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1.
This simulation study demonstrates how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Using a fully crossed design, data were generated for 11 conditions of peakedness, 3 conditions of misspecification, and 5 different sample sizes. Three estimation methods (maximum likelihood [ML], generalized least squares [GLS], and weighted least squares [WLS]) were compared in terms of overall fit and the discrepancy between estimated parameter values and the true parameter values used to generate the data. Consistent with earlier findings, the results show that ML compared to GLS under conditions of misspecification provides more realistic indexes of overall fit and less biased parameter values for paths that overlap with the true model. However, despite recommendations found in the literature that WLS should be used when data are not normally distributed, we find that WLS under no conditions was preferable to the 2 other estimation procedures in terms of parameter bias and fit. In fact, only for large sample sizes (N = 1,000 and 2,000) and mildly misspecified models did WLS provide estimates and fit indexes close to the ones obtained for ML and GLS. For wrongly specified models WLS tended to give unreliable estimates and over-optimistic values of fit.  相似文献   

2.
Ridge generalized least squares (RGLS) is a recently proposed estimation procedure for structural equation modeling. In the formulation of RGLS, there is a key element, ridge tuning parameter, whose value determines the efficiency of parameter estimates. This article aims to optimize RGLS by developing formulas for the ridge tuning parameter to yield the most efficient parameter estimates in practice. For the formulas to have a wide scope of applicability, they are calibrated using empirical efficiency and via many conditions on population distribution, sample size, number of variables, and model structure. Results show that RGLS with the tuning parameter determined by the formulas can substantially improve the efficiency of parameter estimates over commonly used procedures with real data being typically nonnormally distributed.  相似文献   

3.
Six procedures for combining sets of IRT item parameter estimates obtained from different samples were evaluated using real and simulated response data. In the simulated data analyses, true item and person parameters were used to generate response data for three different-sized samples. Each sample was calibrated separately to obtain three sets of item parameter estimates for each item. The six procedures for combining multiple estimates were each applied, and the results were evaluated by comparing the true and estimated item characteristic curves. For the real data, the two best methods from the simulation data analyses were applied to three different-sized samples and the resulting estimated item characteristic curves were compared to the curves obtained when the three samples were combined and calibrated simultaneously. The results support the use of covariance matrix-weighted averaging and a procedure that involves sample-size-weighted averaging of estimated item characteristic curves at the center of the ability distribution  相似文献   

4.
《教育实用测度》2013,26(4):351-368
Through a large-scale simulation study, this article compares item parameter estimates obtained by the marginal maximum likelihood estimation (MMLE) and marginal Bayes modal estimation (MBME) procedures in the 3-parameter logistic model. The impact of different prior specifications on the MBME estimates is also investigated using carefully selected prior distributions. The results indicate that, in general, the MBME provides more accurate item parameter estimates than the MMLE procedure. The impact of different priors on the Bayesian estimates is modest when the examinee sample size is not extremely small.  相似文献   

5.
This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality assumption and using data transformation on repeated measures. Based on unconditional GMM with two latent trajectories, data were generated under different sample sizes (300, 800, and 1500), skewness (0.7, 1.2, and 1.6) and kurtosis (2 and 4) of outcomes, numbers of time points (4 and 8), and class proportions (0.5:0.5 and 0.25:0.75). Of the four distributions, it was found that skew-t GMM had the highest accuracy in terms of parameter estimation. In GMM based on data transformations, the adjusted logarithmic method was more effective in obtaining unbiased parameter estimates than the use of van der Waerden quantile normal scores. Even though adjusted logarithmic transformation in nonnormal GMM reduced computation time, skew-t GMM produced much more accurate estimation and was more robust over a range of simulation conditions. This study is significant in that it considers different levels of kurtosis and class proportions, which has not been investigated in depth in previous studies. The present study is also meaningful in that investigated the applicability of data transformation to nonnormal GMM.  相似文献   

6.
Ill conditioning of covariance and weight matrices used in structural equation modeling (SEM) is a possible source of inadequate performance of SEM statistics in nonasymptotic samples. A maximum a posteriori (MAP) covariance matrix is proposed for weight matrix regularization in normal theory generalized least squares (GLS) estimation. Maximum likelihood (ML), GLS, and regularized GLS test statistics (RGLS and rGLS) are studied by simulation in a 15-variable, 3-factor model with 15 levels of sample size varying from 60 to 100,000. A key result showed that in terms of nominal rejection rates, RGLS outperformed ML at all sample sizes below 500, and GLS at most sample sizes below 500. In larger samples, their performance was equivalent. The second regularization methodology (rGLS) performed well asymptotically, but poorly in small samples. Regularization in SEM deserves further study.  相似文献   

7.
Practical use of the matrix sampling (i.e. item sampling) technique requires the assumption that an examinee's response to an item is independent of the context in which the item occurs. This assumption was tested experimentally by comparing the responses of examinees to a population of items with the responses of examinees to item samples. Matrix sampling mean and variance estimates for verbal, quantitative, and attitude tests were used as dependent variables to test for differences between the “context” and “out-of-context” groups. The estimates obtained from both treatment groups were also compared with actual population values. No significant differences were found between treatments on matrix sample parameter estimates for any of the three types of tests.  相似文献   

8.
This study was designed to determine the minimum number of points required for continuous scaled variables before the Pearson product moment correlation coefficient (PPMCC) ceases to be an accurate estimate of their original correlation coefficient. The study was performed on samples from normal, exponential, and uniform distributions by using Monte Carlo techniques. After the PPMCC was determined for each sample, multiple grouping procedures were applied and the PPMCCs were recalculated to determine the effect of scaling on the correlation coefficient. The results showed that the PPMCC obtained by using transformed discrete ordinal-level variables tended to underestimate the true parameter. The minimum number required for precise PPMCC is five and the use of PPMCC with five or more points is recommended.  相似文献   

