USING INSTRUMENTAL VARIABLE TESTS TO EVALUATE MODEL SPECIFICATION IN LATENT VARIABLE STRUCTURAL EQUATION MODELS

Structural equation modeling (SEM) with latent variables is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood (ML) estimator, but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared with that for full-information estimators. We address this shortcoming by providing several specification tests based on the 2SLS estimator for latent variable structural equation models developed by Bollen (1996) . We explain how these tests can be used not only to identify a misspecified model but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification.     

Three Likelihood-Based Methods For Mean and Covariance Structure Analysis With Nonnormal Missing Data

Survey and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal, and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. We also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal data. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chi-square as long as the underlying sampling distribution enjoys finite fourth-order moments. We also give a characterization for each of the two likelihood ratio test statistics when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also given. Our working assumption is that the missing data mechanism is missing completely at random. Examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that are missing at random.     

FORECASTING U.S. MORTALITY:

This article compares two methodologies for modeling and forecasting statistical time series models of demographic processes: Box-Jenkins ARIMA and structural time series analysis. The Lee-Carter method is used to construct nonlinear demographic models of U.S. mortality rates for the total population, gender, and race and gender combined. Single time varying parameters of k, the index of mortality, are derived from these model and fitted and forecasted using the two methodologies. Forecasts of life expectancy at birth, e₀, are generated from these indexes of k. Results show marginal differences in fit and forecasts between the two statistical approaches with a slight advantage to structural models. Stability across models for both methodologies offers support for the robustness of this approach to demographic forecasting.     

Marginal Structural Models: An Application to Incarceration and Marriage During Young Adulthood

Advanced methods for panel data analysis are commonly used in research on family life and relationships, but the fundamental issue of simultaneous time‐dependent confounding and mediation has received little attention. In this article the authors introduce inverse‐probability‐weighted estimation of marginal structural models, an approach to causal analysis that (unlike conventional regression modeling) appropriately adjusts for confounding variables on the causal pathway linking the treatment with the outcome. They discuss the need for marginal structural models in social science research and describe their estimation in detail. Substantively, the authors contribute to the ongoing debate on the effects of incarceration on marriage by applying a marginal structural model approach to panel data from the National Longitudinal Survey of Youth 1997 (N = 4,781). In line with the increasing evidence on the collateral consequences of contact with the criminal justice system, the authors find that incarceration is associated with reduced chances of entering marriage.     

Multilevel models for social networks: Hierarchical Bayesian approaches to exponential random graph modeling

In many applications, researchers may be interested in studying patterns of dyadic relationships that involve multiple groups, with a focus on modeling the systematic patterns within groups and how these structural patterns differ across groups. A number of different models – many of them potentially quite powerful – have been developed that allow for researchers to study these differences. However, as with any set of models, these are limited in ways that constrain the types of questions researchers may ask, such as those involving the variance in group-wise structural features. In this paper, we demonstrate some of the ways in which multilevel models based on a hierarchical Bayesian approach might be used to further develop and extend existing exponential random graph models to address such constraints. These include random coefficient extensions to the standard ERGM for sets of multiple unconnected or connected networks and examples of multilevel models that allow for the estimation of structural entrainment among connected groups. We demonstrate the application of these models to real-world and simulated data sets.     

Modelling free social spaces and the diffusion of social mobilization

Free social spaces have long been emphasized in the social movement literature. Under names such as safe spaces, social havens, and counterpublics, they have been characterized as protective shelters against prevailing hegemonic ideologies and as hubs for the diffusion of ideas and ideologies. However, the vast literature on these spaces has predominantly focused on internal dynamics and processes, thus neglecting how they relate to the diffusion of collective mobilization. Inspired by formal modeling in collective action research, we develop a network model to investigate how the structural properties of free social spaces impact the diffusion of collective mobilization. Our results show that the assumption of clustering is enough for structural effects to emerge, and that clustering furthermore interacts synergistically with political deviance. This indicates that it is not only internal dynamics that play a role in the relevance of free social spaces for collective action. Our approach also illustrates how formal modeling can deepen our understanding of diffusion processes in collective mobilizations through analysis of emergent structural effects.     

Using Mixture Regression to Identify Varying Effects: A Demonstration With Paternal Incarceration

The most widely used techniques for identifying the varying effects of stressors involve testing moderator effects via interaction terms in regression or multiple‐group analysis in structural equation modeling. The authors present mixture regression as an alternative approach. In contrast to more widely used approaches, mixture regression identifies varying effects without reliance on tests of moderator variables, such as using interaction terms or multiple group analyses. In many instances, the use of mixture regression also more effectively tests higher order and multiple interactions. A mixture regression example is presented using 214 families from the Fragile Families and Child Wellbeing study, half of whom had experienced paternal incarceration. Whereas typical regression and moderator analyses fail to find an effect or varying effects, mixture regression identified 4 classes uniquely influenced by the incarceration.     

