Output from calis36.sas

	Output from calis36.sas	Source 0 Graphs

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                1
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                    Test circular correlation pattern: C = D * P * D

                               Covariance Structure Analysis: Pattern and Initial Values

                                   COSAN Model Statement
                              -------------------------------
                                   Matrix         Rows & Cols          Matrix Type

                      TERM   1-----------------------------------------------------------
                                1    D              6       6    DIAGONAL
                                2    P              6       6    SYMMETRIC

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                2
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                    Test circular correlation pattern: C = D * P * D

                                Covariance Structure Analysis: Least-Squares Estimation

                                            Levenberg-Marquardt Optimization
                                             Scaling Update of More (1978)
                                            Number of Parameter Estimates 9
                                         Number of Functions (Observations) 21

Optimization Start: Active Constraints= 0  Criterion= 2.373 Maximum Gradient Element= 1.317 Radius= 4.003

                             Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho

                                1    0    3   0    0.5300   1.8428   0.463   1.273   1.129
                                2    0    4   0    0.2190   0.3110   1.558  0.0448   0.633
                                3    0    5   0    0.0251   0.1939  0.0447       0   0.992
                                4    0    6   0    0.0247 0.000378 0.00168       0   0.981
                                5    0    7   0    0.0247 7.158E-7 0.00008       0   0.992
                                6    0    8   0    0.0247 1.754E-9 5.33E-6       0   0.999

Optimization Results: Iterations= 6 Function Calls= 9 Jacobian Calls= 7 Active Constraints= 0  Criterion= 0.024727182
Maximum Gradient Element= 5.32787E-6 Lambda= 0 Rho= 0.9993 Radius= 0.0001215

NOTE:  ABSGCONV convergence criterion satisfied.

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                3
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                    Test circular correlation pattern: C = D * P * D

                                Covariance Structure Analysis: Least-Squares Estimation

                              Fit criterion . . . . . . . . . . . . . . . . . .     0.0247
                              Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9947
                              GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9907
                              Root Mean Square Residual (RMR) . . . . . . . . .     0.0358
                              Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.7958

                                           Estimated Parameter Matrix P[6:6]
                                                    Symmetric Matrix

                      COL1              COL2              COL3              COL4              COL5              COL6

    ROW1        1.0000            0.3960[R1]        0.2956[R2]        0.2507[R3]        0.2956[R2]        0.3960[R1]
    ROW2        0.3960[R1]        1.0000            0.3960[R1]        0.2956[R2]        0.2507[R3]        0.2956[R2]
    ROW3        0.2956[R2]        0.3960[R1]        1.0000            0.3960[R1]        0.2956[R2]        0.2507[R3]
    ROW4        0.2507[R3]        0.2956[R2]        0.3960[R1]        1.0000            0.3960[R1]        0.2956[R2]
    ROW5        0.2956[R2]        0.2507[R3]        0.2956[R2]        0.3960[R1]        1.0000            0.3960[R1]
    ROW6        0.3960[R1]        0.2956[R2]        0.2507[R3]        0.2956[R2]        0.3960[R1]        1.0000

                                           Estimated Parameter Matrix D[6:6]
                                                    Diagonal Matrix

               COL1            COL2            COL3            COL4            COL5            COL6

 V1      1.0071[D1]      0.              0.              0.              0.              0.            Association
 V2      0.              1.0079[D2]      0.              0.              0.              0.            Incomplete Words
 V3      0.              0.              1.0133[D3]      0.              0.              0.            Multiplication
 V4      0.              0.              0.              0.9856[D4]      0.              0.            Dot patterns
 V5      0.              0.              0.              0.              0.9766[D5]      0.            ABC
 V6      0.              0.              0.              0.              0.              1.0068[D6]    Directions

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                4
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                    Test circular correlation pattern: C = D * P * D

                              Covariance Structure Analysis: Maximum Likelihood Estimation

                                            Levenberg-Marquardt Optimization
                                             Scaling Update of More (1978)
                                            Number of Parameter Estimates 9
                                         Number of Functions (Observations) 21

Optimization Start: Active Constraints= 0  Criterion= 0.045 Maximum Gradient Element= 0.195 Radius= 1.000

                             Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho

                                1    0    2   0    0.0382  0.00716  0.0196       0   0.978
                                2    0    3   0    0.0382 0.000011 0.00029       0   1.002
                                3    0    4   0    0.0382 1.898E-8 0.00004       0   1.008
                                4    0    5   0    0.0382 5.07E-11 8.62E-7       0   1.009

Optimization Results: Iterations= 4 Function Calls= 6 Jacobian Calls= 5 Active Constraints= 0  Criterion= 0.038154417
Maximum Gradient Element= 8.62173E-7 Lambda= 0 Rho= 1.009 Radius= 0.00003198

NOTE:  GCONV convergence criterion satisfied.

