! tetrachoric.mx
! estimating tetrachoric correlations
The following MX script lines were read for group 1
#DEFINE NVAR 1
#DEFINE MAXTHRESF 1 ! NUMBER OF THRESHOLDS
ANALYSIS OF DEPRESSION DATA: ESTIMATING TETRACHORICS & CONFIDENCE INTERVALS
DATA NI=3 NO=2 NG=4
LABELS TWINA TWINB COUNTMZ
ORDINAL FI=DEPMZF.REC
Ordinal data read initiated
NOTE: Rectangular file contained 4 records with data
that contained a total of 12 observations
! Count is a definition variable that we use to tell MX the frequency count
! for each element of the 2x2 table
!
DEFINITION_VARIABLES COUNTMZ /
NOTE: Definition yields 4 data vectors for analysis
NOTE: Vectors contain a total of 8 observations
BEGIN MATRICES;
W LO NVAR NVAR FR ! W*W' IS THE TETRACHORIC CORRELATION
Y LO NVAR NVAR FR ! Y*Y' IS 1-TETRACHORIC CORRELATION
M FU MAXTHRESF NVAR FI
S DI NVAR NVAR ! MATRIX THAT WILL STORE WEIGHT VARIABLE
END MATRICES;
SP M
3
MATRIX M 1.5487
! This tells MX to store the definition variable count in S
SP S
-1
MAT W 0.7
MAT Y 0.7
BEGIN ALGEBRA;
R=W*W';
E=Y*Y';
V=R+E;
END ALGEBRA;
FREQ S; ! TELLS MX THAT S CONTAINS THE WEIGHT (FREQUENCY) VARIABLE
TH M|M; ! TELLS MX THAT ROW AND COLUMN THRESHOLDS CONTAINED IN M_M
CO V|R_R'|V; ! FORMULA FOR CORRELATION MATRIX!
BO 0.001 1.0 Y(1,1)
BO 0.0001 0.999 W(1,1)
BO -5.0 5.0 M(1,1)
INTERVAL R(1,1) ! COMPUTE 95% CONFIDENCE INTERVAL FOR CORRELATION
OPT FUNC=1.E-12
OPT RS
END
The following MX script lines were read for group 2
ANALYSIS OF ORDINAL DATA: DZM
DATA NI=3 NO=4
LABELS TWINA TWINB COUNTDZ
OR FI=DEPDZF.REC
Ordinal data read initiated
NOTE: Rectangular file contained 4 records with data
that contained a total of 12 observations
DEFINITION_VARIABLES COUNTDZ /
NOTE: Definition yields 4 data vectors for analysis
NOTE: Vectors contain a total of 8 observations
BEGIN MATRICES;
W LO NVAR NVAR FR ! W*W' IS THE TETRACHORIC CORRELATION FOR DZ GROUP
Y LO NVAR NVAR FR ! Y*Y' IS 1-TETRACHORIC CORRELATION FOR DZ GROUP
N FU MAXTHRESF NVAR FR
S DI NVAR NVAR ! MATRIX THAT WILL STORE WEIGHT VARIABLE
END MATRICES;
SP N
6
MATRIX N 1.4487
SP S
-1
MAT W 0.6
MAT Y 0.8
BEGIN ALGEBRA;
R=W*W';
E=Y*Y';
V=R+E;
END ALGEBRA;
FREQ S;
TH N|N;
CO V|R_R'|V;
BO 0.001 1.0 Y(1,1)
BO 0.0001 0.999 W(1,1)
BO -5.0 5.0 N(1,1)
INTERVAL R(1,1) ! COMPUTE 95% CONFIDENCE INTERVAL FOR CORRELATION
OPT RS
END
The following MX script lines were read for group 3
CONSTRAINT FUNCTION - CONSTRAIN VARIANCES TO UNITY FOR MZ GROUP
CO NI=1
BEGIN MATRICES = GROUP 1;
U UNIT 1 NVAR
END MATRICES;
CO \D2V(V) = U;
END
The following MX script lines were read for group 4
CONSTRAINT FUNCTION - CONSTRAIN VARIANCES TO UNITY FOR DZ GROUP
CO NI=1
BEGIN MATRICES = GROUP 2;
U UNIT 1 NVAR
END MATRICES;
CO \D2V(V) = U;
END
Summary of VL file data for group 1
COUNTMZ TWINA TWINB
Code -1.0000E+00 1.0000E+00 2.0000E+00
Number 4.0000E+00 4.0000E+00 4.0000E+00
Mean 1.4750E+02 5.0000E-01 5.0000E-01
Variance 1.1005E+04 2.5000E-01 2.5000E-01
Minimum 8.3000E+01 0.0000E+00 0.0000E+00
Maximum 3.2900E+02 1.0000E+00 1.0000E+00
Summary of VL file data for group 2
COUNTDZ TWINA TWINB
Code -1.0000 1.0000 2.0000
Number 4.0000 4.0000 4.0000
Mean 110.0000 0.5000 0.5000
Variance 2882.5000 0.2500 0.2500
Minimum 63.0000 0.0000 0.0000
Maximum 201.0000 1.0000 1.0000
PARAMETER SPECIFICATIONS
GROUP NUMBER: 1
Analysis of depression data: estimating tetrachorics & confidence intervals
MATRIX E
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX M
This is a FULL matrix of order 1 by 1
1
1 3
MATRIX R
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 -1
MATRIX V
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 1
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 2
GROUP NUMBER: 2
Analysis of ordinal data: DZm
MATRIX E
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX N
This is a FULL matrix of order 1 by 1
1
1 6
MATRIX R
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 -1
MATRIX V
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 4
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 5
GROUP NUMBER: 3
Constraint function - constrain variances to unity for MZ group
MATRIX E
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX M
This is a FULL matrix of order 1 by 1
1
1 3
MATRIX R
