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GENETIC ANALYSIS OF BINARY and CATEGORICAL TRAITS PART ONE

GENETIC ANALYSIS OF BINARY and CATEGORICAL TRAITS PART ONE. TABLE 1. Twin Pair Concordances for Major Depression (Virginia Twin Study data, adapted from Neale and Cardon, 1992). 166+95+83 1180. 126+82+94 880. 2 x concordant affected pairs + discordant pairs 2 x Total Pairs.

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GENETIC ANALYSIS OF BINARY and CATEGORICAL TRAITS PART ONE

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  1. GENETIC ANALYSIS OF BINARY and CATEGORICAL TRAITS PART ONE

  2. TABLE 1. Twin Pair Concordances for Major Depression (Virginia Twin Study data, adapted from Neale and Cardon, 1992)

  3. 166+95+83 1180 126+82+94 880 2 x concordant affected pairs + discordant pairs 2 x Total Pairs Prevalence = e.g. for MZ pairs = e.g. for DZ pairs = = 29.2% = 34.3% Prevalance = proportion of affected (alcoholic) twins in the general population.

  4. 166 166 + 95 + 83 126 126 + 82 + 94 Probandwise concordance rate Prevalence 2 x concordant affected pairs 2 x concordant affected pairs + discordant pairs Probandwise concordance rate = e.g. for MZ pairs = e.g. for DZ pairs = = 48.3% = 41.7% Probandwise concordance rate = probability that cotwin of a depressed twin will also have a history of depression. Recurrence Risk-ratio =

  5. Why do we have (2 x number of concordant affected pairs) in the numerator and denominator of the expression for the probandwise concordance rate? Consider a simple example where there are 4 affected individuals, who came from 3 twin pairs, ie, 1 — 0 1 — 0 1 — 1 There are 4 potential probands, so if we randomly select an affected individual, the probability that the cotwin of that individual is also affected will be 50%

  6. TABLE 1a. Twin Pair Concordances for Alcohol Dependence (DSM-IIIR) (Virginia Twin Study data, from Kendler et al., 1992)

  7. Number of concordant alcoholic pairs = N pairs x prevalence x probandwise concordance MZ: 15 pairs DZ: 11 pairs Number of discordant pairs = 2 x N pairs x prevalence x (1 - probandwise concordance) MZ: 65 pairs DZ: 68 pairs Number of concordant unaffected pairs MZ: 510 pairs DZ: 361 pairs

  8. Some investigators also report a “PAIRWISE” CONCORDANCE RATE - the proportion of pairs with at least one twin affected who are concordant. The “PAIRWISE” concordance rate is redundant -- CR 2-CR PAIRWISE CONCORDANCE RATE = where CR is the probandwise concordance rate

  9. a) Normal Liability Threshold Model b) Multiple-threshold Model t 1 t 1 t 2 0 0 UNAFFECTED AFFECTED UNAFFECTED MILD SEVERE CASES CASES Alcoholism Risk Alcoholism Risk

  10. CUMULATIVE NORMAL FREQUENCY DISTRIBUTION

  11. Table 3. Population distribution of pairs of relatives with both alcoholic, neither alcoholic, or only one relative alcoholic, as a function of (i) lifetime prevalence of alcoholism, and (ii) liability correlation for alcoholism in relatives ai.e. Probandwise concordance rate

  12. EXAMPLE DATA-FILE FOR MX RAW ORDINAL DATA: MZF DEPRESSION DATA (depmzf.dat) 0 0 329 0 1 83 1 0 95 1 1 83

  13. EXAMPLE DATA-FILE (II): DERIVED FROM PUBLISHED SOURCES MZF ALCOHOL DEPENDENCE DATA (alcmzf.dat) 0 0 310 0 1 32.5 1 0 32.5 1 1 15