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                5
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                    Test circular correlation pattern: C = D * P * D

                              Covariance Structure Analysis: Maximum Likelihood Estimation

                              Fit criterion . . . . . . . . . . . . . . . . . .     0.0382
                              Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9874
                              GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9779
                              Root Mean Square Residual (RMR) . . . . . . . . .     0.0399
                              Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.7899
                              Chi-square = 27.0515       df = 12      Prob>chi**2 = 0.0076
                              Null Model Chi-square:     df = 15                  819.3150
                              RMSEA Estimate  . . . . . .  0.0421  90%C.I.[0.0207, 0.0634]
                              Probability of Close Fit  . . . . . . . . . . . .     0.7044
                              ECVI Estimate . . . . . . .  0.0638  90%C.I.[0.0477, 0.0909]
                              Bentler's Comparative Fit Index . . . . . . . . .     0.9813
                              Normal Theory Reweighted LS Chi-square  . . . . .    27.2145
                              Akaike's Information Criterion. . . . . . . . . .     3.0515
                              Bozdogan's (1987) CAIC. . . . . . . . . . . . . .   -63.7317
                              Schwarz's Bayesian Criterion. . . . . . . . . . .   -51.7317
                              McDonald's (1989) Centrality. . . . . . . . . . .     0.9895
                              Bentler & Bonett's (1980) Non-normed Index. . . .     0.9766
                              Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9670
                              James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.7736
                              Z-Test of Wilson & Hilferty (1931). . . . . . . .     2.4229
                              Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9587
                              Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9814
                              Hoelter's (1983) Critical N . . . . . . . . . . .        553

                                           Estimated Parameter Matrix P[6:6]
                                                    Symmetric Matrix

                      COL1              COL2              COL3              COL4              COL5              COL6

    ROW1        1.0000            0.3957[R1]        0.2951[R2]        0.2498[R3]        0.2951[R2]        0.3957[R1]
    ROW2        0.3957[R1]        1.0000            0.3957[R1]        0.2951[R2]        0.2498[R3]        0.2951[R2]
    ROW3        0.2951[R2]        0.3957[R1]        1.0000            0.3957[R1]        0.2951[R2]        0.2498[R3]
    ROW4        0.2498[R3]        0.2951[R2]        0.3957[R1]        1.0000            0.3957[R1]        0.2951[R2]
    ROW5        0.2951[R2]        0.2498[R3]        0.2951[R2]        0.3957[R1]        1.0000            0.3957[R1]
    ROW6        0.3957[R1]        0.2951[R2]        0.2498[R3]        0.2951[R2]        0.3957[R1]        1.0000

                                           Estimated Parameter Matrix D[6:6]
                                                    Diagonal Matrix

               COL1            COL2            COL3            COL4            COL5            COL6

 V1      0.9881[D1]      0.              0.              0.              0.              0.            Association
 V2      0.              0.9909[D2]      0.              0.              0.              0.            Incomplete Words
 V3      0.              0.              0.9970[D3]      0.              0.              0.            Multiplication
 V4      0.              0.              0.              1.0090[D4]      0.              0.            Dot patterns
 V5      0.              0.              0.              0.              1.0161[D5]      0.            ABC
 V6      0.              0.              0.              0.              0.              0.9998[D6]    Directions

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                6
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                Test quasi circumplex model: C = D * C * DP * C * D + T

                               Covariance Structure Analysis: Pattern and Initial Values

                                   COSAN Model Statement
                              -------------------------------
                                   Matrix         Rows & Cols          Matrix Type

                      TERM   1-----------------------------------------------------------
                                1    D              6       6    DIAGONAL
                                2    C              6       6    GENERAL
                                3    DP             6       6    DIAGONAL
                      TERM   2-----------------------------------------------------------
                                4    T              6       6    DIAGONAL

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                7
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                Test quasi circumplex model: C = D * C * DP * C * D + T

                              Covariance Structure Analysis: Maximum Likelihood Estimation

                                            Levenberg-Marquardt Optimization
                                             Scaling Update of More (1978)
                                            Number of Parameter Estimates 17
                                         Number of Functions (Observations) 21

Optimization Start: Active Constraints= 0  Criterion= 8.288 Maximum Gradient Element= 1.165 Radius= 5.381

                             Iter rest nfun act   optcrit  difcrit maxgrad  lambda     rho

                                1    0    2   0    0.7650   7.5229   1.793       0   3.120
                                2    0    3   0    0.0825   0.6825   0.771       0   1.413
                                3    0    4   0    0.0243   0.0581   0.128       0   1.100
                                4    0    5   0    0.0232  0.00110 0.00383       0   0.914
                                5    0    6   0    0.0232 9.631E-6 0.00064       0   0.939
                                6    0    7   0    0.0232 2.619E-7 0.00012       0   1.003
                                7    0    8   0    0.0232 1.379E-8 0.00003       0   1.013
                                8    0    9   0    0.0232 1.081E-9 9.06E-6       0   0.933

Optimization Results: Iterations= 8 Function Calls= 10 Jacobian Calls= 9 Active Constraints= 0  Criterion= 0.023233285
Maximum Gradient Element= 9.06416E-6 Lambda= 0 Rho= 0.9332 Radius= 0.0007822

NOTE:  ABSGCONV convergence criterion satisfied.

