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1.
Steffen Nestler 《Structural equation modeling》2013,20(3):461-473
This article applies Bollen’s (1996) 2-stage least squares/instrumental variables (2SLS/IV) approach for estimating the parameters in an unconditional and a conditional second-order latent growth model (LGM). First, the 2SLS/IV approach for the estimation of the means and the path coefficients in a second-order LGM is derived. An empirical example is then used to show that 2SLS/IV yields estimates that are similar to maximum likelihood (ML) in the estimation of a conditional second-order LGM. Three subsequent simulation studies are then presented to show that the new approach is as accurate as ML and that it is more robust against misspecifications of the growth trajectory than ML. Together, these results suggest that 2SLS/IV should be considered as an alternative to the commonly applied ML estimator. 相似文献
2.
Nonrecursive structural equation models generally take the form of feedback loops, involving 2 latent variables that are connected by 2 unidirectional paths, 1 starting with each variable and terminating in the other variable. Nonrecursive models belong to a larger class of path models that require the use of instrumental variables (IVs) to achieve model identification. Prior research has focused on SEM parameter estimation with IVs when indicators were continuous and normally distributed. Much less is known about how estimators function in the presence of categorical indicators, which are commonly used in the social sciences, such as with cognitive and affective instruments. In this study, there was specific interest in comparing the 2-stage least squares (2SLS) estimator and its categorical variant to other recommended estimators. This study compares the performance of several estimation approaches for fitting structural equation models with categorical indicator variables when IVs are necessary to obtain proper model estimates. Across conditions, 1 extension of the nonlinear 2SLS (N2SLS) approach, the nonlinear 3-stage least squares (N3SLS), which accounts for correlated errors among regressors within each model (as does the N2SLS), as well as correlations of errors across models, which N2SLS does not, appears to work the best among methods compared. 相似文献
3.
A great obstacle for wider use of structural equation modeling (SEM) has been the difficulty in handling categorical variables. Two data sets with known structure between 2 related binary outcomes and 4 independent binary variables were generated. Four SEM strategies and resulting apparent validity were tested: robust maximum likelihood (ML), tetrachoric correlation matrix input followed by SEM ML analysis, SEM ML estimation for the sum of squares and cross-products (SSCP) matrix input obtained by the log-linear model that treated all variables as dependent, and asymptotic distribution-free (ADF) SEM estimation. SEM based on the SSCP matrix obtained by the log-linear model and SEM using robust ML estimation correctly identified the structural relation between the variables. SEM using ADF added an extra parameter. SEM based on tetrachoric correlation input did not specify the data generating process correctly. Apparent validity was similar for all models presented. Data transformation used in log-linear modeling can serve as an input for SEM. 相似文献
4.
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
5.
《Structural equation modeling》2013,20(3):347-368
Several papers have been devoted to the use of structural equation modeling (SEM) software in fitting autoregressive moving average (ARMA) models to a univariate series observed in a single subject. Van Buuren (1997) went beyond specification and examined the nature of the estimates obtained with SEM software. Although the results were mixed, he concluded that these parameter estimates resemble true maximum likelihood (ML) estimates. Molenaar (1999) argued that the negative findings for pure moving average models might be due to the absence of invertibility constraints in Van Buuren's simulation experiment. The aim of this article is to (a) reexamine the nature of SEM estimates of ARMA parameters; (b) replicate Van Buuren's simulation experiment in light of Molenaar's comment; and (c) examine the behavior of the log-likelihood ratio test. We conclude that estimates of ARMA parameters obtained with SEM software are identical to those obtained by univariate stochastic model preliminary estimation, and are not true ML estimates. Still, these estimates, which may be viewed as moment estimates, have the same asymptotic properties as ML estimates for pure autoregressive (AR) processes. For pure moving average (MA) processes, they are biased and less efficient. The estimates from SEM software for mixed processes seem to have the same asymptotic properties as ML estimates. Furthermore, the log-likelihood ratio is reliable for pure AR processes, but this is not the case for pure MA processes. For mixed processes, the behavior of the log-likelihood ratio varies, and in this case these statistics should be handled with caution. 相似文献
6.
