Hypothesis Formulation,Model Interpretation,and Model Equivalence: Implications of a Mereological Causal Interpretation of Structural Equation Models

One can distinguish statistical models used in causal modeling from the causal interpretations that align them with substantive hypotheses. Causal modeling typically assumes an efficient causal interpretation of the statistical model. Causal modeling can also make use of mereological causal interpretations in which the state of the parts determines the state of the whole. This interpretation shares several properties with efficient causal interpretations but also differs in terms of other important properties. The availability of alternative causal interpretations of the same statistical models has implications for hypothesis specification, research design, causal inference, data analysis, and the interpretation of research results.     

潜变量交互效应模型标准化估计中的检验问题

讨论了潜变量交互效应模型是否能直接用统计软件输出的原始估计的t值对模型的标准化估计进行检验的问题,详细介绍了标准化估计的t值计算及其难点,用Bootstrap方法算出标准化估计的标准误和相应的t值（记为t_bs）,并将其与原始估计的t值比较.结果发现,当原始估计t值超过3时,无论用t值还是用t_ bs检验,结果都是显著,即可以使用t值进行检验.而当t值不超过3时,与t_bs很接近,也可以用t值检验,但t值在临界值附近（例如1.5 ～2.5）时,最好还是使用Bootstrap法计算t_bs进行检验.     

Equivalent Structural Equation Models and Group Equality Constraints

This article is concerned with equivalent structural equation models that have been extended to multigroup models. It is shown that imposing cross-group equality constraints upon (a) no parameters or all parameters, or (b) any number of parameters in which the models are identical, preserves the model equivalence property. Alternatively, constraining for equality across groups some of those parameters in which the models differ can yield nonequivalent multiple-group models. The results are illustrated on two-group cognitive intervention data.     

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.     

The Specific Analysis of Structural Equation Models

Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory checks identifiability and lists and tests the implied constraints. This approach is complete for Markov models, but has remained incomplete for models with correlated disturbances. Some new algebraic results overcome the limitations of DAG theory and give a specific form of structural equation analysis that checks identifiability, tests the implied constraints, equation by equation, and gives consistent estimators of the parameters in closed form from the equations. At present the method is limited to recursive models subject to exclusion conditions. With further work, specific structural equation modeling may yield a complete alternative to the present, rather unsatisfactory, global covariance structure analysis.     

On Structural Equation Model Equivalence

A necessary and sufficient condition for equivalence of structural equation models is presented. Compared to existing rules for equivalent model generation (Stelzl, 1986; Lee & Hershberger, 1990; Hershberger, 1994), it is applicable to a more general class including models with parameter restrictions and models that may or may not fulfil assumptions of the rules, to show that two models are nonequivalent, or to nonidentified models. The validity of the replacement rule by Lee and Hershberger, Stelzl's rules, and Hershberger's inverse indicator rule is implied from the present method. Its application for studying model equivalence or lack thereof is demonstrated on a series of empirical examples.     

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

Correlated 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.     

Moment Testing for Interaction Terms in Structural Equation Modeling

Starting with Kenny and Judd (Psychol. Bull. 96:201–210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to adding just a selection of the third-order moments. The key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third-order moments in assessing interaction terms of the model. To select the third-order moments, we propose to be guided by the power of the goodness-of-fit test of a model with no interactions, which varies with each selection of third-order moments. A theorem is presented that relates the power of the usual goodness-of-fit test of the model with the power of a moment test for the significance of third-order moments; the latter has the advantage that it can be computed without fitting a model. The main conclusion is that the selection of third-order moments can be based on the power of a moment test, thus assessing the relevance in the analysis of different sets of third-order moments can be computationally simple. The paper gives an illustration of the method and argues for the need of refraining from adding into the analysis an excess of higher-order moments.     

Bayesian Semiparametric Structural Equation Models with Latent Variables

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.     

Abstract: Parameter Influence In Structural Equation Models

In applications of SEM, investigators obtain and interpret parameter estimates that are computed so as to produce optimal model fit in the sense that the obtained model fit would deteriorate to some degree if any of those estimates were changed. This property raises a question: to what extent would model fit deteriorate if parameter estimates were changed? And which parameters have the greatest influence on model fit? This is the idea of parameter influence. The present paper will cover two approaches to quantifying parameter influence. Both are based on the principle of likelihood displacement (LD), which quantifies influence as the discrepancy between the likelihood under the original model and the likelihood under the model in which a minor perturbation is imposed (Cook, 1986 Cook, R. D. 1986. Assessment of local influence. Journal of the Royal Statistical Society. Series B (Methodological)., 48: 133–169. [Crossref], [Web of Science ®] , [Google Scholar]). One existing approach for quantifying parameter influence is a vector approach (Lee &; Wang, 1996 Lee, S-Y. and Wang, S. J. 1996. Sensitivity analysis of structural equation models. Psychometrika, 61: 93–108. [Crossref], [Web of Science ®] , [Google Scholar]) that determines a vector in the parameter space such that altering parameter values simultaneously in this direction will cause maximum change in LD. We propose a new approach, called influence mapping for single parameters, that determines the change in model fit under perturbation of a single parameter holding other parameter estimates constant. An influential parameter is defined as one that produces large change in model fit under minor perturbation. Figure 1 illustrates results from this procedure for three different parameters in an empirical application. Flatter curves represent less influential parameters. Practical implications of the results are discussed. The relationship with statistical power in structural equation models is also discussed.

