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The CALIS Procedure |

If there are exogenous manifest variables in the
linear structural equation model, then there is a one-to-one
relationship between the given covariances and
corresponding estimates in the central model matrix
(** P** or ).
In general, using exogenous manifest variables reduces the degrees
of freedom since
the corresponding sample
correlations or covariances are not part of the exogenous information
provided for the parameter estimation. See the section "Counting the Degrees of Freedom"
for more information.

If you specify a RAM or LINEQS model statement, or if such a model is recognized in an INRAM= data set, those elements in the central model matrices that correspond to the exogenous manifest variables are reset to the sample values after computing covariances or correlations within the current BY group.

The COSAN statement does not automatically set the covariances in the central model matrices that correspond to manifest exogenous variables.

You can use the output of the predetermined values in the predicted model matrix (PREDET option) that correspond to manifest exogenous variables to see which of the manifest variables are exogenous variables and to help you set the corresponding locations of the central model matrices with their covariances.

The following two examples show how different
the results of PROC CALIS can be if manifest variables are
considered either as endogenous or as exogenous variables.
(See Figure 19.5.)
In both examples, a correlation matrix ** S** is tested against an
identity model matrix

title2 'Data: FULLER (1987, p.18)'; data corn; input y x; datalines; 86 70 115 97 90 53 86 64 110 95 91 64 99 50 96 70 99 94 104 69 96 51 ; title3 'Endogenous Y and X'; proc calis data=corn; cosal corr(2,ide); run; proc calis data=corn; lineqs y=ey, x=ex; std ey ex=2 * 1; run; proc calis data=corn; ram 1 1 3 1., 1 2 4 1., 2 3 3 1., 2 4 4 1.; run;

The two runs of the second example (specified by the LINEQS and
RAM statements)
consider ** y** and

title3 'Exogenous Y and X'; proc calis data=corn; std y x=2 * 1; run; proc calis data=corn; ram 2 1 1 1., 2 2 2 1.; run;

**Figure 19.5:** Exogenous and Endogenous Variables

The LINEQS and the RAM model statements set the covariances (correlations) of exogenous manifest variables in the estimated model matrix and automatically reduce the degrees of freedom.

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