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The CALIS Procedure

RAM Model Statement

RAM list-entry < , list-entry ... > ;
          where list-entry represents
               matrix-number row-number column-number <value><parameter-name> The RAM statement defines the elements of the symmetric RAM matrix model

v= A{v}+ {\mu}

in the form of a list type input (McArdle and McDonald 1984).

The covariance structure is given by
C = J(I- A)-1P((I- A)-1)'J'
with selection matrix J and
C= {\cal E}\{J{v}v^'J^'\} ,  P= {\cal E}\{{\mu}{\mu}^'\}

You can specify only one RAM statement with each PROC CALIS statement. Using the RAM statement requires that the first n variable numbers in the path diagram and in the vector v correspond to the numbers of the n manifest variables of the given covariance or correlation matrix. If you are not sure what the order of the manifest variables in the DATA= data set is, use a VAR statement to specify the order of these observed variables. Using the AUGMENT option includes the INTERCEPT variable as a manifest variable with number n+1 in the RAM model. In this case, latent variables have to start with n+2. The box of each manifest variable in the path diagram is assigned the number of the variable in the covariance or correlation matrix.

The selection matrix J is always a rectangular identity (IDE) matrix, and it does not have to be specified in the RAM statement.

A constant matrix element is defined in a RAM statement by a list-entry with four numbers. You define a parameter element by three or four numbers followed by a name for the parameter. Separate the list entries with a comma. Each list-entry in the RAM statement corresponds to a path in the diagram, as follows:

If the initial value of a parameter is not specified in the list, the initial value is chosen in one of the following ways:

If your model contains many unconstrained parameters and it is too cumbersome to find different parameter names, you can specify all those parameters by the same prefix name. A prefix is a short name followed by a colon. The CALIS procedure then generates a parameter name by appending an integer suffix to this prefix name. The prefix name should have no more than five or six characters so that the generated parameter name is not longer than eight characters. To avoid unintentional equality constraints, the prefix names should not coincide with explicitly defined parameter names.

For example, you can specify the confirmatory second-order factor analysis model
S = F1 F2 P2 F2' F1' + F1 U22 F1' + U12

using the following RAM model statement.

      1  1 10    x1,
      1  2 10    x2,
      1  3 10    x3,
      1  4 11    x4,
      1  5 11    x5,
      1  6 11    x6,
      1  7 12    x7,
      1  8 12    x8,
      1  9 12    x9,
      1 10 13    y1,
      1 11 13    y1,
      1 11 14    y2,
      1 12 14    y2,
      2  1  1    u:,
      2  2  2    u:,
      2  3  3    u:,
      2  4  4    u:,
      2  5  5    u:,
      2  6  6    u:,
      2  7  7    u:,
      2  8  8    u:,
      2  9  9    u:,
      2 10 10    v:,
      2 11 11    v:,
      2 12 12    v:,
      2 13 13    p ,
      2 14 14    p ;

The confirmatory second-order factor analysis model corresponds to the path diagram displayed in Figure 19.2.

\put( 10.,130.){
\put( 10...

Figure 19.2: Path Diagram of Second-Order Factor Analysis Model

There is a very close relationship between the RAM model algebra and the specification of structural linear models by path diagrams. See Figure 19.3 for an example.


\put( 10.,350.){
\put( 9...
 ...ut(275., 15.){d_3}

\put(200., 0.){4. Second-Order Factor Analysis}\end{picture}

Figure 19.3: Examples of RAM Nomography

Refer to McArdle (1980) for the interpretation of the models displayed in Figure 19.3.

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