Structural Equation ModelingIntro to SEMPsy 524AinsworthAKAn SEM – Structural Equation Modelingn CSA – Covariance Structure Analysisn Causal Modelsn Simultaneous Equationsn Path Analysisn Confirmatory Factor AnalysisSEM in a nutshelln Combination of factor analysis and regressionn Continuous and discrete predictors and outcomesn Relationships among measured or latent variablesn Direct link between Path Diagrams and equations and fit statisticsn Models contain both measurement and path modelsJargonn Measured variablen Observed variables, indicators or manifest variables in an SEM designn Predictors and outcomes in path analysisn Squares in the diagramn Latent Variablen Un-observable variable in the model, factor, constructn Construct driving measured variables in the measurement modeln Circles in the diagramJargonn Error or En Variance left over after prediction of a measured variablen Disturbance or Dn Variance left over after prediction of a factorn Exogenous Variablen Variable that predicts other variablesn Endogenous Variablesn A variable that is predicted by another variablen A predicted variable is endogenous even if it in turn predicts another variableJargonn Measurement Modeln The part of the model that relates indicators to latent factorsn The measurement model is the factor analytic part of SEMn Path modeln This is the part of the model that relates variable or factors to one another (prediction)n If no factors are in the model then only path model exists between indicatorsJargonn Direct Effectn Regression coefficients of direct predictionn Indirect Effectn Mediating effect of x1 on y through x2n Confirmatory Factor Analysisn Covariance Structuren Relationships based on variance and covariancen Mean Structuren Includes means (intercepts) into the modelDiagram elementsn Single-headed arrow ?n This is predictionn Regression Coefficient or factor loadingn Double headed arrow ?n This is correlationn Missing Pathsn Hypothesized absence of relationshipn Can also set path to zeroPath DiagramDepressionBDICES-DZDRSNegative ParentalInfluenceDep parentInsecureAttachmentNeglectGenderEEEDEEESEM questionsn Does the model produce an estimated population covariance matrix that “fits” the sample data?n SEM calculates many indices of fit; close fit, absolute fit, etc.n Which model best fits the data?n What is the percent of variance in the variables explained by the factors?n What is the reliability of the indicators?n What are the parameter estimates from the model?SEM questionsn Are there any indirect or mediating effects in the model?n Are there group differences?n Multigroup modelsn Can change in the variance (or mean) be tracked over time?n Growth Curve or Latent Growth Curve AnalysisSEM questionsn Can a model be estimated with individual and group level components?n Multilevel Modelsn Can latent categorical variables be estimated?n Mixture modelsn Can a latent group membership be estimated from continuous and discrete variables?n Latent Class AnalysisSEM questionsn Can we predict the rate at which people will drop out of a study or end treatment?n Discrete-time survival mixture analysisn Can these techniques be combined into a huge mess?n Multiple group multilevel growth curve latent class analysis???????SEM limitationsn SEM is a confirmatory approachn You need to have established theory about the relationshipsn Cannot be used to explore possible relationships when you have more than a handful of variablesn Exploratory methods (e.g. model modification) can be used on top of the original theoryn SEM is not causal; experimental design = causeSEM limitationsn SEM is often thought of as strictly correlational but can be used (like regression) with experimental data if you know how to use it.n Mediation and manipulation can be tested n SEM is by far a very fancy technique but this does not make up for a bad experiment and the data can only be generalized to the population at handSEM limitationsn Biggest limitation is sample sizen It needs to be large to get stable estimates of the covariances/correlationsn 200 subjects for small to medium sized modeln A minimum of 10 subjects per estimated parametern Also affected by effect size and required powerSEM limitationsn Missing datan Can be dealt with in the typical ways (e.g. regression, EM algorithm, etc.) through SPSS and data screeningn Most SEM programs will estimate missing data and run the model simultaneouslyn Multivariate Normality and no outliersn Screen for univariate and multivariate outliersn SEM programs have tests for multi-normalityn SEM programs have corrected estimators when there’s a violationSEM limitationsn Linearityn No multicollinearity/singularityn Residuals Covariances (R minus reproduced R)n Should be smalln Centered around zeron Symmetric distribution of errorsn If asymmetric than some covariances are being estimated better than