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                8
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                Test quasi circumplex model: C = D * C * DP * C * D + T

                              Covariance Structure Analysis: Maximum Likelihood Estimation

                              Fit criterion . . . . . . . . . . . . . . . . . .     0.0232
                              Goodness of Fit Index (GFI) . . . . . . . . . . .     0.9923
                              GFI Adjusted for Degrees of Freedom (AGFI). . . .     0.9594
                              Root Mean Square Residual (RMR) . . . . . . . . .     0.0298
                              Parsimonious GFI (Mulaik, 1989) . . . . . . . . .     0.2646
                              Chi-square = 16.4724       df = 4       Prob>chi**2 = 0.0024
                              Null Model Chi-square:     df = 15                  819.3150
                              RMSEA Estimate  . . . . . .  0.0663  90%C.I.[0.0352, 0.1010]
                              Probability of Close Fit  . . . . . . . . . . . .     0.1743
                              ECVI Estimate . . . . . . .  0.0717  90%C.I.[0.0590, 0.0950]
                              Bentler's Comparative Fit Index . . . . . . . . .     0.9845
                              Normal Theory Reweighted LS Chi-square  . . . . .    16.5920
                              Akaike's Information Criterion. . . . . . . . . .     8.4724
                              Bozdogan's (1987) CAIC. . . . . . . . . . . . . .   -13.7887
                              Schwarz's Bayesian Criterion. . . . . . . . . . .    -9.7887
                              McDonald's (1989) Centrality. . . . . . . . . . .     0.9913
                              Bentler & Bonett's (1980) Non-normed Index. . . .     0.9418
                              Bentler & Bonett's (1980) NFI . . . . . . . . . .     0.9799
                              James, Mulaik, & Brett (1982) Parsimonious NFI. .     0.2613
                              Z-Test of Wilson & Hilferty (1931). . . . . . . .     2.7935
                              Bollen (1986) Normed Index Rho1 . . . . . . . . .     0.9246
                              Bollen (1988) Non-normed Index Delta2 . . . . . .     0.9847
                              Hoelter's (1983) Critical N . . . . . . . . . . .        410

                                           Estimated Parameter Matrix DP[6:6]
                                                    Diagonal Matrix

                    COL1               COL2               COL3               COL4               COL5               COL6

 ROW1        1.0000             0.                 0.                 0.                 0.                 0.
 ROW2        0.                 2.0160[DP1]        0.                 0.                 0.                 0.
 ROW3        0.                 0.                 3.1399[DP2]        0.                 0.                 0.
 ROW4        0.                 0.                 0.                 2.1346[DP3]        0.                 0.
 ROW5        0.                 0.                 0.                 0.                 2.7983[DP4]        0.
 ROW6        0.                 0.                 0.                 0.                 0.                 2.7712[DP5]

                                           Estimated Parameter Matrix C[6:6]
                                                     General Matrix
                                                 Constant Model Matrix

                                          *** Constant or Unchanged Matrix ***

                                TEST36: Six Different Kinds of Abilties, GUTTMAN (1954)                                9
                            Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24)
                                Test quasi circumplex model: C = D * C * DP * C * D + T

                              Covariance Structure Analysis: Maximum Likelihood Estimation

                                           Estimated Parameter Matrix D[6:6]
                                                    Diagonal Matrix

               COL1            COL2            COL3            COL4            COL5            COL6

 V1      0.2678[D1]      0.              0.              0.              0.              0.            Association
 V2      0.              0.2190[D2]      0.              0.              0.              0.            Incomplete Words
 V3      0.              0.              0.2099[D3]      0.              0.              0.            Multiplication
 V4      0.              0.              0.              0.2354[D4]      0.              0.            Dot patterns
 V5      0.              0.              0.              0.              0.2198[D5]      0.            ABC
 V6      0.              0.              0.              0.              0.              0.2536[D6]    Directions

                                           Estimated Parameter Matrix T[6:6]
                                                    Diagonal Matrix

               COL1            COL2            COL3            COL4            COL5            COL6

 V1      0.3913[T1]      0.              0.              0.              0.              0.            Association
 V2      0.              0.5024[T2]      0.              0.              0.              0.            Incomplete Words
 V3      0.              0.              0.5068[T3]      0.              0.              0.            Multiplication
 V4      0.              0.              0.              0.5051[T4]      0.              0.            Dot patterns
 V5      0.              0.              0.              0.              0.5758[T5]      0.            ABC
 V6      0.              0.              0.              0.              0.              0.4088[T6]    Directions

Output from calis36.sas

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 1 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test circular correlation pattern: C = D * P * D

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 2 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test circular correlation pattern: C = D * P * D

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 3 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test circular correlation pattern: C = D * P * D

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 4 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test circular correlation pattern: C = D * P * D

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 5 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test circular correlation pattern: C = D * P * D

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 6 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test quasi circumplex model: C = D * C * DP * C * D + T

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 7 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test quasi circumplex model: C = D * C * DP * C * D + T

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 8 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test quasi circumplex model: C = D * C * DP * C * D + T

TEST36: Six Different Kinds of Abilties, GUTTMAN (1954) 9 Two Circumplex Models, Joreskog (1978, p.475) LISREL (p.III.24) Test quasi circumplex model: C = D * C * DP * C * D + T