### The Measurement Model for x

The second component of the LISMOD specification is the measurement model for x, as shown in the following equation: The measurement model for x is similar to that for y. Assuming that x and are centered, this equation states that x is a function of the true scores vector plus the error term , which is independent of . The model matrices involved in this measurement model are (effects of on x) and , which is the covariance matrix of .

For the career aspiration data, you specify the following MATRIX statement for this measurement model:

   matrix _lambdax_ [1,1] = 0.837 0.894 0.949 0.949 0.894 0.837;


Figure 17.48 shows the output related to the specification of the measurement model for x.

Figure 17.48: Career Aspiration Analysis 3: Initial Measurement Model for x

Initial _LAMBDAX_ Matrix
f_rpa f_riq f_rses f_fses f_fiq f_fpa
rpa 0.8370 0 0 0 0 0
riq 0 0.8940 0 0 0 0
rses 0 0 0.9490 0 0 0
fses 0 0 0 0.9490 0 0
fiq 0 0 0 0 0.8940 0
fpa 0 0 0 0 0 0.8370

Initial _THETAX_ Matrix
rpa riq rses fses fiq fpa
rpa
 0
 0
 0
 0
 0
riq
 0
 0
 0
 0
 0
rses
 0
 0
 0
 0
 0
fses
 0
 0
 0
 0
 0
fiq
 0
 0
 0
 0
 0
fpa
 0
 0
 0
 0
 0
In Figure 17.48, the initial _LAMBDAX_ matrix is a 6 6 matrix. The _LAMBDAX_ matrix contains information about the relationships between the row indicator variables x (XVAR= variables) and the column factors (XI= variables). As specified in the MATRIX statement for _LAMBDAX_, the diagonal elements are filled with the fixed values provided. The [1,1] specification in the MATRIX statement for _LAMBDAX_ provides the starting element for the subsequent parameter list to fill in. In this case, the list contains six fixed values, and PROC CALIS proceeds from [1,1] to [2,2], [3,3] and so on until the entire list of parameters is consumed. This kind of notation is a shortcut of the following equivalent specification:
   matrix _lambdax_ [1,1]=0.837, [2,2]=0.894, [3,3]=0.949,