LINEQS Model Statement
LINEQS equation < , equation ... > ;
          where equation represents dependent = term < + term ... > 
          and where term represents one of the following: 
                coefficient-name < (number) > variable-name 
                prefix-name < (number) > variable-name 
                < number > variable-name

The LINEQS statement defines the LINEQS model 

You can specify only one LINEQS statement with each PROC CALIS statement. There are some differences from Bentler's notation in choosing the variable names. The length of each variable name is restricted to eight characters. The names of the manifest variables are defined in the DATA= input data set. The VAR statement can be used to select a subset of manifest variables in the DATA= input data set to analyze. You do not need to use a V prefix for manifest variables in the LINEQS statement nor do you need to use a numerical suffix in any variable name. The names of the latent variables must start with the prefix letter F (for Factor); the names of the residuals must start with the prefix letters E (for Error) or D (for Disturbance). The trailing part of the variable name can contain letters or digits. The prefix letter E is used for the errors of the manifest variables, and the prefix letter D is used for the disturbances of the latent variables. The names of the manifest variables in the DATA= input data set can start with F, E, or D, but these names should not coincide with the names of latent or error variables used in the model. The left-hand side (that is, endogenous dependent variable) of each equation should be either a manifest variable of the data set or a latent variable with prefix letter F. The left-hand-side variable should not appear on the right-hand side of the same equation; this means that matrix should not have a nonzero diagonal element. Each equation should contain, at most, one E or D variable. 

The equations must be separated by a comma. The order of the equations is arbitrary. The displayed output generally contains equations and terms in an order different from the input. 

Coefficients to estimate are indicated in the equations by a name preceding the independent variable's name. The coefficient's name can be followed by a number inside parentheses indicating the initial value for this coefficient. A number preceding the independent variable's name indicates a constant coefficient. If neither a coefficient name nor a number precedes the independent variable's name, a constant coefficient of 1 is assumed. 

If the initial value of a parameter is not specified in the equation, the initial value is chosen in one of the following ways: 
•	If you specify the RANDOM= option in the PROC CALIS statement, the variable obtains a randomly generated initial value r, such that . The uninitialized parameters in the diagonals of the central model matrices are given the nonnegative random values r multiplied by 10, 100, or the value specified in the DEMPHAS= option. 
•	If the RANDOM= option is not used, PROC CALIS tries to estimate the initial values. 
•	If the initial values cannot be estimated, the value of the START= option is used as an initial value. 

In Bentler's notation, estimated coefficients are indicated by asterisks. Referring to a parameter in Bentler's notation requires the specification of two variable names that correspond to the row and column of the position of the parameter in the matrix. Specifying the estimated coefficients by parameter names makes it easier to impose additional constraints with code. You do not need any additional statements to express equality constraints. Simply specify the same name for parameters that should have equal values. 

If your model contains many unconstrained parameters and it is too cumbersome to find different parameter names, you can specify all those parameters by the same prefix name. A prefix is a short name followed by a colon. The CALIS procedure then generates a parameter name by appending an integer suffix to this prefix name. The prefix name should have no more than five or six characters so that the generated parameter name is not longer than eight characters. To avoid unintentional equality constraints, the prefix names should not coincide with explicitly defined parameter names. 

For example, you can specify confirmatory second-order factor analysis model 
S = F1 F2 P2 F2' F1' + F1 U22 F1' + U12 

by using the LINEQS and STD statements: 
   lineqs
          V1 = X1 F1 + E1,
          V2 = X2 F1 + E2,
          V3 = X3 F1 + E3,
          V4 = X4 F2 + E4,
          V5 = X5 F2 + E5,
          V6 = X6 F2 + E6,
          V7 = X7 F3 + E7,
          V8 = X8 F3 + E8,
          V9 = X9 F3 + E9,
          F1 = Y1 F4 + D1,
          F2 = Y1 F4 + Y2 F5 + D2,
          F3 = Y2 F5 + D3;

   std
          E1-E9 = 9 * U:,
          D1-D3 = 3 * V:,
          F4 F5 = 2 * P;
   run;

