Constrained versus unconstrained estimation in structural equation modeling.

Savalei, Victoria; Kolenikov, Stanislav

doi:10.1037/1082-989x.13.2.150

Cited by 93 publications

(83 citation statements)

References 50 publications

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“…We then controlled these two coefficients to be equal and re-ran the estimation in the constrained structural model. The results indicated that the constrained model fitted to the data worse than the unconstrained model [Dv 2 (1) = 3.851, p \ .05], suggesting that the regression weight between green management and radical product innovation was significantly stronger than that between green management and incremental product innovation (Savalei and Kolenikov 2008). Thus, H1 was supported.…”

Section: Resultsmentioning

confidence: 47%

How Green Management Influences Product Innovation in China: The Role of Institutional Benefits

et al. 2014

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Does being green facilitate product innovation? This study examines whether green management in firms operating in China fosters radical product innovation to a greater extent than it does incremental product innovation and investigates the underlying institutional mechanisms involved in the relationship between green management and product innovation. The findings show that green management is more likely to lead to radical product innovation than to incremental product innovation. Moreover, government support as a formal institutional benefit more strongly mediates the effect of green management on radical product innovation than its effect on incremental product innovation; whereas social legitimacy as an informal institutional benefit more strongly mediates the effect of green management on incremental product innovation than its effect on radical product innovation. These findings provide important implications for explaining how firms employ green management to facilitate product innovation.

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Section: Resultsmentioning

confidence: 47%

How Green Management Influences Product Innovation in China: The Role of Institutional Benefits

et al. 2014

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“…Standard Z-tests may be appropriate in such situations, since the parameter space is no longer bounded and the null value is no longer on the boundary of the parameter space. Interested readers are referred to Savalei and Kolenikov (2008) for a more thorough discussion of constrained versus non-constrained variance component estimates.…”

Section: Level-2 Variance Component Point Estimate Simulation Study Fmentioning

confidence: 99%

The Effect of Small Sample Size on Two-Level Model Estimates: A Review and Illustration

2014

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Multilevel models are an increasingly popular method to analyze data that originate from a clustered or hierarchical structure. To effectively utilize multilevel models, one must have an adequately large number of clusters; otherwise, some model parameters will be estimated with bias. The goals for this paper are to (1) raise awareness of the problems associated with a small number of clusters, (2) review previous studies on multilevel models with a small number of clusters, (3) to provide an illustrative simulation to demonstrate how a simple model becomes adversely affected by small numbers of clusters, (4) to provide researchers with remedies if they encounter clustered data with a small number of clusters, and (5) to outline methodological topics that have yet to be addressed in the literature.Keywords Multilevel model . HLM . Small sample . Mixed model . Small number of clusters Frequently in educational psychology research, observations have a hierarchical structure (Raudenbush and Bryk 2002). Students are nested within classrooms; children are nested within families, or teachers are nested within schools. When data are sampled in a multi-stage manner or if observations are clustered, modeling data by ignoring the clustering will often result in standard error estimates that are underestimated if the outcome variable demonstrates dependence based on the clustering (i.e., the intraclass correlation is greater than zero). When clustering is ignored, the residuals will not be identically and independently distributed, violating an assumption of single-level models such as ordinary least-squares regression. This dependence will ultimately result in an inflated type-I error rate for significance tests of regression coefficients. However, in the statistical literature, methods have been developed for addressing data that come from a hierarchical structure and can account for the dependence among observations. One such method has many names and acronyms but is often referred to as hierarchical linear models (HLMs), multilevel models (MLMs, used in this paper), or mixed-effects models (Raudenbush and Bryk 2002). This is the method on which this paper will focus.To estimate MLMs without bias, adequate sample sizes must be obtained, since MLMs are often estimated with maximum likelihood (ML) methods. ML estimates are asymptomatically Educ Psychol Rev

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“…For sample size 200 and 2 response categories, despite the convergence rate being 100% for all three methods, the rate of proper solutions is 97.8% for PML and DWLS and 94.9% for ULS. The results regarding the test statistics reported below are based on the total number of replications because the full output is produced for all of them and improper solutions are expected to happen in small sample sizes and do not necessarily represent a statistical anomaly (Savalei & Kolenikov, 2008;Savalei & Rhemtulla, 2013). Figure 1 gives the empirical type I error rates for each method and experimental condition.…”

Section: On the Performance Of Plrt For Overall Fitmentioning

confidence: 99%

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Katsikatsou

Moustaki

2016

Psychometrika

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.Pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variablesCorrelated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on 'trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan 1 .

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Constrained versus unconstrained estimation in structural equation modeling.

Cited by 93 publications

References 50 publications

How Green Management Influences Product Innovation in China: The Role of Institutional Benefits

How Green Management Influences Product Innovation in China: The Role of Institutional Benefits

The Effect of Small Sample Size on Two-Level Model Estimates: A Review and Illustration

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

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