/*--------------------------------------------------------------
  *
  *                  SAS/STAT TEST LIBRARY
  *
  *       NAME: calis21
  *    SUPPORT: Wolfgang M. Hartmann
  *     UPDATE:
  *  REFERENCE: Meyer & Bendig Multimode FA, McDONALD (1980)
  *             Data of MEYER & BENDIG, McDONALD (1980)
  * EVALUATION:
  *   FUNCTION: CMP Tests & Active Bounds
  *             Indefinite central model matrices
  *       MISC:
  *
  --------------------------------------------------------------*/

* OPTIONS NODATE NOSTIMER LS=120 PS=60;

TITLE CALIS'21: MEYER-BENDIG Multimode Factor Analysis Model, McDONALD(1980)';
DATA MEYBEN(TYPE=COV);
   _TYPE_ = 'COV'; INPUT _NAME_ $ OBS1-OBS10;
   CARDS;

OBS1  48.14    .      .      .      .      .      .      .      .      .
OBS2  25.25  92.74    .      .      .      .      .      .      .      .
OBS3  17.67  19.13  36.00    .      .      .      .      .      .      .
OBS4  28.89  10.47  17.83  61.15    .      .      .      .      .      .
OBS5  29.17  10.83  13.23  20.03 116.86    .      .      .      .      .
OBS6  57.56  33.75  29.63  46.13  34.83 102.01    .      .      .      .
OBS7  25.32  64.81  12.53  -2.90  12.68  35.54 105.88    .      .      .
OBS8  17.75  18.49  26.93  21.40  17.19  27.69  10.83  36.00    .      .
OBS9  25.41  11.81  21.21  51.23  18.19  50.17   5.71  28.11  80.10    .
OBS10 20.05  17.27  12.02  13.75  54.60  28.17  18.45  13.85  16.99 137.36
  ;


PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=LM EDF=99 ALL ;
TITLE2 'Use modified formula (2.12) of Mc DONALD (1980)';
COSAN F(2,GEN) * I(2,IDE) + U(10,SYM) * J(10,IDE);
 MATRIX F
            [ ,1]= X1-X10 ,
            [ ,2]= X11-X20;
 MATRIX U
            [1,1]= X21-X30,
            [6,1]= X31-X35;
 PARMS A1-A2;
 X6  = A1 * X1;
 X7  = A1 * X2;
 X8  = A1 * X3;
 X9  = A1 * X4;
 X10 = A1 * X5;
 X16 = A2 * X11;
 X17 = A2 * X12;
 X18 = A2 * X13;
 X19 = A2 * X14;
 X20 = A2 * X15;
 RUN;


PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=LM EDF=99 ALL ;
TITLE2 'Use formula (2.13) of Mc DONALD (1980)';
COSAN B(14,GEN) * AU(12,GEN) * J(12,IDE);
 MATRIX B
            [ ,1]= B1-B5 ,
            [ ,2]= B6-B10,
            [ ,3]= 5 * 0. B1-B5 ,
            [ ,4]= 5 * 0. B6-B10,
            [1,5]= 10 * 1. ;
 MATRIX AU
            [ ,1] = 1. 0. A1 0. ,
            [ ,2] = 0. 1. 0. A2 ,
            [5,3] = U1-U10  ,
            [5,8] = U11-U15 ,
            [10,3]= U11-U15 ;
 RUN;


PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=LM EDF=99 ALL ;
TITLE2 'Use formula (2.12) of Mc DONALD (1980)';
TITLE3 'BOUNDS Statement';
COSAN F(2,GEN) * I(2,IDE) + U(10,SYM);
 MATRIX F
            [ ,1]= X1-X10 ,
            [ ,2]= X11-X20;
 MATRIX U
            [1,1]= X21-X30,
            [6,1]= X31-X35;
 BOUNDS
            X21-X30 >= 0.;
 PARMS A1-A2;
 X6  = A1 * X1;
 X7  = A1 * X2;
 X8  = A1 * X3;
 X9  = A1 * X4;
 X10 = A1 * X5;
 X16 = A2 * X11;
 X17 = A2 * X12;
 X18 = A2 * X13;
 X19 = A2 * X14;
 X20 = A2 * X15;
 RUN;


PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=NR EDF=99 ALL ;
TITLE2 'Use formula (2.12) of Mc DONALD (1980)';
TITLE3 'BOUNDS Statement';
COSAN F(2,GEN) * I(2,IDE) + U(10,SYM);
 MATRIX F
            [ ,1]= X1-X10 ,
            [ ,2]= X11-X20;
 MATRIX U
            [1,1]= X21-X30,
            [6,1]= X31-X35;
 BOUNDS
            X21-X30 >= 0.;
 PARMS A1-A2;
 X6  = A1 * X1;
 X7  = A1 * X2;
 X8  = A1 * X3;
 X9  = A1 * X4;
 X10 = A1 * X5;
 X16 = A2 * X11;
 X17 = A2 * X12;
 X18 = A2 * X13;
 X19 = A2 * X14;
 X20 = A2 * X15;
 RUN;


PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=LM EDF=99;
TITLE2 'More constrained model: Heywood Case';
COSAN F(2,GEN) * I(2,IDE) + U(10,SYM) * J(10,IDE);
 MATRIX F
            [ ,1]= 1. X2-X10 ,
            [ ,2]= X11-X20;
 MATRIX U
            [1,1]= X21-X30,
            [6,1]= X31-X35;
 PARMS A1-A2;
 X6  = A1;
 X7  = A1 * X2;
 X8  = A1 * X3;
 X9  = A1 * X4;
 X10 = A1 * X5;
 X16 = A2 * X11;
 X17 = A2 * X12;
 X18 = A2 * X13;
 X19 = A2 * X14;
 X20 = A2 * X15;
 RUN;

PROC CALIS DATA=MEYBEN METHOD=LSMAX TECH=LM EDF=99 ALL ;
TITLE2 'More constrained model: Boundary Constraints';
TITLE3 'BOUNDS Statement';
COSAN F(2,GEN) * I(2,IDE) + U(10,SYM) * J(10,IDE);
 MATRIX F
            [ ,1]= 1. X2-X10 ,
            [ ,2]= X11-X20;
 MATRIX U
            [1,1]= X21-X30,
            [6,1]= X31-X35;
 BOUNDS
            0. <= X21-X30;
 PARMS A1-A2;
 X6  = A1;
 X7  = A1 * X2;
 X8  = A1 * X3;
 X9  = A1 * X4;
 X10 = A1 * X5;
 X16 = A2 * X11;
 X17 = A2 * X12;
 X18 = A2 * X13;
 X19 = A2 * X14;
 X20 = A2 * X15;
 RUN;