OPTIONS PAGENO=1 PAGESIZE=56 NOLABEL; * Kim #13, Table 3, Table 4, Figure 5. *; DATA FACTOR(TYPE=CORR); _TYPE_='CORR'; INPUT _TYPE_ $ 1-4 _NAME_ $

Transcription

1 OPTIONS PAGENO=1 PAGESIZE=56 NOLABEL; * Kim #13, Table 3, Table 4, Figure 5. DATA FACTOR(TYPE=CORR); _TYPE_='CORR'; INPUT _TYPE_ $ 1-4 _NAME_ $ 6-10 X X X X X ; CARDS; N CORR X CORR X CORR X CORR X CORR X PROC REG; MODEL X1 = X2 X3 X4 X5 / STB; PROC REG; MODEL X2 = X1 X3 X4 X5 / STB; PROC REG; MODEL X3 = X1 X2 X4 X5 / STB; PROC REG; MODEL X4 = X1 X2 X3 X5 / STB; PROC REG; MODEL X5 = X1 X2 X3 X4 / STB; PROC FACTOR METHOD=ML MIN=0 ROTATE=VARIMAX; VAR X1-X5; RUN;

2 Monday, September 23, :13 PM 1 The REG Procedure Model: MODEL1 Dependent Variable: X1 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 0 Adj R-Sq Coeff Var. Parameter s Variable DF Parameter Standard Error t Value Pr > t Standardized Intercept X < X < X X

3 Monday, September 23, :13 PM 2 The REG Procedure Model: MODEL1 Dependent Variable: X2 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 0 Adj R-Sq Coeff Var. Parameter s Variable DF Parameter Standard Error t Value Pr > t Standardized Intercept X < X X X

4 Monday, September 23, :13 PM 3 The REG Procedure Model: MODEL1 Dependent Variable: X3 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 0 Adj R-Sq Coeff Var. Parameter s Variable DF Parameter Standard Error t Value Pr > t Standardized Intercept X < X X < X

5 Monday, September 23, :13 PM 4 The REG Procedure Model: MODEL1 Dependent Variable: X4 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 0 Adj R-Sq Coeff Var. Parameter s Variable DF Parameter Standard Error t Value Pr > t Standardized Intercept X X X < X <

6 Monday, September 23, :13 PM 5 The REG Procedure Model: MODEL1 Dependent Variable: X5 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean 0 Adj R-Sq Coeff Var. Parameter s Variable DF Parameter Standard Error t Value Pr > t Standardized Intercept X X X X <

7 Monday, September 23, :13 PM 6 The FACTOR Procedure Input Data Type Correlations N Set/Assumed in Data Set 200 N for Significance Tests 200

8 Monday, September 23, :13 PM 7 The FACTOR Procedure Initial Factor Method: Maximum Likelihood Prior Communality s: SMC X1 X2 X3 X4 X Preliminary Eigenvalues: Total = Average = Eigenvalue Difference Proportion Cumulative factors will be retained by the MINEIGEN criterion. Iteration Criterion Ridge Change Communalities Convergence criterion satisfied. Significance Tests Based on 200 Observations Test DF Chi-Square Pr > ChiSq H0: No common factors <.0001 HA: At least one common factor H0: 2 Factors are sufficient HA: More factors are needed Chi-Square without Bartlett's Correction Akaike's Information Criterion Schwarz's Bayesian Criterion Tucker and Lewis's Reliability Coefficient Squared Canonical Correlations Factor1 Factor Eigenvalues of the Weighted Reduced Correlation Matrix: Total = Average = Eigenvalue Difference Proportion

9 Monday, September 23, :13 PM 8 The FACTOR Procedure Initial Factor Method: Maximum Likelihood 2 factors will be retained by the MINEIGEN criterion. Eigenvalues of the Weighted Reduced Correlation Matrix: Total = Average = Cumulative Eigenvalues of the Weighted Reduced Correlation Matrix: Total = Average = Eigenvalue Difference Proportion Eigenvalues of the Weighted Reduced Correlation Matrix: Total = Average = Cumulative Factor Pattern Factor1 Factor2 X X X X X Variance Explained by Each Factor Factor Weighted Unweighted Factor Factor

10 Monday, September 23, :13 PM 9 The FACTOR Procedure Initial Factor Method: Maximum Likelihood 2 factors will be retained by the MINEIGEN criterion. Final Communality s and Variable Weights Total Communality: Weighted = Unweighted = Variable Communality Weight X X X X X

11 Monday, September 23, :13 PM 10 The FACTOR Procedure Rotation Method: Varimax Orthogonal Transformation Matrix Rotated Factor Pattern Factor1 Factor2 X X X X X Variance Explained by Each Factor Factor Weighted Unweighted Factor Factor Final Communality s and Variable Weights Total Communality: Weighted = Unweighted = Variable Communality Weight X X X X X

12 * * CALCULATE WEIGHTED INPUT MATRIX FOR MAXIMUM LIKELIHOOD SOLUTION * TO DATA IN KIM #13, TABLE 4. * * USE CALL EIGEN PROCEDURE TO PRINT EIGENVALUES FOR COMPARISION OF RESULTS. TITLE1 'Results'; OPTIONS NOCENTER; PROC IML; START MAIN; * * DEFINE CORRELATION MATRIX. R = { , , , , }; * * DEFINE COMMUNALITIES H2 = { , , , , }; ID5 = I(5); U2 = ID5-H2; U = SQRT(U2); IU = INV(U); RR = IU*(R-U2)*IU; M = EIGVAL(RR); CALL EIGEN(M,E,RR); PRINT, RR; PRINT, M; FINISH MAIN; RUN; Results RR M (Eigenvalues) E E E-16