The CALIS Procedure

Table 29.1: Default Analysis Type and Parameterization

• Covariance structure analysis is the default analysis type in SAS/STAT 9.22 or later.

  Covariance structure analysis has been the default since SAS/STAT 9.22. The statistical theory for structural equation modeling has been developed largely for covariance structures rather than correlation structures. Also, most practical structural equation models nowadays are concerned with covariance structures. Therefore, the default analysis type with covariance structure analysis is more reasonable. You must now use the CORR option for correlation structure analysis.

• Variances of any types of variables are free parameters by default in SAS/STAT 9.22 or later.

  Variances of any types of variables are assumed to be free parameters in almost all applications for functional models. Prior to SAS/STAT 9.22, default variances of independent factors and errors were set to fixed zeros. This default has changed since SAS/STAT 9.22. Variances of any types of variables in functional models are now free parameters by default. This eliminates the need to specify these commonly assumed variance parameters.

• Covariances between all exogenous variables (factors or observed variables), except for error variables, are free parameters by default in functional models in SAS/STAT 9.22 or later.

  Since SAS/STAT 9.22, covariances between all exogenous variables, except for error variables, are free parameters by default in functional models such as LINEQS, LISMOD, PATH, RAM, and confirmatory FACTOR models. In exploratory FACTOR models, covariances between unrotated factors are set to zeros by default. This change of default setting reflects the structural equation modeling practice much better. The default covariances between error variables, or between errors and other exogenous variables, are fixed at zero in all versions. Also, the default covariances between independent observed variables are free parameters in all versions.

Table 29.2: Changes in the LINEQS Model Syntax

• The use of parameter names for free parameters is optional in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you must use parameter names to specify free parameters. In SAS/STAT 9.22 or later, the use of parameter names is optional. For example, prior to SAS/STAT 9.22, you might use the following LINEQS model specifications:

  lineqs
     A = x1 * B +  x2(.5) * C + E1;
  std
     B = var_b, C = var_c(1.2);
  cov
     B C = cov_b_c;
  

  In SAS/STAT 9.22 or later, you can simply use the following:

  lineqs
     A = * B  +  (.5) * C + E1;
  variance
     B,  C = (1.2);
  cov
     B C;
  

  This example shows that the parameter names x1, x2, var_b, var_c, and cov_b_c for free parameters are not necessary in SAS/STAT 9.22 or later. PROC CALIS generates names for these unnamed free parameters automatically. Also, you can specify initial estimates in parentheses without using parameter names. Certainly, you can still use parameter names wherever you want to, especially when you need to constrain parameters by referring to their names. Notice that the STD statement prior to SAS/STAT 9.22 has a more meaningful alias, VARIANCE, in SAS/STAT 9.22 or later.

• An error term is required in each equation in the LINEQS statement in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you can set an equation in the LINEQS statement without providing an error term such as the following:

  lineqs
      A  = x1 * F1;
  

  This means that A is perfectly predicted from F1 without an error. In SAS/STAT 9.22 or later, you need to provide an error term in each question, and the preceding specification is not syntactically valid. If a perfect relationship is indeed desirable, you can equivalently set the corresponding error variance to zero. For example, the following specification in SAS/STAT 9.22 or later achieves the purpose of specifying a perfect relationship between A and F1:

  lineqs
     A  = x1 * F1  + E1;
  variance
     E1 = 0.;
  

  In the VARIANCE statement, the error variance of E1 is fixed at zero, resulting in a perfect relationship between A and F1.

• Mean structure analysis is invoked by the MEANSTR option in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you use the AUG and UCOV options together in the PROC CALIS statement to invoke the analysis of mean structures. These two options became obsolete in SAS/STAT 9.22. This change actually reflects more than a name change. Prior to SAS/STAT 9.22, mean structures are analyzed as augmented covariance structures in the uncorrected covariance matrix (hence the AUG and UCOV options). There are many problems with this "augmented" matrix approach. In SAS/STAT 9.22 or later, the augmented matrix was abandoned in favor of the direct parameterization approach for the mean structures. Now you must use the MEANSTR option in the PROC CALIS statement to invoke the analysis of mean structures. Alternatively, you can specify the intercepts directly in the LINEQS statement or specify the means directly in the MEAN statement. See the next two items for more information.

