receiver operating characteristics curves and found the HT statistic to be the most powerful in identifying aberrant examinees. He found three statistics, C, MCI, and U3, to be the next most powerful. These four statistics, all of which are nonparametric, were found to perform considerably better than each of 25 parametric person-fit statistics. Dimitrov and Smith replicated part of this finding in a similar study. The present article raises some issues with the comparisons performed in Karabatsos and Dimitrov and Smith and points to literature that suggests that the comparisons could have been performed in a more traditional and more fair manner. The present article then replicates the simulations of Karabatsos and demonstrates in several ways that the parametric person-fit statistics lz and ECI4z (that were also considered by Karabatsos) are as powerful as are HT and U3 in identifying aberrant examinees in more traditional and fair comparisons. Two parametric person-fit statistics are shown to lead to similar results as HT and U3 in a real data example. 相似文献
10.
A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-based F statistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort. 相似文献
11.
This study presents a theory by which to understand how pigeons learn response patterns in simple choice situations. The theory assumes that, in a choice situation, patterns of responses compete for the final common path; that the competition is governed by two variables, the overall reinforcement probability obtained by emitting the patterns,T, and the differences in reinforcement probabilities among the patterns,D; and that the ratioD/T determines the final strength of specific response patterns. To test these predictions, three experiments were run in which pigeons were more likely to receive food when they pecked the momentarily least-preferred of three response keys. On the basis of previous research, it was predicted that the birds would be indifferent among the keys (molar aspect) and would also acquire a response pattern that consisted of pecking each key once during three consecutive trials (molecular aspect). The present theory went further and predicted that the strength of that pattern would increase with the ratioD/T. In the first two experiments,D was manipulated whileT remained constant, and in the third,T was manipulated whileD remained constant. The results agreed with the theory, for the strength of the response pattern increased withD and decreased withT, whereas overall choice proportions were always close to the matching equilibrium. 相似文献
12.
The purpose of this study is to investigate the effects of missing data techniques in longitudinal studies under diverse conditions. A Monte Carlo simulation examined the performance of 3 missing data methods in latent growth modeling: listwise deletion (LD), maximum likelihood estimation using the expectation and maximization algorithm with a nonnormality correction (robust ML), and the pairwise asymptotically distribution-free method (pairwise ADF). The effects of 3 independent variables (sample size, missing data mechanism, and distribution shape) were investigated on convergence rate, parameter and standard error estimation, and model fit. The results favored robust ML over LD and pairwise ADF in almost all respects. The exceptions included convergence rates under the most severe nonnormality in the missing not at random (MNAR) condition and recovery of standard error estimates across sample sizes. The results also indicate that nonnormality, small sample size, MNAR, and multicollinearity might adversely affect convergence rate and the validity of statistical inferences concerning parameter estimates and model fit statistics. 相似文献
13.
Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test statistics. A modification to the Satorra–Bentler scaled statistic is developed for the condition that sample size is smaller than degrees of freedom. The behavior of the 4 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study that varies 7 sample sizes and 3 distributional conditions obtained using Headrick's fifth-order transformation to nonnormality. The new statistic performs badly in most conditions except under the normal distribution. The goodness-of-fit χ2 test based on maximum-likelihood estimation performed well under normal distributions as well as under a condition of asymptotic robustness. The Satorra–Bentler scaled test statistic performed best overall, whereas the mean scaled and variance adjusted test statistic outperformed the others at small and moderate sample sizes under certain distributional conditions. 相似文献
14.
Supersaturated solid solutions Fe1-xCx （0≤x≤0.9 ） of wide composition range have been prepared by mechanical alloying process. Nanocrystalline phase was formed for 0 ≤ x ≤ 0.67 and a large grain phase for 0.75 ≤ x ≤ 0.9. The large fraction of graphite volume puts off formation of nanocrystalline phase for high carbon content. In the large grain phase, magnetization follows simple magnetic dilution, and eoereivity He is mainly due to dissolution of carbon at grain boundaries. In the nanocrystalline phase the alloying effect of carbon is revealed by a distinct reduction of average magnetic moment. The increasing lattice constant with increasing carbon content is observed for x ≤ 0.5, suggesting that the high carbon concentration may enhance diffusion of carbon into the Fe lattice. It shows a discontinuity in the Hc variation with a grain size D of nanocrystalline phase. For small grain D below the critical value, Hc increases with D. For a large grain D, Hc decreases with increasing D. The solubility limit of carbon in a-Fe extended by nanocry- stalline phase formation is discussed. 相似文献
15.