Random-Effects Modeling of Categorical Response Data

In many applications observations have some type of clustering, with observations within clusters tending to be correlated. A common instance of this occurs when each subject in the sample undergoes repeated measurement, in which case a cluster consists of the set of observations for the subject. One approach to modeling clustered data introduces cluster-level random effects into the model. The use of random effects in linear models for normal responses is well established. By contrast, random effects have only recently seen much use in models for categorical data. This chapter surveys a variety of potential social science applications of random effects modeling of categorical data. Applications discussed include repeated measurement for binary or ordinal responses, shrinkage to improve multiparameter estimation of a set of proportions or rates, multivariate latent variable modeling, hierarchically structured modeling, and cluster sampling. The models discussed belong to the class of generalized linear mixed models (GLMMs), an extension of ordinary linear models that permits nonnormal response variables and both fixed and random effects in the predictor term. The models are GLMMs for either binomial or Poisson response variables, although we also present extensions to multicategory (nominal or ordinal) responses. We also summarize some of the technical issues of model-fitting that complicate the fitting of GLMMs even with existing software.     

A comprehensive literature review of the pelvis and the lower extremity FE human models under quasi-static conditions

Finite Element Modeling (FEM) has become a vital tool in the automotive design and development processes. FEM of the human body is a technique capable of estimating parameters that are difficult to measure in experimental studies with the human body segments being modeled as complex and dynamic entities. Several studies have been dedicated to attain close-to-real FEMs of the human body (Pankoke and Siefert 2007; Amann, Huschenbeth et al. 2009; ESI 2010). The aim of this paper is to identify and appraise the state-of-the art models of the human body which incorporate detailed pelvis and/or lower extremity models. Six databases and search engines were used to obtain literature, and the search was limited to studies published in English since 2000. The initial search results identified 636 pelvis-related papers, 834 buttocks-related papers, 505 thigh-related papers, 927 femur-related papers, 2039 knee-related papers, 655 shank-related papers, 292 tibia-related papers, 110 fibula-related papers, 644 ankle-related papers, and 5660 foot-related papers. A refined search returned 100 pelvis-related papers, 45 buttocks-related papers, 65 thigh-related papers, 162 femur-related papers, 195 knee-related papers, 37 shank-related papers, 80 tibia-related papers, 30 fibula-related papers and 102 ankle-related papers and 246 foot-related papers. The refined literature list was further restricted by appraisal against a modified LOW appraisal criteria. Studies with unclear methodologies, with a focus on populations with pathology or with sport related dynamic motion modeling were excluded. The final literature list included fifteen models and each was assessed against the percentile the model represents, the gender the model was based on, the human body segment/segments included in the model, the sample size used to develop the model, the source of geometric/anthropometric values used to develop the model, the posture the model represents and the finite element solver used for the model. The results of this literature review provide indication of bias in the available models towards 50th percentile male modeling with a notable concentration on the pelvis, femur and buttocks segments.     

A structural model of consumption: An application to China during the global financial crisis

In this paper, we develop a structural model of consumption by incorporating psychological constructs which constitute important antecedents of household consumption and provide crucial structural linkages to the mental accounting evaluation of saving or consumption. Our model is tested using structural equation modeling (SEM). The model is applied to China for measuring consumption expenditure under uncertainty emanating from the 2008 global financial crisis. An empirical test using 9784 new Chinese household survey data show that our structural model is a significant improvement over the existing behavioral life cycle model, as it is able to capture the psychological states affecting different groups of consumers such as employed workers and unemployed retirees. Our new structural model of consumption fits the data very well. The results have important implications for public policy assessment.     

A comparison of linear and systems thinking approaches for program evaluation illustrated using the Indiana Interdisciplinary GK-12

Logic models are based on linear relationships between program resources, activities, and outcomes, and have been used widely to support both program development and evaluation. While useful in describing some programs, the linear nature of the logic model makes it difficult to capture the complex relationships within larger, multifaceted programs. Causal loop diagrams based on a systems thinking approach can better capture a multidimensional, layered program model while providing a more complete understanding of the relationship between program elements, which enables evaluators to examine influences and dependencies between and within program components. Few studies describe how to conceptualize and apply systems models for educational program evaluation. The goal of this paper is to use our NSF-funded, Interdisciplinary GK-12 project: Bringing Authentic Problem Solving in STEM to Rural Middle Schools to illustrate a systems thinking approach to model a complex educational program to aid in evaluation. GK-12 pairs eight teachers with eight STEM doctoral fellows per program year to implement curricula in middle schools. We demonstrate how systems thinking provides added value by modeling the participant groups, instruments, outcomes, and other factors in ways that enhance the interpretation of quantitative and qualitative data. Limitations of the model include added complexity. Implications include better understanding of interactions and outcomes and analyses reflecting interacting or conflicting variables.     

