Structural Equation Models: A Broad Overview by Doug Baer
For the first five days of SPIDA, Doug Baer will present a comprehensive overview of structural equation models, covering recursive and non-recursive simultaneous equation models for observed variables, multiple indicator models, confirmatory factor analysis models, simultaneous estimation in multiple groups, and models for means and intercepts. Participants will be introduced to both the scalar and matrix notation form of the models that will be discussed.
Introduction to Simultaneous Equation Models
In this introductory overview, the topics to be discussed include non-recursive models: identification and estimation; direct and indirect effects; two-stage least squares [2SLS] models; the SEM framework for simultaneous equation models; and testable hypotheses. In the afternoon lab session, we will deal with observed variable models using 2SLS and Maximum Likelihood Estimation [MLE], as well as introduce SEM software [primarily AMOS and LISREL].
Multiple Indicators and Confirmatory Factor Models
Topics discussed include the covariance algebra for SEM models and the implications of measurement error (an overview); confirmatory factor [CFA] models; identification in CFA models; standardized vs. unstandardized models; fixed vs. free parameters; goodness of fit indices; model modification; and testable hypotheses. The lab will cover multiple indicator models, as well as CFA and EFA [Exploratory Factor Analysis] model comparisons.
Estimation, Model Properties, Scaling and Interpretation Issues
Estimation issues are treated in this lecture: the properties of the Maximum Likelihood estimator, distributional assumptions, and a very brief introduction to alternative estimators; standardization; latent variable metrics; single and multiple-indicator variables; item parceling; and some problem areas: non-convergence and implausible parameter estimates. The lab session is an exercise in model fitting.
Topics discussed are as follows: replicating models across groups; across-group parameter constraints; testing for measurement equivalency; testing for equivalency of causal effects; and some comparisons with analysis of variance/covariance designs. The lab will deal with multiple group models.
Simultaneous Estimation in Multiple Groups
Models for Means and Intercepts
The final session in this overview will provide the bases for the next two special topics: we discuss intercepts in latent variable models; factor mean comparisons across groups; factor mean comparisons within groups (longitudinal data); and hypothesis tests involving mean and intercept vectors. These lab sessions conclude with work on latent variable intercepts and means.
Structural Equation Models: Two Special Topics by Ken Bollen
For the last two days of SPIDA 2006, Ken Bollen will present extensions of the earlier materials in considering two special topics. The first of these is the use of SEM models in the presence of missing data. SEM approaches to estimation in the presence of missing data provide researchers with the ability to reduce or eliminate bias caused by the presence of missing data points that are not MCAR (missing completely at random). Some of the techniques do not require the imputation of data points, and will be useful even to those researchers interested in estimating simpler multiple regression or simultaneous equation models. The second special topic is latent curve ("growth curve") models for longitudinal data. The SEM framework enables us to estimate a variety of trajectory models where each individual can have a distinct trajectory; the lecture and lab will provide an outline and introduction to these models.
Missing Data in Structural Equation Models
Growth Curve Models
Keynote Speaker: Rod Little