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 -1
MATRIX U
This is a UNIT matrix of order 1 by 1
MATRIX V
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 1
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 2
GROUP NUMBER: 4
Constraint function - constrain variances to unity for DZ group
MATRIX E
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX N
This is a FULL matrix of order 1 by 1
1
1 6
MATRIX R
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 -1
MATRIX U
This is a UNIT matrix of order 1 by 1
MATRIX V
This is a computed FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 4
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 5
Mx starting optimization; number of parameters = 6
MX PARAMETER ESTIMATES
GROUP NUMBER: 1
Analysis of depression data: estimating tetrachorics & confidence intervals
MATRIX E
This is a computed FULL matrix of order 1 by 1
[=Y*Y']
1
1 0.5660
MATRIX M
This is a FULL matrix of order 1 by 1
1
1 0.5489
MATRIX R
This is a computed FULL matrix of order 1 by 1
[=W*W']
1
1 0.4340
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 83.0000
MATRIX V
This is a computed FULL matrix of order 1 by 1
[=R+E]
1
1 1.0000
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.6588
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.7523
Matrix of EXPECTED thresholds
TWINA TWINB
Threshold 1 0.5489 0.5489
EXPECTED COVARIANCE MATRIX
TWINA TWINB
TWINA 1.0000
TWINB 0.4340 1.0000
Function value of this group: 1383.2565
Where the fit function is -2 * Log-likelihood of raw ordinal
GROUP NUMBER: 2
Analysis of ordinal data: DZm
MATRIX E
This is a computed FULL matrix of order 1 by 1
[=Y*Y']
1
1 0.8157
MATRIX N
This is a FULL matrix of order 1 by 1
1
1 0.4038
MATRIX R
This is a computed FULL matrix of order 1 by 1
[=W*W']
1
1 0.1843
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 63.0000
MATRIX V
This is a computed FULL matrix of order 1 by 1
[=R+E]
1
1 1.0000
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.4294
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.9031
Matrix of EXPECTED thresholds
TWINA TWINB
Threshold 1 0.4038 0.4038
EXPECTED COVARIANCE MATRIX
TWINA TWINB
TWINA 1.0000
TWINB 0.1843 1.0000
Function value of this group: 1126.3757
Where the fit function is -2 * Log-likelihood of raw ordinal
GROUP NUMBER: 3
Constraint function - constrain variances to unity for MZ group
MATRIX E
This is a computed FULL matrix of order 1 by 1
[=Y*Y']
1
1 0.5660
MATRIX M
This is a FULL matrix of order 1 by 1
1
1 0.5489
MATRIX R
This is a computed FULL matrix of order 1 by 1
[=W*W']
1
1 0.4340
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 83.0000
MATRIX U
This is a UNIT matrix of order 1 by 1
MATRIX V
This is a computed FULL matrix of order 1 by 1
[=R+E]
1
1 1.0000
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.6588
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.7523
GROUP NUMBER: 4
Constraint function - constrain variances to unity for DZ group
MATRIX E
This is a computed FULL matrix of order 1 by 1
[=Y*Y']
1
1 0.8157
MATRIX N
This is a FULL matrix of order 1 by 1
1
1 0.4038
MATRIX R
This is a computed FULL matrix of order 1 by 1
[=W*W']
1
1 0.1843
MATRIX S
This is a DIAGONAL matrix of order 1 by 1
1
1 63.0000
MATRIX U
This is a UNIT matrix of order 1 by 1
MATRIX V
This is a computed FULL matrix of order 1 by 1
[=R+E]
1
1 1.0000
MATRIX W
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.4294
MATRIX Y
This is a LOWER TRIANGULAR matrix of order 1 by 1
1
1 0.9031
Your model has 6 estimated parameters and 18 Observed statistics
Observed statistics include 2 constraints.
-2 times log-likelihood of data >>> 2509.632
Degrees of freedom >>>>>>>>>>>>>>>> 12
1 Confidence intervals requested in group 1
Matrix Element Int. Estimate Lower Upper Lfail Ufail
R 1 1 1 95.0 0.4340 0.3086 0.5477 0 0 0 0
1 Confidence intervals requested in group 2
Matrix Element Int. Estimate Lower Upper Lfail Ufail
R 2 1 1 95.0 0.1843 0.0306 0.3316 0 0 0 0
This problem used 2.0% of my workspace
Task Time elapsed (DD:HH:MM:SS)
Reading script & data 0: 0: 0: 0.00
Execution 0: 0: 0: 2.03
TOTAL 0: 0: 0: 2.03
Total number of warnings issued: 0
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