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 is as easy as adding group(sex). Also easily add or relax constraints—ginvariant(mcoef) constrains all coefficients in the measurement model to be equal across groups. Or add paths for some groups but not others.

Watch Multiple-group generalized SEM.

 

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

Watch Using the SEM Builder in Stata tutorial.

 

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 mixed-effects models

Latent growth curve models with generalized-linear responses

Multilevel mediation models

Latent class analysis (LCA)

Selection models

with random intercepts and slopes

with binary, count, and ordinal outcomes

Endogenous treatment-effect models

Any multilevel structural equation models with generalized-linear responses

 

Structural equation models with survival outcomes

Latent predictors of survival outcomes

Path models, growth curve models, and more

Weibull, exponential, lognormal, loglogistic, or gamma models

Survival outcomes with other outcomes

Watch Survival models for SEM.

 

Linear and generalized-linear responses

Models for continuous, binary, count, ordinal, and nominal outcomes

Thirteen distribution families

Gaussian

Bernoulli

Binomial

Poisson

Negative binomial

Ordinal

Multinomial

Beta

Exponential

Gamma

Lognormal

Loglogistic

Weibull

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 higher-level structural equation models

Multilevel mixed-effects 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

Mean-variance or mode-curvature adaptive Gauss–Hermite quadrature

Nonadaptive Gauss–Hermite quadrature

Laplace approximation

 

Standard-error methods

OIM—observed information matrix

EIM—expected information matrix

OPG—outer product of gradients

Satorra—Bentler estimator

Robust—distribution-free linearized estimator

Cluster–robust—robust adjusting for correlation within groups of observations

Bootstrap—nonparametric bootstrap and clustered bootstrap

Jackknife—delete-one, delete-n, and clustered jackknife

Watch Satorra—Benthler adjustments for SEM.

 

Survey support for linear SEM and generalized SEM

Sampling weights and stage-level weights

Stratification and poststratification

Clustered sampling at one or more levels

Watch Survey data support for SEM.

 

Postestimation Selector

View and run all postestimation features for your command

Automatically updated as estimation commands are run

Watch Postestimation Selector.

 

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 goodness-of-fit 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

 

Equation-level goodness-of-fit statistics for linear SEM

R-squared

Equation-level variance decomposition

Bentler–Raykov squared multiple-correlation coefficient

 

Group-level goodness-of-fit statistics for linear SEM

SRMR

CD

Model vs. saturated chi-squared 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

Likelihood-ratio 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

 

Group-level 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)

Equation-level first derivatives

In- and out-of-sample 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

Density function*

Distribution function*

Survivor function

Predict observed endogenous variables marginally with respect to latent variables

User-defined nonlinear predictions*

 

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 user-written 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

Least-squares means

Predictive margins

Adjusted predictions, means, and effects

Works with multiple outcomes simultaneously*

Integrates over latent variables

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

ANOVA-style tests

Contrasts of nonlinear responses

Multiple-comparison 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

Multiple-comparison adjustments: Bonferroni, Sidak, Scheffe, Tukey HSD, Duncan, and Student–Newman–Keuls adjustments

Group comparisons that are significant

Graphs of pairwise comparisons

 

Additional resources

Discovering Structural Equation Modeling Using Stata, Revised Edition by Alan C. Acock

In the spotlight: SEM for economists (and others who think they don’t care)

In the spotlight: Path diagram for multinomial logit with random effects