Factor Analysis with COSAN Model and Constraints (PROC CALIS)
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Type : CREATION_INTERNE
The data is a correlation matrix (TYPE=CORR) created directly in the script via a DATA STEP and datalines.
| 1 | DATA kinzer(type=corr); |
| 2 | title "Data Matrix of Kinzer & Kinzer, see GUTTMAN (1957)"; |
| 3 | _type_ = 'corr'; |
| 4 | INPUT _name_ $ var1-var6; |
| 5 | DATALINES; |
| 6 | var1 1.00 . . . . . |
| 7 | var2 .51 1.00 . . . . |
| 8 | var3 .46 .51 1.00 . . . |
| 9 | var4 .46 .47 .54 1.00 . . |
| 10 | var5 .40 .39 .49 .57 1.00 . |
| 11 | var6 .33 .39 .47 .45 .56 1.00 |
| 12 | ; |
| 1 | PROC CALIS DATA=Kinzer nobs=326 nose; |
| 2 | cosan |
| 3 | var= var1-var6, |
| 4 | D(6,DIA) * B(2,GEN) + D(6,DIA) * Psi(6,DIA); |
| 5 | matrix B |
| 6 | [ ,1] = b11 b21 b31 b41 b51 b61, |
| 7 | [ ,2] = b12 b22 b32 b42 b52 b62; |
| 8 | matrix Psi |
| 9 | [1,1] = psi1-psi6; |
| 10 | matrix D |
| 11 | [1,1] = d1-d6; |
| 12 | parameters alpha (1.); |
| 13 | |
| 14 | /* SAS Programming Statements to Define Dependent Parameters*/ |
| 15 | /* 6 constraints on the factor loadings */ |
| 16 | b12 = alpha - b11; |
| 17 | b22 = alpha - b21; |
| 18 | b32 = alpha - b31; |
| 19 | b42 = alpha - b41; |
| 20 | b52 = alpha - b51; |
| 21 | b62 = alpha - b61; |
| 22 | |
| 23 | /* 6 Constraints on Correlation structures */ |
| 24 | psi1 = 1. - b11 * b11 - b12 * b12; |
| 25 | psi2 = 1. - b21 * b21 - b22 * b22; |
| 26 | psi3 = 1. - b31 * b31 - b32 * b32; |
| 27 | psi4 = 1. - b41 * b41 - b42 * b42; |
| 28 | psi5 = 1. - b51 * b51 - b52 * b52; |
| 29 | psi6 = 1. - b61 * b61 - b62 * b62; |
| 30 | vnames |
| 31 | D = [var1-var6], |
| 32 | B = [factor1 factor2], |
| 33 | Psi = D; |
| 34 | RUN; |