Structural Equation Models
You can use the CALIS procedure for analysis of covariance structures, fitting systems of linear structural equations, and path analysis.
These terms are more or less interchangeable, but they emphasize different aspects of the analysis. The analysis of covariance structures refers to
the formulation of a model for the variances and covariances among a set of variables and the fitting of the model to an observed covariance matrix.
In linear structural equations, the model is formulated as a system of equations relating several random variables with assumptions about the variances
and covariances of the random variables. In path analysis, the model is formulated as a path diagram, in which arrows connecting variables represent
variances, covariances, and regression (or path) coefficients. Path models and linear structural equation models can be converted to models of the
covariance matrix and can, therefore, be fitted by the methods of covariance structure analysis. All of these methods support the use of hypothetical
latent variables and measurement errors in the models.
Below are highlights of the capabilities of the CALIS procedure:
CALIS Procedure
The CALIS procedure fits structural equation models, which express relationships among a system of variables
that can be either observed variables (manifest variables) or unobserved hypothetical variables (latent variables).
PROC CALIS enables you to do the following:
 estimate parameters and test hypotheses for constrained and unconstrained problems in the following:
 multiple and multivariate linear regression
 linear measurementerror models
 path analysis and causal modeling
 simultaneous equation models with reciprocal causation
 exploratory and confirmatory factor analysis of any order
 canonical correlation
 a wide variety of other (non)linear latent variable models
 estimate parameters by using the following criteria:
 unweighted least squares
 generalized least squares
 weighted least squares
 diagonally weighted least squares
 maximum likelihood
 full information maximum likelihood
 maximum likelihood with SatorraBentler scaled model fit chisquare statistic and sandwichtype standard error estimation
 robust estimation with maximum likelihood model evaluation
 specify models using the following modeling languages:
 FACTOR—supports the input of factorvariable relations
 LINEQS—uses equations to describe variable relationships
 LISMOD—utilizes LISREL model matrices for defining models
 MSTRUCT—supports direct parameterization in the mean and covariance matrices
 PATH—provides an intuitive causal path specification interface
 RAM—utilizes the formulation of the reticular action model
 REFMODEL—provides a quick way for model referencing and respecification
 choose among the following optimization algorithms:
 LevenbergMarquardt algorithm (More, 1978)
 trustregion algorithm (Gay 1983)
 NewtonRaphson algorithm with line search
 ridgestabilized NewtonRaphson algorithm
 various quasiNewton and dual quasiNewton algorithms: BroydenFletcherGoldfarbShanno and
DavidonFletcherPowell, including a sequential quadratic programming algorithm
for processing nonlinear equality and inequality constraints
 various conjugate gradient algorithms: automatic restart algorithm of Powell (1977),
FletcherReeves, PolakRibiere, and conjugate descent algorithm of Fletcher (1980)

 use the following methods to automatically generate initial values for the optimization process:
 twostage least squares estimation
 instrumental variable factor analysis
 approximate factor analysis
 ordinary least squares estimation
 McDonald's (McDonald and Hartmann 1992) method
 formulate general equality and inequality constraints by using programming statements
 specify free unnamed parameters in all models
 analyze linear dependencies in the information matrix (approximate Hessian matrix) that might be helpful in detecting unidentified models
 perform multiplegroup analysis. Groups can also be fitted by multiple models simultaneously.
 specify linear and nonlinear equality and inequality constraints on the parameters with several
different statements, depending on the type of input
 compute Lagrange multiplier test indices for simple constant and equality parameter constraints and for active boundary constraints
 produce a SAS data set that contains information about the optimal parameter estimates
(parameter estimates, gradient, Hessian, projected Hessian and Hessian of Lagrange function for constrained optimization, the information matrix, and standard errors)
 produce a SAS data set that contains residuals and, for exploratory factor analysis, the rotated and unrotated factor loadings
 perform analysis of multiple samples with equal sample size by analyzing a moment supermatrix that contains the
individual moment matrices as block diagonal submatrices
 perform residual analysis at the case level or observation level
 perform direct robust estimation based on residual weighting or twostage robust estimation based on analyzing
the robust mean and covariance matrices
 input the model fit information of the customized baseline model of your choice.
PROC CALIS then computes various fit indices (mainly the incremental fit indices) based on your customized model fit
rather than the fit of the default uncorrelatedness model.
 compute weighted covariances or correlations
 create a SAS data set that corresponds to any output table
 perform BY group processing, which enables you to obtain separate analyses on grouped observations
 automatically create the following types of graphs:
 distribution of residuals in the moment matrices
 caselevel residual diagnostics
 path diagrams

For further details, see
CALIS Procedure