A Dyadic Approach to Understanding the Link Between Sexual Functioning and Sexual Satisfaction in Heterosexual Couples

Researchers have demonstrated that several dimensions of sexual functioning (e.g., sexual desire, arousal, orgasm) are associated with the sexual satisfaction of individuals in a committed mixed-sex (male–female) relationship. We extended this research by comparing a dyadic model that included both own (i.e., actor effect) and partner (i.e., partner effect) domains of sexual functioning to an individual model that included only actor effects. Participants were 124 mixed-sex couples who completed online measures of sexual functioning and sexual satisfaction. Data analysis using the actor–partner interdependence model (APIM) and structural equation modeling (SEM) indicated that the dyadic model had a better fit than the individual model. Women’s sexual desire and orgasm and men’s erectile functioning were significant positive predictors of both own and partner’s sexual satisfaction. These results are discussed in terms of the importance of taking a dyadic approach to research and clinical work related to sexual satisfaction.     

Measurement quality issues in dyadic models of relationships

Interpersonal relationships are an important and integral part of numerous social science research agendas. Analytical tools have been created in the last 10 years that model dyadic interactions. In particular, this article focuses on the dyadic models of Fienberg and Wasserman [Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology. Jossey-Bass, San Francisco.], Holland and Leinhardt [Holland, P.W., Leinhardt, S., 1981. An exponential family of probability densities for directed graphs. Journal of the American Statistical Association 76 (1981) 33–51.], Iacobucci and Wasserman [Iacobucci, D., Wasserman, S., 1988. A general framework for the statistical analysis of sequential dyadic interaction data. Psychological Bulletin 103 (1988) 379–390.] and Wasserman and Iacobucci [Wasserman, S., Iacobucci, D., 1986. Statistical analysis of discrete relational data. British Journal of Mathematical and Statistical Psychology 39 (1986) 41–64.]. However, measurement issues like reliability and validity, as discussed by Allen and Yen [Allen, M.J., Yen, W.M., 1979. Introduction to Measurement Theory. Brooks/Cole, Monterey, CA, 1979.], Nunnally [Nunnally, J., 1978. Psychometric Theory, 2nd edn. McGraw-Hill, New York, NY, 1978.] and Uebersax [Uebersax, J.S., 1988. Validity inferences from interobserver agreement. Psychological Bulletin 104 (1988) 405–416.], have not been considered in conjunction with these models, and little is known about the empirical performance of the dyadic models under sub-optimal measurement quality conditions. We offer two essential approaches to ascertaining the level of measurement error in the observed indicators of social ties and relationships. The first approach combines latent class and social network models in one integrated framework and allows for the simultaneous study of measurement and dyadic structural issues. The second approach is an alternative that may be more useful to social science researchers, both because the method is more accessible and because researchers could apply the techniques to data they have already partially analyzed. This approach is a two-staged procedure whereby in the first stage, a probability model based on latent class analysis is estimated which provides an indication of the measurement quality in the data. In the second stage, traditional social network models are estimated. To investigate the implications of different levels of measurement error for interpreting the nature of the network ties and the dyadic parametric performance, we also designed a Monte Carlo experiment. Measurement error is simulated as the likelihood of a binary relational choice (for simplicity) being inaccurately classified, where incorrect diagnoses can result from poor interitem agreement (i.e., unreliability) or poor interrater agreement. The simulation can be used by researchers in combination with the two-stage approach. The results of the simulation provide guidelines for situations when social network models can withstand a reasonable degree of sub-optimal measurement quality and highlight adverse conditions which can significantly affect the performance of the modeling approach. Further, the simulation shows that sample size assists in reducing the chances of making Type II errors, but it does not compensate for biases in parameter estimates in the presence of increasing error. Finally, the measurement and dyadic analytical methods are applied to a real dataset describing interorganizational relational activity using multiple raters. Recommendations are offered to guide the researcher in making decisions about research design when using dyadic models.     