• Intercept parameters are set as the coefficient effects of the Intercept variable in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you specify the intercept variable in the equations of the LINEQS statement by using the special "variable" named 'INTERCEP'. For example, in the following specification, a1 is the intercept parameter for the equation with dependent variable A:

  proc calis ucov aug;
  lineqs
     A = a1 * INTERCEP + b1 * B  + E1;
  

  In SAS/STAT 9.22 or later, although 'INTERCEP' is still accepted by PROC CALIS, a more meaningful alias 'Intercept' is also supported, as shown in the following:

  proc calis;
  lineqs
     A = a1 * Intercept + b1 * B  + E1;
  

  Intercept or INTERCEP can be typed in uppercase, lowercase, or mixed case in all versions. In addition, with the use of the Intercept variable in the LINEQS statement specification, mean structure analysis is automatically invoked for all parts of the model without the need to use the MEANSTR option in the PROC CALIS statement in SAS/STAT 9.22 or later.

• Mean parameters are specified directly in the MEAN statement in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you need to specify mean parameters as covariances between the corresponding variables and the INTERCEP variable. For example, the following statements specify the mean parameters, mean_b and mean_c, of variables B and C, respectively:

  proc calis ucov aug;
  lineqs
     A = a1 * INTERCEP + b1 * B + b2 * C + E1;
  cov
     B INTERCEP = mean_b (3),
     C INTERCEP = mean_c;
  

  In SAS/STAT 9.22 or later, you can specify these mean parameters directly in the MEAN statement, as in the following example:

  proc calis;
  lineqs
     A = a1 * Intercept + b1 * B + b2 * C + E1;
  mean
     B = mean_b (3),
     C = mean_c;
  

  This way, the types of parameters that are being specified are clearer.

• Short parameter lists do not generate constrained parameters in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, if you provide a shorter parameter list than expected, the last parameter specified is replicated automatically. For example, the following specification results in replicating varx as the variance parameters for variables x2–x10:

  std
     x1-x10 = var0 varx;
  

  This means that all variances for the last nine variables in the list are constrained to be the same. In SAS/STAT 9.22 or later, this is not the case. That is, var0 and varx are the variance parameters for x1 and x2, respectively, while the variances for x3–x10 are treated as unconstrained free parameters.

  If you want to constrain the remaining parameters to be the same in the current version of PROC CALIS, you can use the following continuation syntax [...] at the end of the parameter list:

  std
     x1-x10 = var0 varx [...];
  

  The continuation syntax [...] repeats the specification of varx for all the remaining variance parameters for x3–x10.

• The parameter-prefix uses a new notation in SAS/STAT 9.22 or later.

  Prior to SAS/STAT 9.22, you can use the parameter-prefix to generate parameter names as in the following example:

  lineqs
     A = x: * B +  x: * C + E1;
  std
     B = var:, C = var: ;
  

  In SAS/STAT 9.22 or later, you must replace the ':' notation with two trailing underscores, '__', as in the following:

  lineqs
     A = x__ * B  +  x__ * C + E1;
  variance
     B = var__,  C = var__;
  

  Both versions generate parameter names by appending unique integers to the prefix, as if the following has been specified:

  lineqs
     A = x1 * B  +  x2 * C + E1;
  variance
     B = var1,  C = var2;
  

  In SAS/STAT 9.22 or later, you can even omit the parameter-prefix altogether. For example, you can specify the following with a null parameter-prefix:

  lineqs
     A = __ * B  +  __ * C + E1;
  variance
     B = __,  C = __;
  

  In this case, PROC CALIS uses the internal prefix '_Parm' to generate names, as if the following has been specified:

  lineqs
     A = _Parm1 * B  +  _Parm2 * C + E1;
  variance
     B = _Parm3,  C = _Parm4;