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1.
This Monte Carlo simulation study investigated the impact of nonnormality on estimating and testing mediated effects with the parallel process latent growth model and 3 popular methods for testing the mediated effect (i.e., Sobel’s test, the asymmetric confidence limits, and the bias-corrected bootstrap). It was found that nonnormality had little effect on the estimates of the mediated effect, standard errors, empirical Type I error, and power rates in most conditions. In terms of empirical Type I error and power rates, the bias-corrected bootstrap performed best. Sobel’s test produced very conservative Type I error rates when the estimated mediated effect and standard error had a relationship, but when the relationship was weak or did not exist, the Type I error was closer to the nominal .05 value.  相似文献   

2.
The standardized log-likelihood of a response vector (lz) is a popular IRT-based person-fit test statistic for identifying model-misfitting response patterns. Traditional use of lz is overly conservative in detecting aberrance due to its incorrect assumption regarding its theoretical null distribution. This study proposes a method for improving the accuracy of person-fit analysis using lz which takes into account test unreliability when estimating the ability and constructs the distribution for each lz through resampling methods. The Type I error and power (or detection rate) of the proposed method were examined at different test lengths, ability levels, and nominal α levels along with other methods, and power to detect three types of aberrance—cheating, lack of motivation, and speeding—was considered. Results indicate that the proposed method is a viable and promising approach. It has Type I error rates close to the nominal value for most ability levels and reasonably good power.  相似文献   

3.
Although much is known about the performance of recent methods for inference and interval estimation for indirect or mediated effects with observed variables, little is known about their performance in latent variable models. This article presents an extensive Monte Carlo study of 11 different leading or popular methods adapted to structural equation models with latent variables. Manipulated variables included sample size, number of indicators per latent variable, internal consistency per set of indicators, and 16 different path combinations between latent variables. Results indicate that some popular or previously recommended methods, such as the bias-corrected bootstrap and asymptotic standard errors had poorly calibrated Type I error and coverage rates in some conditions. Likelihood-based confidence intervals, the distribution of the product method, and the percentile bootstrap emerged as leading methods for both interval estimation and inference, whereas joint significance tests and the partial posterior method performed well for inference.  相似文献   

4.
This article used the Wald test to evaluate the item‐level fit of a saturated cognitive diagnosis model (CDM) relative to the fits of the reduced models it subsumes. A simulation study was carried out to examine the Type I error and power of the Wald test in the context of the G‐DINA model. Results show that when the sample size is small and a larger number of attributes are required, the Type I error rate of the Wald test for the DINA and DINO models can be higher than the nominal significance levels, while the Type I error rate of the A‐CDM is closer to the nominal significance levels. However, with larger sample sizes, the Type I error rates for the three models are closer to the nominal significance levels. In addition, the Wald test has excellent statistical power to detect when the true underlying model is none of the reduced models examined even for relatively small sample sizes. The performance of the Wald test was also examined with real data. With an increasing number of CDMs from which to choose, this article provides an important contribution toward advancing the use of CDMs in practical educational settings.  相似文献   

5.
Mechanisms accounting for the effects of mutually responsive orientation (MRO) at 7, 15, and 25 months in 102 mother-child and father-child dyads on child internalization and self-regulation at 52 months were examined. Two mediators at 38 months were tested: parental power assertion and child self-representation. For mother-child relationships, the causal pathway involving power assertion was supported for both outcomes. Diminished power assertion fully mediated beneficial effect of mother-child MRO on internalization and partially mediated its effect on self-regulation. For father-child relationships, MRO predicted self-regulation, but the mediational paths were unsupported. Paternal power assertion correlated negatively with both outcomes but was not a mediator. Although MRO with both parents correlated with child self-representation, and it correlated with self-regulation, this mediational path was unsupported.  相似文献   

6.
This article extends the Bonett (2003a) approach to testing the equality of alpha coefficients from two independent samples to the case of m ≥ 2 independent samples. The extended Fisher-Bonett test and its competitor, the Hakstian-Whalen (1976) test, are illustrated with numerical examples of both hypothesis testing and power calculation. Computer simulations are used to compare the performance of the two tests and the Feldt (1969) test (for m = 2) in terms of power and Type I error control. It is shown that the Fisher-Bonett test is just as effective as its competitors in controlling Type I error, is comparable to them in power, and is equally robust against heterogeneity of error variance.  相似文献   

