Structural Equation ModelingAKASEM in a nutshellJargonSlide 5Slide 6Slide 7Diagram elementsPath DiagramSEM questionsSlide 11Slide 12Slide 13SEM limitationsSlide 15Slide 16Slide 17Slide 18Structural Equation ModelingIntro to SEMPsy 524AinsworthAKASEM – Structural Equation ModelingCSA – Covariance Structure AnalysisCausal ModelsSimultaneous EquationsPath AnalysisConfirmatory Factor AnalysisSEM in a nutshellCombination of factor analysis and regressionContinuous and discrete predictors and outcomesRelationships among measured or latent variablesDirect link between Path Diagrams and equations and fit statisticsModels contain both measurement and path modelsJargonMeasured variableObserved variables, indicators or manifest variables in an SEM designPredictors and outcomes in path analysisSquares in the diagramLatent VariableUn-observable variable in the model, factor, constructConstruct driving measured variables in the measurement modelCircles in the diagramJargonError or EVariance left over after prediction of a measured variableDisturbance or DVariance left over after prediction of a factorExogenous VariableVariable that predicts other variablesEndogenous VariablesA variable that is predicted by another variableA predicted variable is endogenous even if it in turn predicts another variableJargonMeasurement ModelThe part of the model that relates indicators to latent factorsThe measurement model is the factor analytic part of SEMPath modelThis is the part of the model that relates variable or factors to one another (prediction)If no factors are in the model then only path model exists between indicatorsJargonDirect EffectRegression coefficients of direct predictionIndirect EffectMediating effect of x1 on y through x2Confirmatory Factor AnalysisCovariance StructureRelationships based on variance and covarianceMean StructureIncludes means (intercepts) into the modelDiagram elementsSingle-headed arrow →This is predictionRegression Coefficient or factor loadingDouble headed arrow ↔This is correlationMissing PathsHypothesized absence of relationshipCan also set path to zeroPath DiagramDepressionBDICES-DZDRSNegative ParentalInfluenceDep parentInsecureAttachmentNeglectGenderEEEDEEESEM questionsDoes the model produce an estimated population covariance matrix that “fits” the sample data?SEM calculates many indices of fit; close fit, absolute fit, etc.Which model best fits the data?What is the percent of variance in the variables explained by the factors?What is the reliability of the indicators?What are the parameter estimates from the model?SEM questionsAre there any indirect or mediating effects in the model?Are there group differences?Multigroup modelsCan change in the variance (or mean) be tracked over time?Growth Curve or Latent Growth Curve AnalysisSEM questionsCan a model be estimated with individual and group level components?Multilevel ModelsCan latent categorical variables be estimated?Mixture modelsCan a latent group membership be estimated from continuous and discrete variables?Latent Class AnalysisSEM questionsCan we predict the rate at which people will drop out of a study or end treatment?Discrete-time survival mixture analysisCan these techniques be combined into a huge mess?Multiple group multilevel growth curve latent class analysis???????SEM limitationsSEM is a confirmatory approachYou need to have established theory about the relationshipsCannot be used to explore possible relationships when you have more than a handful of variablesExploratory methods (e.g. model modification) can be used on top of the original theorySEM is not causal; experimental design = causeSEM limitationsSEM is often thought of as strictly correlational but can be used (like regression) with experimental data if you know how to use it.Mediation and manipulation can be tested 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 limitationsBiggest limitation is sample sizeIt needs to be large to get stable estimates of the covariances/correlations200 subjects for small to medium sized modelA minimum of 10 subjects per estimated parameterAlso affected by effect size and required powerSEM limitationsMissing dataCan be dealt with in the typical ways (e.g. regression, EM algorithm, etc.) through SPSS and data screeningMost SEM programs will estimate missing data and run the model simultaneouslyMultivariate Normality and no outliersScreen for univariate and multivariate outliersSEM programs have tests for multi-normalitySEM programs have corrected estimators when there’s a violationSEM limitationsLinearityNo multicollinearity/singularityResiduals Covariances (R minus reproduced R)Should be smallCentered around zeroSymmetric distribution of errorsIf asymmetric than some covariances are being estimated better than