PROC CALIS Statement
PROC CALIS < options > ;
This statement invokes the procedure. The options available with the PROC CALIS statement are summarized in Table 19.1 and discussed in the following six sections. 
Table 19.1: PROC CALIS Statement Options 
Data Set Options 	Short Description 	
DATA=	input data set	
INEST=	input initial values, constraints	
INRAM=	input model	
INWGT=	input weight matrix	
OUTEST=	covariance matrix of estimates	
OUTJAC	Jacobian into OUTEST= data set	
OUTRAM=	output model	
OUTSTAT=	output statistic	
OUTWGT=	output weight matrix	

Data Processing 	Short Description 	
AUGMENT	analyzes augmented moment matrix	
COVARIANCE	analyzes covariance matrix	
EDF=	defines nobs by number error df	
NOBS=	defines number of observations nobs	
NOINT	analyzes uncorrected moments	
RDF=	defines nobs by number regression df	
RIDGE	specifies ridge factor for moment matrix	
UCORR	analyzes uncorrected CORR matrix	
UCOV	analyzes uncorrected COV matrix	
VARDEF=	specifies variance divisor	

Estimation Methods 	Short Description 	
METHOD=	estimation method	
ASYCOV=	formula of asymptotic covariances	
DFREDUCE=	reduces degrees of freedom	
G4=	algorithm for STDERR	
NODIAG	excludes diagonal elements from fit	
WPENALTY=	penalty weight to fit correlations	
WRIDGE=	ridge factor for weight matrix	

Optimization Techniques 	Short Description 	
TECHNIQUE=	minimization method	
UPDATE=	update technique	
LINESEARCH=	line-search method	
FCONV=	function convergence criterion	
GCONV=	gradient convergence criterion	
INSTEP=	initial step length (RADIUS=, SALPHA=)	
LSPRECISION=	line-search precision (SPRECISION=)	
MAXFUNC=	max number function calls	
MAXITER=	max number iterations	

Displayed Output Options 	Short Description 	
KURTOSIS	compute and display kurtosis	
MODIFICATION	modification indices	
NOMOD	no modification indices	
NOPRINT	suppresses the displayed output	
PALL	all displayed output (ALL)	
PCORR	analyzed and estimated moment matrix	
PCOVES	covariance matrix of estimates	
PDETERM	determination coefficients	
PESTIM	parameter estimates	
PINITIAL	pattern and initial values	
PJACPAT	displays structure of variable and constant	
 	elements of the Jacobian matrix	
PLATCOV	latent variable covariances, scores	
PREDET	displays predetermined moment matrix	
PRIMAT	displays output in matrix form	
PRINT	adds default displayed output	
PRIVEC	displays output in vector form	
PSHORT	reduces default output (SHORT)	
PSUMMARY	displays only fit summary (SUMMARY)	
PWEIGHT	weight matrix	
RESIDUAL=	residual matrix and distribution	
SIMPLE	univariate statistics	
STDERR	standard errors	
NOSTDERR	computes no standard errors	
TOTEFF	displays total and indirect effects	

Miscellaneous Options 	Short Description 	
ALPHAECV=	probability Browne & Cudeck ECV	
ALPHARMS=	probability Steiger & Lind RMSEA	
BIASKUR	biased skewness and kurtosis	
DEMPHAS=	emphasizes diagonal entries	
FDCODE	uses numeric derivatives for code	
HESSALG=	algorithm for Hessian	
NOADJDF	no adjustment of df for active constraints	
RANDOM=	randomly generated initial values	
SINGULAR=	singularity criterion	
ASINGULAR=	absolute singularity information matrix	
COVSING=	singularity tolerance of information matrix	
MSINGULAR=	relative M singularity of information matrix	
VSINGULAR=	relative V singularity of information matrix	
SLMW=	probability limit for Wald test	
START=	constant initial values	

Data Set Options
DATA=SAS-data-set 
specifies an input data set that can be an ordinary SAS data set or a specially structured TYPE=CORR, TYPE=COV, TYPE=UCORR, TYPE=UCOV, TYPE=SSCP, or TYPE=FACTOR SAS data set, as described in the section "Input Data Sets". If the DATA= option is omitted, the most recently created SAS data set is used.