Abstract: Parameter Influence In Structural Equation Models

All authors

Taehun Lee &; Robert MacCallum

https://doi.org/10.1080/00273170802640491

Published online:

19 December 2008

FIGURE 1 Influence mapping for single parameters.     

11.

Predicting Health-related Quality of Life: Testing the Contextual Model Using Structural Equation Modeling     

Kimlin T. Ashing-Giwa  Jung-Won Lim 《Applied research in quality of life》2008,3(3):215-230

This study aims to investigate the utility of the Contextual Model of Health-Related Quality of Life (HRQOL) to explain the relationship among the domains of HRQOL with a diverse, population-based sample of breast cancer survivors (BCS). We employed a cross-sectional design to investigate HRQOL among 703 multiethnic, population-based BCS. The study methodology was guided by the Contextual Model of HRQOL. Structural Equation Modeling (SEM) was conducted to assess the hypothesized model. SEM identified significant relationships among the bio-psychological domain (general health status, cancer-related factors, and psychological factors), the cultural-socio-ecological domain (health care satisfaction, socio-ecological factor, and socio-economic status), and HRQOL. The best fitting model indicates direct pathways from ‘general health status’, ‘years since diagnosis’, ‘health care satisfaction’ and ‘socio-ecological factor’ to ‘HRQOL’ variables. Additionally, ‘socio-ecological factor’ and ‘socio-economic status’ variables were indirectly associated with HRQOL through ‘general health status’. Findings suggest that the Contextual Model of HRQOL adds valid factors to explain overall HRQOL and increases our understanding of the socio-ecological dimensions predicting HRQOL outcomes. The revelation of inter-relations among the dimensions of HRQOL may inform the translational and clinical utility of the HRQOL construct.

Jung-Won Lim (Corresponding author)Email:

---

Dr. Kimlin T. Ashing-Giwa   is professor and director of the Center of Community Alliance for Research and Education (CCARE) at City of Hope. She received her doctorate in clinical psychology from the University of Colorado-Boulder. Her scholarship and life work is to understand and investigate how culture, ethnicity, ecological and systemic context influence health outcomes. Currently, she is developing and implementing community participatory interventions to reduce the risk and burden of chronic illness, in particular cancer. Dr. Jung-won Lim    is a research fellow of the CCARE at City of Hope. She received her doctorate from the University of Southern California, School of Social Work. Her research focuses on adjustment and quality of life among patients with chronic physical illness and their family. She is currently conducting studies related to health beliefs, health behaviors, and quality of life among breast cancer survivors.     

12.

Frequentist Model Averaging in Structural Equation Modelling     

Jin  Shaobo  Ankargren  Sebastian 《Psychometrika》2019,84(1):84-104

     

13.

管理胜任力特征分析:结构方程模型检验   总被引：171，自引：0，他引：171  

王重鸣  陈民科 《心理科学》2002,25(5):513-516

管理胜任力特征分析是人事选拔与评价的重要内容之一。本研究在运用基于胜任力的职位分析并总结国内外有关文献的基础上,编制了管理综合素质评价量表,并运用此量表调查了220名中高层管理者,采用因素分析和结构方程模型检验企业高级管理者胜任力特征的结构。结果表明,管理胜任力特征结构由管理素质和管理技能等两个维度构成,但在维度要素及其关键度上,职位层次间存在显著差异。本研究为管理职位的测评选拔提供了新的理论依据。     

14.

Sensitivity Analysis in Structural Equation Models: Cases and Their Influence     

Jolynn Pek  Robert C. MacCallum 《Multivariate behavioral research》2013,48(2):202-228

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability (Holzinger &; Swineford, 1939 Holzinger, K. and Swineford, F. 1939. A study in factor analysis: The stability of a bi-factor solution. Chicago, IL: University of Chicago..  [Google Scholar]) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data (Bollen, 1989 Bollen, K. A. 1989. Structural equation models with latent variables New York, NY: Wiley.. [Crossref] , [Google Scholar]; Bollen &; Arminger, 1991 Bollen, K. A. and Arminger, G. 1991. Observational residuals in factor analysis and structural equation models. Sociological Methodology, 21: 235–262. [Crossref], [Web of Science ®] , [Google Scholar]). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced—these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.     

