Model specification
 Use the SEM Builder or command language
 SEM Builder uses standard path diagrams
 Command language is a natural variation on path diagrams
 Group estimation in linear models as easy as adding group(sex);
easily add or relax constraints including adding or omitting paths
for some groups but not others
SEM Builder
 Drag, drop, and connect to create path diagrams
 Estimate models from path diagrams
 Display results on the path diagram
 Save and modify diagrams
 Tools to create measurement and regression components
 Set constant and equality constraints by clicking
 Complete control of how your diagrams look
Classes of models for linear SEM
 Linear regression
 Multivariate regression
 Path analysis
 Mediation analysis
 Measurement models
 Confirmatory factor analysis
 Multiple indicators and multiple causes (MIMIC) models
 Latent growth curve models
 Hierarchical confirmatory factor analysis
 Correlated uniqueness models
 Arbitrary structural equation models
Additional classes of models for generalized SEM
 Generalized linear models
 Item response theory models
 Measurement models with binary, count, and ordinal measurements
 Multilevel CFA models
 Multilevel mixedeffects models
 Latent growth curve models with generalizedlinear responses
 Multilevel mediation models
 Selection models
 with random intercepts and slopes
 with binary, count, and ordinal outcomes
 Endogenous treatmenteffect models
 Any multilevel structural equation models with
generalizedlinear responses
Linear and generalizedlinear responses
 Models for continuous, binary, count, ordinal, and nominal outcomes
 Eight distribution families
 Gaussian
 Gamma
 Bernoulli
 Binomial
 Poisson
 Negative binomial
 Ordinal
 Multinomial
 Five links
 Identity
 Log
 Logit
 Probit
 Cloglog
 Support for common regression models: linear, logistic, probit, ordered
logit, ordered probit, Poisson, multinomial logistic, tobit, interval measurements, and more
Multilevel models
 Two, three, and higherlevel structural equation models
 Multilevel mixedeffects models
 Random intercepts and random slopes
 Crossed and nested random effects
Estimation methods for linear SEM
 ML—maximum likelihood
 MLMV—maximum likelihood for missing values; sometimes called FIML
 ADF—asymptotic distribution free, meaning GMM (generalized method of
moments) using ADF weighting matrix
Estimation methods for generalized SEM
 Maximum likelihood
 Meanvariance or modecurvature adaptive Gauss–Hermite quadrature
 Nonadaptive Gauss–Hermite quadrature
 Laplace approximation
Standarderror methods
 OIM—observed information matrix
 EIM—expected information matrix
 OPG—outer product of gradients
 Robust—distributionfree linearized estimator
 Cluster–robust—robust adjusting for correlation within groups of
observations
 Bootstrap—nonparametric bootstrap and clustered bootstrap
 Jackknife—deleteone, deleten, and clustered jackknife
Survey support for linear SEM
 Sampling weights
 Stratification and poststratification
 Clustered sampling at one or more levels
Summary statistics data (SSD)
 Fit linear SEMs on observed or summary (SSD) data
 Fit models on covariances or correlations and optionally variances and
means
 SSD may be group specific
 Easily create and manage SSDs
 Build SSDs from original (raw) data for distribution or publication
 Automatic corruption/error checking and repairing
 Electronic signatures
Starting values
 Automatic
 May specify for some or all parameters
 Grid search available
 May fit one model, subset or superset, and use fitted values for another model
Identification
 Automatic normalization (anchoring) constraints provide scale for latent
variables; may be overridden
Reliability
 May specify fraction of variance not due to measurement error

Direct and indirect effects for linear SEM
 Confidence intervals
 Unstandardized or standardized units
Overall goodnessoffit statistics for linear SEM
 Model vs. saturated
 Baseline vs. saturated
 RMSEA, root mean squared error of approximation
 AIC, Akaike's information criterion
 BIC, Bayesian information criterion
 CFI, comparative fit index
 TLI, Tucker–Lewis index, a.k.a. nonnormed fit index
 SRMR, standardized root mean squared residual
 CD, coefficient of determination
Equationlevel goodnessoffit statistics for linear SEM
 Rsquared
 Equationlevel variance decomposition
 Bentler–Raykov squared multiplecorrelation coefficient
Grouplevel goodnessoffit statistics for linear SEM
 SRMR
 CD
 Model vs. saturated chisquared contribution
Residual analysis for linear SEM
 Mean residuals
 Variance and covariance residuals
 Raw, normalized, and standardized values available
Parameter tests
 Modification indices
 Wald tests
 Score tests
 Likelihoodratio tests
 Easy to specify single or joint custom tests for omitted paths, included
paths, and relaxing constraints
 Linear and nonlinear tests of estimated parameters
 Tests may be specified in standardized or unstandardized parameter units
Grouplevel parameter tests for linear SEM
 Group invariance by parameter class or user specified
Linear and nonlinear combinations of estimated parameters
 Confidence intervals
 Unstandardized or standardized units
Assess nonrecursive system stability
Predictions for linear SEM
 Observed endogenous variables
 Latent endogenous variables
 Latent variables (factor scores)
 Equationlevel first derivatives
 In and outofsample prediction; may estimate on one sample and form
predictions in another
Predictions for generalized SEM
 Means of observed endogenous variables—probabilities for 0/1
outcomes, mean counts, etc.
 Linear predictions of observed endogenous variables
 Latent variables using empirical Bayes means and modes
 Standard errors of empirical Bayes means and modes
 Observed endogenous variables with and without
predictions of latent variables
Results
 May be used with postestimation features
 May be saved to disk for restoration and use later
 Displayed in standardized or unstandardized units
 Optionally display results in Bentler–Weeks form
 Optionally display results in exponentiated form as odds ratios,
incidence rate ratios, and relative risk ratios
 All results accessible for userwritten programs
Factor variables with generalized SEM
 Automatically create indicators based on categorical variables
 Form interactions among discrete and continuous variables
 Include polynomial terms
 Perform contrasts of categories/levels
Marginal analysis
 Estimated marginal means
 Marginal and partial effects
 Average marginal and partial effects
 Leastsquares means
 Predictive margins
 Adjusted predictions, means, and effects
 Contrasts of margins
 Pairwise comparisons of margins
 Profile plots
 Graphs of margins and marginal effects
Contrasts for generalized SEM
 Analysis of main effects, simple effects, interaction effects, partial
interaction effects, and nested effects
 Comparisons against reference groups, of adjacent levels, or against the
grand mean
 Orthogonal polynomials
 Helmert contrasts
 Custom contrasts
 ANOVAstyle tests
 Contrasts of nonlinear responses
 Multiplecomparison adjustments
 Balanced and unbalanced data
 Contrasts of means, intercepts, and slopes
 Graphs of contrasts
 Interaction plots
Pairwise comparisons for generalized SEM
 Compare estimated means, intercepts, and slopes
 Compare marginal means, intercepts, and slopes
 Balanced and unbalanced data
 Nonlinear responses
 Multiplecomparison adjustments: Bonferroni, Sidak, Scheffe, Tukey HSD,
Duncan, and Student–Newman–Keuls adjustments
 Group comparisons that are significant
 Graphs of pairwise comparisons
Explore more about SEM in Stata.
Additional resources