A comparison of various approaches to the exponential random graph model: A reanalysis of 102 student networks in school classes

This paper describes an empirical comparison of four specifications of the exponential family of random graph models (ERGM), distinguished by model specification (dyadic independence, Markov, partial conditional dependence) and, for the Markov model, by estimation method (Maximum Pseudolikelihood, Maximum Likelihood). This was done by reanalyzing 102 student networks in 57 junior high school classes. At the level of all classes combined, earlier substantive conclusions were supported by all specifications. However, the different specifications led to different conclusions for individual classes. PL produced unreliable estimates (when ML is regarded as the standard) and had more convergence problems than ML. Furthermore, the estimates of covariate effects were affected considerably by controlling for network structure, although the precise specification of the structural part (Markov or partial conditional dependence) mattered less.     

Economic analysis of volunteers’ motivations—A cross-country study

While some core theories on volunteer labor supply decisions can be found in the economic literature, little efforts were made so far to operationalize these models and verify their implications in an empirical context. This paper aims at narrowing the research gap between the theoretical economic literature on volunteer motivations and the empirically observed motivations for volunteer labor supply. A common indicator ‘voluntary contributions by others’ linking the theories of public goods, private consumption and investment has been identified and examined on the basis of structural equation modeling and regression analysis. Using representative micro data collected for volunteers in Bangladesh, Ghana, Poland and South Korea, the paper finds that this indicator significantly influences an individual's motivation. Particularly, observed findings are in accordance with theoretical predictions.     

Structural Equation Modeling With Robust Covariances

Existing methods for structural equation modeling involve fitting the ordinary sample covariance matrix by a proposed structural model. Since a sample covariance is easily influenced by a few outlying cases, the standard practice of modeling sample covariances can lead to inefficient estimates as well as inflated fit indices. By giving a proper weight to each individual case, a robust covariance will have a bounded influence function as well as a nonzero breakdown point. These robust properties of the covariance estimators will be carried over to the parameter estimators in the structural model if a technically appropriate procedure is used. We study such a procedure in which robust covariances replace ordinary sample covariances in the context of the Wishart likelihood function. This procedure is easy to implement in practice. Statistical properties of this procedure are investigated. A fit index is given based on sampling from an elliptical distribution. An estimating equation approach is used to develop a variety of robust covariances, and consistent covariances of these robust estimators, needed for standard errors and test statistics, follow from this approach. Examples illustrate the inflated statistics and distorted parameter estimates obtained by using sample covariances when compared with those obtained by using robust covariances. The merits of each method and its relevance to specific types of data are discussed.     

A latent space model for cognitive social structures data

This paper introduces a novel approach for modeling a set of directed, binary networks in the context of cognitive social structures (CSSs) data. We adopt a relativist approach in which no assumption is made about the existence of an underlying true network. More specifically, we rely on a generalized linear model that incorporates a bilinear structure to model transitivity effects within networks, and a hierarchical specification on the bilinear effects to borrow information across networks. This is a spatial model, in which the perception of each individual about the strength of the relationships can be explained by the perceived position of the actors (themselves and others) on a latent social space. A key goal of the model is to provide a mechanism to formally assess the agreement between each actors’ perception of their own social roles with that of the rest of the group. Our experiments with both real and simulated data show that the capabilities of our model are comparable with or, even superior to, other models for CSS data reported in the literature.     

A multi-group structural equation model (SEM) examining asset holding effects on educational attainment by race and gender

Little is known about the processes through which parents' and children's wealth may influence children's math and reading scores. Even less is known about how these processes may vary across race and gender. In this study we analyze Panel Study of Income Dynamics (PSID) data using multi-group structural equation modeling (SEM) to examine wealth effects by gender (male/female) and race (white/black). Results suggest that there are important statistical differences across race and gender. For example, we find that children's school savings predict math scores among white children but not black children. Net worth is a positive predictor of black males' math scores but a negative predictor of black females'. In the case of income, we find that it is directly related to black females' math scores but not black males'. In general, findings suggest that liquid forms of wealth (i.e., forms of wealth that are easily converted into cash) may be better predictors of children's academic achievement than net worth.     

The Relationship of Birth Order and Gender with Academic Standing and Substance Use Among Youth in Latin America

Alfred Adler attempted to understand how family affects youth outcomes by considering the order of when a child enters a family (Adler, 1964). Adler's theory posits that birth order formation impacts individuals. We tested Adler's birth order theory using data from a cross-sectional survey of 946 Chilean youths. We examined how birth order and gender are associated with drug use and educational outcomes using three different birth order research models including: (1) Expedient Research, (2) Adler's birth order position, and (3) Family Size theoretical models. Analyses were conducted with structural equation modeling (SEM). We conclude that birth order has an important relationship with substance use outcomes for youth but has differing effects for educational achievement across both birth order status and gender.