15.

Consistent Partial Least Squares for Nonlinear Structural Equation Models     

Theo K. Dijkstra  Karin Schermelleh-Engel 《Psychometrika》2014,79(4):585-604

Partial Least Squares as applied to models with latent variables, measured indirectly by indicators, is well-known to be inconsistent. The linear compounds of indicators that PLS substitutes for the latent variables do not obey the equations that the latter satisfy. We propose simple, non-iterative corrections leading to consistent and asymptotically normal (CAN)-estimators for the loadings and for the correlations between the latent variables. Moreover, we show how to obtain CAN-estimators for the parameters of structural recursive systems of equations, containing linear and interaction terms, without the need to specify a particular joint distribution. If quadratic and higher order terms are included, the approach will produce CAN-estimators as well when predictor variables and error terms are jointly normal. We compare the adjusted PLS, denoted by PLSc, with Latent Moderated Structural Equations (LMS), using Monte Carlo studies and an empirical application.     

16.

Abstract: Case Diagnostics in Structural Equation Models: Illustrations and Issues     

Jolynn Pek  Robert C. MacCallum 《Multivariate behavioral research》2013,48(6)

     

17.

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models     

Xin-Yuan Song  Zhao-Hua Lu  Jing-Heng Cai  Edward Hak-Sing Ip 《Psychometrika》2013,78(4):624-647

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

18.

Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables     

《Multivariate behavioral research》2013,48(3):337-365

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the proposed model. Markov chain Monte Carlo methods for obtaining Bayesian estimates and their standard error estimates, highest posterior density intervals, and a PP p value are developed. Results obtained from two simulation studies are reported to respectively reveal the empirical performance of the proposed Bayesian estimation in analyzing complex nonlinear SEMs, and in analyzing nonlinear SEMs with the normal assumption of the exogenous latent variables violated. The proposed methodology is further illustrated by a real example. Detailed interpretation about the interaction terms is presented.     

19.

Testing Two Contrasting Structural Models of Innovativeness in a Contractual Network     

J. DAVID JOHNSON  MARCY E. MEYER  JUDY M. BERKOWITZ  VERNOND. MILLER  CAROLINE T. ETHINGTON 《人类交流研究》1997,24(2):320-348

This study examined contrasting models of the impact of formal and informal structural factors and the communication environment on organizational innovativeness. Specifically, three formal structural variables (decentralization, formalization, and slack resources), two informal structural variables (range and prominence), and two communication environment variables (communication quality and acceptance) are posited to be antecedents of organizational innovativeness. In the traditional model, formal structural impacts are posited to be shaped by informal structure. Conversely, the coexisting model argues that both formal and informal structural variables directly affect the communication environment, which, in turn, shapes perceptions of innovativeness. Data were gathered from self-report questionnaires and network analysis communication logs completed by organizational members (N = 79) of a geographically dispersed government health information agency, the Cancer Information Service (CIS). Tests of the models demonstrate that the coexisting model is clearly superior. These results suggest that the dual role of formal and informal structures needs to be more systematically specified as we focus on innovation in new organizational forms, such as the CIS.     

20.

How to Generate Non-normal Data for Simulation of Structural Equation Models     

《Multivariate behavioral research》2013,48(4):355-373

A procedure for generating non-normal data for simulation of structural equation models is proposed. A simple transformation of univariate random variables is used for the generation of data on latent and error variables under some restrictions for the elements of the covariance matrices for these variables. Data on the observed variables is then computed from latent and error variables according to the model. It is shown that by controlling univariate skewness and kurtosis on pre-specified random latent and error variables, observed variables can be made to have a relatively wide range of univariate skewness and kurtosis characteristics according to the pre-specified model. Univariate distributions are used for the generation of data which enables a user to choose from a large number of different distributions. The use of the proposed procedure is illustrated for two different structural equation models and it is shown how PRELIS can be used to generate the data.     

Predicting Health-related Quality of Life: Testing the Contextual Model Using Structural Equation Modeling

This study aims to investigate the utility of the Contextual Model of Health-Related Quality of Life (HRQOL) to explain the relationship among the domains of HRQOL with a diverse, population-based sample of breast cancer survivors (BCS). We employed a cross-sectional design to investigate HRQOL among 703 multiethnic, population-based BCS. The study methodology was guided by the Contextual Model of HRQOL. Structural Equation Modeling (SEM) was conducted to assess the hypothesized model. SEM identified significant relationships among the bio-psychological domain (general health status, cancer-related factors, and psychological factors), the cultural-socio-ecological domain (health care satisfaction, socio-ecological factor, and socio-economic status), and HRQOL. The best fitting model indicates direct pathways from ‘general health status’, ‘years since diagnosis’, ‘health care satisfaction’ and ‘socio-ecological factor’ to ‘HRQOL’ variables. Additionally, ‘socio-ecological factor’ and ‘socio-economic status’ variables were indirectly associated with HRQOL through ‘general health status’. Findings suggest that the Contextual Model of HRQOL adds valid factors to explain overall HRQOL and increases our understanding of the socio-ecological dimensions predicting HRQOL outcomes. The revelation of inter-relations among the dimensions of HRQOL may inform the translational and clinical utility of the HRQOL construct.

