LINEQS Model Statement
where equation represents dependent = term < + term ... >
- LINEQS equation < , equation ... > ;
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
S = F1 F2 P2 F2' F1' + F1 U22 F1' + U12
by using the LINEQS and STD statements:
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;
E1-E9 = 9 * U:,
D1-D3 = 3 * V:,
F4 F5 = 2 * P;
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.