7.
Mechanisms accounting for the effects of mutually responsive orientation (MRO) at 7, 15, and 25 months in 102 mother–child and father–child dyads on child internalization and self-regulation at 52 months were examined. Two mediators at 38 months were tested: parental power assertion and child self-representation. For mother–child relationships, the causal pathway involving power assertion was supported for both outcomes. Diminished power assertion fully mediated beneficial effect of mother–child MRO on internalization and partially mediated its effect on self-regulation. For father–child relationships, MRO predicted self-regulation, but the mediational paths were unsupported. Paternal power assertion correlated negatively with both outcomes but was not a mediator. Although MRO with both parents correlated with child self-representation, and it correlated with self-regulation, this mediational path was unsupported.  相似文献   

8.
Two simulation studies investigated Type I error performance of two statistical procedures for detecting differential item functioning (DIF): SIBTEST and Mantel-Haenszel (MH). Because MH and SIBTEST are based on asymptotic distributions requiring "large" numbers of examinees, the first study examined Type 1 error for small sample sizes. No significant Type I error inflation occurred for either procedure. Because MH has the potential for Type I error inflation for non-Rasch models, the second study used a markedly non-Rasch test and systematically varied the shape and location of the studied item. When differences in distribution across examinee group of the measured ability were present, both procedures displayed inflated Type 1 error for certain items; MH displayed the greater inflation. Also, both procedures displayed statistically biased estimation of the zero DIF for certain items, though SIBTEST displayed much less than MH. When no latent distributional differences were present, both procedures performed satisfactorily under all conditions.  相似文献   

9.
The authors compared the Type I error rate and the power to detect differences in slopes and additive treatment effects of analysis of covariance (ANCOVA) and randomized block (RB) designs with a Monte Carlo simulation. For testing differences in slopes, 3 methods were compared: the test of slopes from ANCOVA, the omnibus Block × Treatment interaction, and the linear component of the Block × Treatment interaction of RB. In the test for adjusted means, 2 variations of both ANCOVA and RB were used. The power of the omnibus test of the interaction decreased dramatically as the number of blocks used increased and was always considerably smaller than the specific test of differences in slopes found in ANCOVA. Tests for means when there were concomitant differences in slopes showed that only ANCOVA uniformly controlled Type I error under all configurations of design variables. The most powerful option in almost all simulations for tests of both slopes and means was ANCOVA.  相似文献   

10.
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11.
This study examined the effect of sample size ratio and model misfit on the Type I error rates and power of the Difficulty Parameter Differences procedure using Winsteps. A unidimensional 30-item test with responses from 130,000 examinees was simulated and four independent variables were manipulated: sample size ratio (20/100/250/500/1000); model fit/misfit (1 PL and 3PLc =. 15 models); impact (no difference/mean differences/variance differences/mean and variance differences); and percentage of items with uniform and nonuniform DIF (0%/10%/20%). In general, the results indicate the importance of ensuring model fit to achieve greater control of Type I error and adequate statistical power. The manipulated variables produced inflated Type I error rates, which were well controlled when a measure of DIF magnitude was applied. Sample size ratio also had an effect on the power of the procedure. The paper discusses the practical implications of these results.  相似文献   

12.
For the two-way factorial design in analysis of variance, the current article explicates and compares three methods for controlling the Type I error rate for all possible simple interaction contrasts following a statistically significant interaction, including a proposed modification to the Bonferroni procedure that increases the power of statistical tests for deconstructing interaction effects when they are of primary substantive interest. Results indicate the general superiority of the modified Bonferroni procedure over Scheffé and Roy-type procedures, where the Bonferroni and Scheffé procedures have been modified to accommodate the logical implications of a false omnibus interaction null hypothesis. An applied example is provided and considerations for applied researchers are offered.  相似文献   

13.
Monte Carlo simulations with 20,000 replications are reported to estimate the probability of rejecting the null hypothesis regarding DIF using SIBTEST when there is DIF present and/or when impact is present due to differences on the primary dimension to be measured. Sample sizes are varied from 250 to 2000 and test lengths from 10 to 40 items. Results generally support previous findings for Type I error rates and power. Impact is inversely related to test length. The combination of DIF and impact, with the focal group having lower ability on both the primary and secondary dimensions, results in impact partially masking DIF so that items biased toward the reference group are less likely to be detected.  相似文献   