管理胜任力特征分析:结构方程模型检验

管理胜任力特征分析是人事选拔与评价的重要内容之一。本研究在运用基于胜任力的职位分析并总结国内外有关文献的基础上,编制了管理综合素质评价量表,并运用此量表调查了220名中高层管理者,采用因素分析和结构方程模型检验企业高级管理者胜任力特征的结构。结果表明,管理胜任力特征结构由管理素质和管理技能等两个维度构成,但在维度要素及其关键度上,职位层次间存在显著差异。本研究为管理职位的测评选拔提供了新的理论依据。     

Sensitivity Analysis in Structural Equation Models: Cases and Their Influence

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability (Holzinger &; Swineford, 1939 Holzinger, K. and Swineford, F. 1939. A study in factor analysis: The stability of a bi-factor solution. Chicago, IL: University of Chicago..  [Google Scholar]) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data (Bollen, 1989 Bollen, K. A. 1989. Structural equation models with latent variables New York, NY: Wiley.. [Crossref] , [Google Scholar]; Bollen &; Arminger, 1991 Bollen, K. A. and Arminger, G. 1991. Observational residuals in factor analysis and structural equation models. Sociological Methodology, 21: 235–262. [Crossref], [Web of Science ®] , [Google Scholar]). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced—these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.     

Consistent Partial Least Squares for Nonlinear Structural Equation Models

Partial Least Squares as applied to models with latent variables, measured indirectly by indicators, is well-known to be inconsistent. The linear compounds of indicators that PLS substitutes for the latent variables do not obey the equations that the latter satisfy. We propose simple, non-iterative corrections leading to consistent and asymptotically normal (CAN)-estimators for the loadings and for the correlations between the latent variables. Moreover, we show how to obtain CAN-estimators for the parameters of structural recursive systems of equations, containing linear and interaction terms, without the need to specify a particular joint distribution. If quadratic and higher order terms are included, the approach will produce CAN-estimators as well when predictor variables and error terms are jointly normal. We compare the adjusted PLS, denoted by PLSc, with Latent Moderated Structural Equations (LMS), using Monte Carlo studies and an empirical application.     

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the proposed model. Markov chain Monte Carlo methods for obtaining Bayesian estimates and their standard error estimates, highest posterior density intervals, and a PP p value are developed. Results obtained from two simulation studies are reported to respectively reveal the empirical performance of the proposed Bayesian estimation in analyzing complex nonlinear SEMs, and in analyzing nonlinear SEMs with the normal assumption of the exogenous latent variables violated. The proposed methodology is further illustrated by a real example. Detailed interpretation about the interaction terms is presented.     

Testing Two Contrasting Structural Models of Innovativeness in a Contractual Network

This study examined contrasting models of the impact of formal and informal structural factors and the communication environment on organizational innovativeness. Specifically, three formal structural variables (decentralization, formalization, and slack resources), two informal structural variables (range and prominence), and two communication environment variables (communication quality and acceptance) are posited to be antecedents of organizational innovativeness. In the traditional model, formal structural impacts are posited to be shaped by informal structure. Conversely, the coexisting model argues that both formal and informal structural variables directly affect the communication environment, which, in turn, shapes perceptions of innovativeness. Data were gathered from self-report questionnaires and network analysis communication logs completed by organizational members (N = 79) of a geographically dispersed government health information agency, the Cancer Information Service (CIS). Tests of the models demonstrate that the coexisting model is clearly superior. These results suggest that the dual role of formal and informal structures needs to be more systematically specified as we focus on innovation in new organizational forms, such as the CIS.     

How to Generate Non-normal Data for Simulation of Structural Equation Models

A procedure for generating non-normal data for simulation of structural equation models is proposed. A simple transformation of univariate random variables is used for the generation of data on latent and error variables under some restrictions for the elements of the covariance matrices for these variables. Data on the observed variables is then computed from latent and error variables according to the model. It is shown that by controlling univariate skewness and kurtosis on pre-specified random latent and error variables, observed variables can be made to have a relatively wide range of univariate skewness and kurtosis characteristics according to the pre-specified model. Univariate distributions are used for the generation of data which enables a user to choose from a large number of different distributions. The use of the proposed procedure is illustrated for two different structural equation models and it is shown how PRELIS can be used to generate the data.