|The TCALIS Procedure|
In the PATH statement, you specify the paths in your model. You can specify at most one PATH statement in a model, within the scope of either the PROC TCALIS statement or a MODEL statement. To complete the PATH model specifications, you might need to add some subsidiary model specification statements. The following is the syntax for the PATH modeling language:
In the PATH statement, you specify paths of variables in your model, excluding paths from the errors or disturbances. Paths in the PATH statement are separated by commas. In the PVAR statement, you specify parameters for either variances or partial variances. In the PCOV statement, you specify parameters for either covariances or partial covariances. In the MEAN statement, you specify parameters for either means or intercepts. For details about these subsidiary model specification statements, refer to the syntax of the individual statements.
In each path, you have one outcome variable and one predictor variable. The variables in a path can be manifest or latent. The specified direction determines the predictor and outcome variables. The variable being aimed at is the outcome variable and the other variable is the predictor variable. The path coefficient parameter is specified after each path in parameter-spec. For example, in the following statement you specify a model with four paths, each with predictor variable F1 and one outcome manifest variable.
PATH V1 <- F1 1, V2 <- F1 b2, V3 <- F1 b2, V4 <- F1 b4 (.4);
As shown in the example, the parameter-spec is one of the following three types:
fixed path coefficients
The parameter-spec for the first path to V1 is a fixed path coefficient at 1.
free or constrained parameters without starting values
The parameter-specs for the second and third paths to V2 and V3, respectively, are the same path coefficient parameter b2 with no starting value given. Because the same parameter name is used for the two path coefficients, the coefficients are constrained in the model.
free or constrained parameters with starting values
The parameter-spec for the last path to V4 is a free parameter named b4 with a starting value at .
If an outcome variable has more than one predictor variable, you have more than one path specification for the outcome variable. The following PATH statement shows an extension of the previous specification.
PATH V1 <- F1 1, V3 -> V1 b1 (.2), V2 <- F1 b2, V3 <- F1 b2, V4 <- F1 b4 (.4);
As compared with the previous example, an additional path is specified in second path specification of the current PATH statement. In the specification V3 is a predictor of V1, in addition to the predictor F1 in the first path specification. The additional path V3 –> V1 has a path coefficient parameter named b1, with a starting value at 0.2.
Note that because the display of path results follows the way you specify the paths, you should arrange the order of the input paths in the most desirable way.
In this section, it is assumed that you use a REFMODEL statement within the scope of a MODEL statement and the reference model (or base model) is also a PATH model. The reference model is referred to as the old model, while the model that makes reference to this old model is referred to as the new model. If the new model is not intended to be an exact copy of the old model, you can use the following extended PATH modeling language to make modifications within the scope of the MODEL statement for the new model. The syntax is the same as the ordinary PATH modeling language, as in the section PATH Statement. The respecification syntax for a PATH model is as follows:
The new model is formed by integrating with the old model in the following ways:
If you do not specify in the new model a parameter location that exists in the old model, the old parameter specification is duplicated in the new model.
If you specify in the new model a parameter location that does not exist in the old model, the new parameter specification is used in the new model.
If you specify in the new model a parameter location that also exists in the old model and the new parameter is denoted by the missing value '.', the old parameter specification is not copied into the new model.
If you specify in the new model a parameter location that also exists in the old model and the new parameter is not denoted by the missing value '.', the new parameter specification replaces the old one in the new model.
For example, consider the following specification of a two-group analysis:
proc tcalis; group 1 / data=d1; group 2 / data=d2; model 1 / group=1; path V1 <- F1 1., V2 <- F1 load1, V3 <- F1 load2, F1 <- V4 b1, F1 <- V5 b2, F1 <- V6 b3; pvar E1-E3 = ve1-ve3, F1 = vd1, V5-V6 = phi4-phi6; pcov V1 V2 = cve12; model 2 / group=2; refmodel 1; path V3 <- F1 load1, pcov V1 V2 = ., V2 V3 = cve23; run;
You specify model 2 by referring to model 1 in the REFMODEL statement. Model 2 is the new model that refers to the old model, model 1. This example illustrates the four types of model integration rules for the new model:
Duplication: All parameter specifications, except for the partial covariance between V1 and V2 and the V3 <– F1 path in the old model, are duplicated in the new model.
Addition: The parameter cve23 for the partial covariance between V2 and V3 is added in the new model because there is no corresponding specification in the old model.
Deletion: The specification of partial covariance between V1 and V2 in the old model is not copied into the new model, as indicated by the missing value '.' specified in the new model.
Replacement: The new path V3 <– F1 replaces the same path in the old model with parameter load1 for the path coefficient. Thus, in the new model paths V3 <– F1 and v2 <– F1 are now constrained to have the same path coefficient parameter load1.
Note: This procedure is experimental.