14.
In the logistic regression (LR) procedure for differential item functioning (DIF), the parameters of LR have often been estimated using maximum likelihood (ML) estimation. However, ML estimation suffers from the finite-sample bias. Furthermore, ML estimation for LR can be substantially biased in the presence of rare event data. The bias of ML estimation due to small samples and rare event data can degrade the performance of the LR procedure, especially when testing the DIF of difficult items in small samples. Penalized ML (PML) estimation was originally developed to reduce the finite-sample bias of conventional ML estimation and also was known to reduce the bias in the estimation of LR for the rare events data. The goal of this study is to compare the performances of the LR procedures based on the ML and PML estimation in terms of the statistical power and Type I error. In a simulation study, Swaminathan and Rogers's Wald test based on PML estimation (PSR) showed the highest statistical power in most of the simulation conditions, and LRT based on conventional PML estimation (PLRT) showed the most robust and stable Type I error. The discussion about the trade-off between bias and variance is presented in the discussion section.  相似文献   

15.
This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. To obtain information about each possible data division, the authors carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. The authors studied robustness and power under several experimental conditions—different autocorrelation levels and different effect sizes as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. The authors obtained satisfactory Type II error rates only for large treatment effects. The relation between the lengths of the four phases appeared to be an important factor for the robustness and power of the randomization test.  相似文献   

16.
This study investigated the Type I error rate and power of four copying indices, K-index (Holland, 1996), Scrutiny! (Assessment Systems Corporation, 1993), g2 (Frary, Tideman, & Watts, 1977), and ω (Wollack, 1997) using real test data from 20,000 examinees over a 2-year period. The data were divided into three different test lengths (20, 40, and 80 items) and nine different sample sizes (ranging from 50 to 20,000). Four different amounts of answer copying were simulated (10%, 20%, 30%, and 40% of the items) within each condition. The ω index demonstrated the best Type I error control and power in all conditions and at all α levels. Scrutiny! and the K-index were uniformly conservative, and both had poor power to detect true copiers at the small α levels typically used in answer copying detection, whereas g2 was generally too liberal, particularly at small α levels. Some comments on the proper uses of copying indices are provided.  相似文献   

17.
Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and evaluate their performance with a Monte Carlo simulation study. We found that the 4 models performed similarly with respect to model fit, bias of parameter estimates, Type I error, and power to test the treatment effect. To demonstrate a multigroup latent growth model with dummy treatment indicators, we estimated the effect of students changing schools during elementary school years on their reading and mathematics achievement, using data from the Early Childhood Longitudinal Study Kindergarten Cohort.  相似文献   

18.
Abstract

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were compared with rates when no multiplicity control was imposed. The results indicate that Type I error rates become severely inflated with no multiplicity control, but also that familywise error controlling procedures were extremely conservative and had very little power for detecting true relations. False discovery rate controlling procedures provided a compromise between no multiplicity control and strict familywise error control and with large sample sizes provided a high probability of making correct inferences regarding all the parameters in the model.  相似文献   

19.
Models to assess mediation in the pretest–posttest control group design are understudied in the behavioral sciences even though it is the design of choice for evaluating experimental manipulations. The article provides analytical comparisons of the four most commonly used models to estimate the mediated effect in this design: analysis of covariance (ANCOVA), difference score, residualized change score, and cross-sectional model. Each of these models is fitted using a latent change score specification and a simulation study assessed bias, Type I error, power, and confidence interval coverage of the four models. All but the ANCOVA model make stringent assumptions about the stability and cross-lagged relations of the mediator and outcome that might not be plausible in real-world applications. When these assumptions do not hold, Type I error and statistical power results suggest that only the ANCOVA model has good performance. The four models are applied to an empirical example.  相似文献   

20.
This study examined and compared various statistical methods for detecting individual differences in change. Considering 3 issues including test forms (specific vs. generalized), estimation procedures (constrained vs. unconstrained), and nonnormality, we evaluated 4 variance tests including the specific Wald variance test, the generalized Wald variance test, the specific likelihood ratio (LR) variance test, and the generalized LR variance test under both constrained and unconstrained estimation for both normal and nonnormal data. For the constrained estimation procedure, both the mixture distribution approach and the alpha correction approach were evaluated for their performance in dealing with the boundary problem. To deal with the nonnormality issue, we used the sandwich standard error (SE) estimator for the Wald tests and the Satorra–Bentler scaling correction for the LR tests. Simulation results revealed that testing a variance parameter and the associated covariances (generalized) had higher power than testing the variance solely (specific), unless the true covariances were zero. In addition, the variance tests under constrained estimation outperformed those under unconstrained estimation in terms of higher empirical power and better control of Type I error rates. Among all the studied tests, for both normal and nonnormal data, the robust generalized LR and Wald variance tests with the constrained estimation procedure were generally more powerful and had better Type I error rates for testing variance components than the other tests. Results from the comparisons between specific and generalized variance tests and between constrained and unconstrained estimation were discussed.  相似文献   

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