Ke-Hai Yuan Wai Chan George A. Marcoulides Peter M. Bentler 《Structural equation modeling》2016,23(3):319-330
Conventional null hypothesis testing (NHT) is a very important tool if the ultimate goal is to find a difference or to reject a model. However, the purpose of structural equation modeling (SEM) is to identify a model and use it to account for the relationship among substantive variables. With the setup of NHT, a nonsignificant test statistic does not necessarily imply that the model is correctly specified or the size of misspecification is properly controlled. To overcome this problem, this article proposes to replace NHT by equivalence testing, the goal of which is to endorse a model under a null hypothesis rather than to reject it. Differences and similarities between equivalence testing and NHT are discussed, and new “T-size” terminology is introduced to convey the goodness of the current model under equivalence testing. Adjusted cutoff values of root mean square error of approximation (RMSEA) and comparative fit index (CFI) corresponding to those conventionally used in the literature are obtained to facilitate the understanding of T-size RMSEA and CFI. The single most notable property of equivalence testing is that it allows a researcher to confidently claim that the size of misspecification in the current model is below the T-size RMSEA or CFI, which gives SEM a desirable property to be a scientific methodology. R code for conducting equivalence testing is provided in an appendix. 相似文献
16.
Surface morphologies of Zr52.5 Al10 Ni10 Cu15 Be12.5 bulk metallic glass after being rolled at both a temperature around T9 and near （ Tx - 50） K were investigated with a scanning electron microscopy. Macroscopic and microscopic observation results show that squamae, cracks, steps and wedges exist on the surface when the samples were rolled at temperatures around Ty. However, a smooth and fiat surface appears when the samples were rolled at temperatures near （ Tx - 50） K. These results indicate that the mode of deformation in the supercooled liquid region is a partially homogeneous flow at a temperature around T9, and a fully homogeneous one at temperatures near （ Tx - 50） K. According to the results, it is more feasible to roll the amorphous alloys at temperatures near （ Tx - 50） K to obtain parts with smooth and fiat surface. 相似文献
17.
Victoria Savalei 《Structural equation modeling》2013,20(1):149-160
Robust corrections to standard errors and test statistics have wide applications in structural equation modeling (SEM). The original SEM development, due to Satorra and Bentler (1988, 1994), was to account for the effect of nonnormality. Muthén (1993) proposed corrections to accompany certain categorical data estimators, such as cat-LS or cat-DWLS. Other applications of robust corrections exist. Despite the diversity of applications, all robust corrections are constructed using the same underlying rationale: They correct for inefficiency of the chosen estimator. The goal of this article is to make the formulas behind all types of robust corrections more intuitive. This is accomplished by building an analogy with similar equations in linear regression and then by reformulating the SEM model as a nonlinear regression model. 相似文献
18.
Kevin J. Grimm Yang An John J. McArdle Alan B. Zonderman Susan M. Resnick 《Structural equation modeling》2013,20(2):268-292
Latent difference score models (e.g., McArdle & Hamagami, 2001) are extended to include effects from prior changes to subsequent changes. This extension of latent difference scores allows for testing hypotheses where recent changes, as opposed to recent levels, are a primary predictor of subsequent changes. These models are applied to bivariate longitudinal data collected as part of the Baltimore Longitudinal Study of Aging on memory performance, measured by the California Verbal Learning Test, and lateral ventricle size, measured by structural MRIs. Results indicate that recent increases in the lateral ventricle size were a leading indicator of subsequent declines in memory performance from age 60 to 90. 相似文献
19.
20.
Patrick C.Y.WOO Samson S.Y.WONG Jade L.L.TENG Kit-Wah LEUNG Antonio H.Y.NGAN Herman TSE Susanna K.P.LAU Kwok-Yung YUEN 《Journal of Zhejiang University. Science. B》2010,11(6):391-401
A straight, non-sporulating, Gram-variable bacillus (HKU24T) was recovered from the blood culture of a patient with metastatic breast carcinoma. After repeated subculturing in BACTEC Plus Anaerobic/F blood culture broth, HKU24T grew on brucella agar as non-hemolytic, pinpoint colonies after 96 h of incubation at 37 °C in an anaerobic environment and aerobic environment with 5% CO2. Growth was enhanced with a streak of Staphylococcus aureus. HKU24T was non-motile and catalase-negative, but positive for alkaline phosphatase, β-glucosidase, and α-glucosidase. It hydrolyzed phenylphosphonate and reduced resazurin. 16S rRNA, groEL, gyrB, recA, and rpoB sequencing showed that HKU24T occupies a distinct phylogenetic position among the Leptotrichia species, being most closely related to Leptotrichia trevisanii. Using HKU24T groEL, gyrB, recA, and rpoB gene-specific primers, fragments of these genes were amplified from one of 20 oral specimens. Based on phenotypic and genotypic characteristics, we propose a new species, Leptotrichia hongkongensis sp. nov., to describe this bacterium. 相似文献