9.
To better understand the statistical properties of the deterministic inputs, noisy “and” gate cognitive diagnosis (DINA) model, the impact of several factors on the quality of the item parameter estimates and classification accuracy was investigated. Results of the simulation study indicate that the fully Bayes approach is most accurate when the prior distribution matches the latent class structure. However, when the latent classes are of indefinite structure, the empirical Bayes method in conjunction with an unstructured prior distribution provides much better estimates and classification accuracy. Moreover, using empirical Bayes with an unstructured prior does not lead to extremely poor results as other prior-estimation method combinations do. The simulation results also show that increasing the sample size reduces the variability, and to some extent the bias, of item parameter estimates, whereas lower level of guessing and slip parameter is associated with higher quality item parameter estimation and classification accuracy.  相似文献   

10.
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   

11.
LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. The implications of the ridge option for model fit statistics, parameter estimates, and standard errors are explored through the use of 2 examples. The results indicate that maximum likelihood estimates are quite stable with the ridge option, though fit statistics and standard errors vary considerably and therefore cannot be trusted. As a result of these findings, the application of the ridge method to structural equation models is not recommended.  相似文献   

12.
This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a Monte Carlo study is conducted. Results indicate that the estimates of factor loading matrix, transition matrix, and unique variances were asymptotically normal, accurate, precise, and robust, especially for moderate and long time series. The estimates of state residual variances were positively biased for shorter time series, but as the length of series increased, these estimates became accurate and precise. To illustrate the application of SSM the technique is applied to empirical multivariate time-series data on daily affect collected from 2 individuals in a dating couple.  相似文献   

13.
This study was an investigation of the relation between the reliability of difference scores, considered as a parameter characterizing a population of examinees, and the reliability estimates obtained from random samples from the population. The parameters in familiar equations for the reliability of difference scores were redefined in such a way that determinants of reliability in both populations and samples become more transparent. Computer simulation was used to find sample values and to plot frequency distributions of various correlations and variance ratios relevant to the reliability of differences. The shape of frequency distributions resulting from the simulations and the means and standard deviations of these distributions reveal the extent to which reliability estimates based on sample data can be expected to meaningfully represent population reliability.  相似文献   

14.
Recently, advancements in Bayesian structural equation modeling (SEM), particularly software developments, have allowed researchers to more easily employ it in data analysis. With the potential for greater use, come opportunities to apply Bayesian SEM in a wider array of situations, including for small sample size problems. Effective use of Bayseian estimation hinges on selection of appropriate prior distributions for model parameters. Researchers have suggested that informative priors may be useful with small samples, presuming that the mean of the prior is accurate with respect to the population mean. The purpose of this simulation study was to examine model parameter estimation for the Multiple Indicator Multiple Cause model when an informative prior distribution had an incorrect mean. Results demonstrated that the use of incorrect informative priors with somewhat larger variance than is typical, yields more accurate parameter estimates than do naïve priors, or maximum likelihood estimation. Implications for practice are discussed.  相似文献   

15.
Local‐influence diagnostics based on maximum likelihood (ML), generalized least squares (GLS), and unweighted least squares (ULS) fit functions are developed for structural equation models (SEMs). The influence of observations, components of observations, and variables is considered. The diagnostics are illustrated with an example data set, and comparisons are made with equivalent global measures of influence. The local influence of the data set on ML and GLS estimates is very similar, but it is much different from that of ULS. The local and global influence of observations is also very different. Although it is not possible to define a uniformly best measure of influence, the local‐influence diagnostics developed here are more versatile than global‐influence diagnostics in assessing an analysis with SEMs.  相似文献   

16.
The Weibull distribution has been widely used in reliability fields. A mixed Weibull distribution represents a population that consists of several Weibull subpopulations. In this paper, a new approach which combines the least-squares method with Bayes＇ theorem, takes advantage of the parameter estimation for single Weibull distribution is developed to estimate the parameters of each subpopulation. The estimates given by this paper also satisfy the maximum likelihood equation. The estimates of the failure rate of the mixed Weibull population are given. An actual test data is computed by using the proposed method. The Kolmogorov-Smirnov goodness-of-fit test turns out that the proposed method yields more accurate result.  相似文献   

17.
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   

18.
Detection of differential item functioning (DIF) on items intentionally constructed to favor one group over another was investigated on item parameter estimates obtained from two item response theory-based computer programs, LOGIST and BILOG. Signed- and unsigned-area measures based on joint maximum likelihood estimation, marginal maximum likelihood estimation, and two marginal maximum a posteriori estimation procedures were compared with each other to determine whether detection of DIF could be improved using prior distributions. Results indicated that item parameter estimates obtained using either prior condition were less deviant than when priors were not used. Differences in detection of DIF appeared to be related to item parameter estimation condition and to some extent to sample size.  相似文献   

19.
Factor analysis models with ordinal indicators are often estimated using a 3-stage procedure where the last stage involves obtaining parameter estimates by least squares from the sample polychoric correlations. A simulation study involving 324 conditions (1,000 replications per condition) was performed to compare the performance of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) in the procedure's third stage. Overall, both methods provided accurate and similar results. However, ULS was found to provide more accurate and less variable parameter estimates, as well as more precise standard errors and better coverage rates. Nevertheless, convergence rates for DWLS are higher. Our recommendation is therefore to use ULS, and, in the case of nonconvergence, to use DWLS, as this method might converge when ULS does not.  相似文献   

20.
Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.  相似文献   

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