Francis L. Huang 《Journal of Experimental Education》2018,86(2):265-281
Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques (e.g., bootstrapping) used when analyzing clustered data sets only make adjustments to standard errors but not to the regression coefficients. Using a Monte Carlo simulation, we analyzed 54,000 data sets using both MLM and OLS under varying conditions and we show that coefficients of not just OLS models, but MLMs as well, may be biased when relevant higher-level variables are omitted from a model, a situation that is likely to occur when using large-scale, secondary data sets. However, we demonstrate that by including aggregated level-one variables at the higher level, the resulting bias can be effectively removed. 相似文献
7.
Data collected from questionnaires are often in ordinal scale. Unweighted least squares (ULS), diagonally weighted least squares (DWLS) and normal-theory maximum likelihood (ML) are commonly used methods to fit structural equation models. Consistency of these estimators demands no structural misspecification. In this article, we conduct a simulation study to compare the equation-by-equation polychoric instrumental variable (PIV) estimation with ULS, DWLS, and ML. Accuracy of PIV for the correctly specified model and robustness of PIV for misspecified models are investigated through a confirmatory factor analysis (CFA) model and a structural equation model with ordinal indicators. The effects of sample size and nonnormality of the underlying continuous variables are also examined. The simulation results show that PIV produces robust factor loading estimates in the CFA model and in structural equation models. PIV also produces robust path coefficient estimates in the model where valid instruments are used. However, robustness highly depends on the validity of instruments. 相似文献
8.
9.
Deborah L. Bandalos 《Structural equation modeling》2013,20(1):102-116
Robust maximum likelihood (ML) and categorical diagonally weighted least squares (cat-DWLS) estimation have both been proposed for use with categorized and nonnormally distributed data. This study compares results from the 2 methods in terms of parameter estimate and standard error bias, power, and Type I error control, with unadjusted ML and WLS estimation methods included for purposes of comparison. Conditions manipulated include model misspecification, level of asymmetry, level and categorization, sample size, and type and size of the model. Results indicate that cat-DWLS estimation method results in the least parameter estimate and standard error bias under the majority of conditions studied. Cat-DWLS parameter estimates and standard errors were generally the least affected by model misspecification of the estimation methods studied. Robust ML also performed well, yielding relatively unbiased parameter estimates and standard errors. However, both cat-DWLS and robust ML resulted in low power under conditions of high data asymmetry, small sample sizes, and mild model misspecification. For more optimal conditions, power for these estimators was adequate. 相似文献
10.
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
11.
《Structural equation modeling》2013,20(4):557-595
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
12.
N. G. Cadigan 《Structural equation modeling》2013,20(1):13-30
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
13.
Previous research indicates that relative fit indices in structural equation modeling may vary across estimation methods. Sugawara and MacCallum (1993) explained that the discrepancy arises from difference in the function values for the null model with no further derivation given. In this study, we derive explicit solutions for parameters of the null model. The null model specifies the variances of the observed variables as model parameters and fixes all the covariances to be zero. Three methods of estimation are considered: the maximum likelihood (ML) method, the ordinary least squares (OLS) method, and the generalized least squares (GLS) method. Results indicate that ML and LS yield an identical estimator, which is different from GLS. Function values and associated chi‐square statistics of the null model vary across estimation methods. Consequently, relative fit indices using the null model as the reference point in computation may yield different results depending on the estimation method chosen. An illustration example is given and implications of this study are discussed. 相似文献
14.
