A linear relationship can also be described by an equation, as in the following lines.
Dim Sem as New AmosEngine
. . .
Sem.AStructure("variable1 = () variable2 + () variable3 + () variable4")
Here, variable1 is specified to be a linear function of variable2, variable3 and variable4. The empty parentheses represent unknown regression weights that Amos will estimate. Actually, the empty parentheses can be left out, as in the following lines, which are equivalent to the ones just previous.
Dim Sem as New AmosEngine
. . .
Sem.AStructure("variable1 = variable2 + variable3 + variable4")
Amos takes it for granted that it is supposed to estimate a regression weight for each variable on the right hand side of this equation. The parentheses sometimes contribute to readability, and, as will be shown below, provide the means for placing constraints on regression weights.
In using this method for specifying linear relationships, it is possible to specify one or more intercepts in a regression equation. For example:
Dim Sem as New AmosEngine
. . .
Sem.AStructure("var1 = () var2 + ()")
Sem.AStructure("var3 = () var4 + () + ()")
. . .
Here, var1 is specified to be a multiple of var2, except for an intercept term. var3 is specified to be a multiple of var4, except for two intercept terms. The five sets of empty parentheses represent five parameters that Amos is supposed to estimate - two regression weights and three intercepts. Again, the empty parentheses can be left out if desired.
Constraints can be placed on regression weights and intercepts as in the following example:
Dim Sem as New AmosEngine
. . .
Sem.AStructure("var1 = (alpha) var2 + (charlie)")
Sem.AStructure("var3 = (alpha) var4 + (charlie) + (50)")
. . .
Here, Amos is required to estimate two parameters. The two regression weights labeled alpha are required to be equal. Their common value constitutes one parameter. The two intercepts labeled charlie are required to be equal. Their common value constitutes the second parameter. The remaining intercept is fixed at 50, so it doesn't have to be estimated.