Paul T. von Hippel 《Structural equation modeling》2016,23(3):422-437
When analyzing incomplete data, is it better to use multiple imputation (MI) or full information maximum likelihood (ML)? In large samples ML is clearly better, but in small samples ML’s usefulness has been limited because ML commonly uses normal test statistics and confidence intervals that require large samples. We propose small-sample t-based ML confidence intervals that have good coverage and are shorter than t-based confidence intervals under MI. We also show that ML point estimates are less biased and more efficient than MI point estimates in small samples of bivariate normal data. With our new confidence intervals, ML should be preferred over MI, even in small samples, whenever both options are available. 相似文献
15.
Julio Antonio Gonzalez-pienda Jose Carlos Nunez Soledad Gonzalez-pumariega Luis Alvarez Cristina Roces Marta Garcia 《Journal of Experimental Education》2013,81(3):257-287
The authors used the structural equation model (SEM) approach to test a model hypothesizing the influence of parental involvement on students' academic aptitudes, self-concept, and causal attributions, as well as the influence of the 3 variables on academic achievement. The theoretical model was contrasted in a group of 12- to 18-year-old adolescents (N = 261) attending various educational centers. The results indicate that (a) parental involvement had a positive and significant influence on the participant's measured characteristics; (b) causal attribution was not causally related to self-concept or academic achievement when the task involved finding causes for success, but, self-concept and causal attributions were found to be significantly and reciprocally related when the task involved finding causes accounting for failure; (c) self-concept was statistically and predominantly causally related to academic achievement, but not vice versa; and (d) aptitude and self-concept accounted for academic achievement, although the effect of self-concept was predominant. These results suggest that in adolescence, cognitive-affective variables become crucial in accounting for academic behavior. 相似文献
16.
Exploratory structural equation modeling (ESEM) is an approach for analysis of latent variables using exploratory factor analysis to evaluate the measurement model. This study compared ESEM with two dominant approaches for multiple regression with latent variables, structural equation modeling (SEM) and manifest regression analysis (MRA). Main findings included: (1) ESEM in general provided the least biased estimation of the regression coefficients; SEM was more biased than MRA given large cross-factor loadings. (2) MRA produced the most precise estimation, followed by ESEM and then SEM. (3) SEM was the least powerful in the significance tests; statistical power was lower for ESEM than MRA with relatively small target-factor loadings, but higher for ESEM than MRA with relatively large target-factor loadings. (4) ESEM showed difficulties in convergence and occasionally created an inflated type I error rate under some conditions. ESEM is recommended when non-ignorable cross-factor loadings exist. 相似文献
17.
Steffen Wirth 《Teaching Statistics》2003,25(1):29-32
This article discusses the influence extreme observations can exert on linear correlation between variables. It shows that standard p‐values obtained according to ordinary least squares and median regression can be misleading. Bootstrapping can prevent underestimation of the standard error of the regression coefficient and therefore unmask the deceiving correlation. 相似文献
18.
Barbara K. Iverson Ernest T. Pascarella Patrick T. Terenzini 《Research in higher education》1984,21(2):123-136
Based on prior research conducted at residential colleges and universities, nonclassroom informal faculty-student contact appears to be an element of student socialization. This study extends this line of research to a commuter student population. The extent to which informal contact socializes students by influencing their educational aspiration level in a commuter setting is investigated using a longitudinal data collection with the student as unit of analysis. Ordinary least squares and two-stage least squares techniques are used to analyze the data. Significant interactions between informal faculty-student contact and race were found. White and nonwhite students were sbusequently analyzed separately. The ordinary least squares (OLS) multiple regression results suggest that informal contact makes a slight but significant contribution to the explanation of freshmen aspirations for whites, but not for nonwhites. The two-stage least squares (2SLS) analysis suggests that the assumption that contact influences aspiration may not be valid and, indeed, that aspiration level may cause students to seek to initiate informal contact with faculty. 相似文献
19.
Carlos G. Forero Alberto Maydeu-Olivares David Gallardo-Pujol 《Structural equation modeling》2013,20(4):625-641
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.
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