  14. ! tetrachoric.mx ! estimating tetrachoric correlations #define nvar 1 #define maxthresf 1 ! number of thresholds Analysis of depression data: estimating tetrachorics & confidence intervals data NI=3 NG=4 LAbels twina twinb countmz Ordinal fi=depmzf.rec ! Count is a definition variable that we use to tell MX the frequency count! for each element of the 2x2 table!Definition_variables countmz /Begin matrices;W LO nvar nvar fr ! w*w' is the tetrachoric correlationY LO nvar nvar fr ! y*y' is 1-tetrachoric correlationM FU maxthresf nvar fiS DI nvar nvar ! Matrix that will store weight variableend matrices;SP M3 MATRIX M 1.5487! This tells MX to store the definition variable count in SSP S-1 mat w 0.7 mat y 0.7

  15. Begin algebra;R=W*W';E=Y*Y';V=R+E;end algebra;FREQ S; ! tells MX that S contains the weight (frequency) variableTH M|M; ! tells MX that row and column thresholds contained in M|MCO 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-12OPT RSEND

  16. Analysis of depression data: DZmdata NI=3LAbels twina twinb countdzOR fi=depdzf.recDefinition_variables countdz /Begin matrices; W LO nvar nvar fr ! w*w' is the tetrachoric correlation for DZ groupY LO nvar nvar fr ! y*y' is 1-tetrachoric correlation for DZ groupN FU maxthresf nvar frS DI nvar nvar ! Matrix that will store weight variableend matrices;SP N6 MATRIX N 1.4487SP S-1 mat w 0.6 mat y 0.8Begin 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 RSEND

  17. Constraint function - constrain variances to unity for MZ groupCO NI=1Begin matrices = group 1;U unit 1 nvarend matrices;CO \d2v(V) = u;endConstraint function - constrain variances to unity for DZ groupCO NI=1Begin matrices = group 2;U unit 1 nvarend matrices;CO \d2v(V) = u;end

  18. 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

  19. 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

  20. GROUP NUMBER: 2 Analysis of ordinal alcohol tolerance and dependence 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

  21. 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

  22. 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 Threshold 2 1.0000 1.5487 (OBSERVED MATRIX is nonexistent for raw data) 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

  23. GROUP NUMBER: 2 Analysis of ordinal alcohol tolerance and dependence 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

  24. 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 Threshold 2 1.0000 1.4487 (OBSERVED MATRIX is nonexistent for raw data) 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

  25. 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 0.2% of my workspace Task Time elapsed (DD:HH:MM:SS) Reading script & data 0: 0: 0: 0.11 Execution 0: 0: 0: 2.85 TOTAL 0: 0: 0: 2.96 Total number of warnings issued: 0 ______________________________________________________________________________ ______________________________________________________________________________

  26. ** Mx startup successful ** **MX-Sunos version 1.49** ! 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 ALCOHOLISM DATA: ESTIMATING TETRACHORICS & CONFIDENCE INTERVALS DATA NI=3 NO=2 NG=4 LABELS TWINA TWINB COUNTMZ ORDINAL FI=ALCMZF.REC Ordinal data read initiated NOTE: Rectangular file contained 4 records with data ! 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

  27. 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 4.3853E+04 2.5000E-01 2.5000E-01 Minimum 1.5000E+01 0.0000E+00 0.0000E+00 Maximum 5.1000E+02 1.0000E+00 1.0000E+00 Summary of VL file data for group 2 COUNTDZ TWINA TWINB Code -1.0000E+00 1.0000E+00 2.0000E+00 Number 4.0000E+00 4.0000E+00 4.0000E+00 Mean 1.1000E+02 5.0000E-01 5.0000E-01 Variance 2.1088E+04 2.5000E-01 2.5000E-01 Minimum 1.1000E+01 0.0000E+00 0.0000E+00 Maximum 3.6100E+02 1.0000E+00 1.0000E+00

  28. MX PARAMETER ESTIMATES GROUP NUMBER: 1Analysis of alcoholism data: estimating tetrachorics & confidence intervals MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.4688 MATRIX M This is a FULL matrix of order 1 by 1 1 1 1.4017 MATRIX R This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.5312 MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 15.0000

  29. 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 0.7288 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.6847 Matrix of EXPECTED thresholds TWINA TWINB Threshold 1 1.4017 1.4017 Threshold 2 1.0000 1.5487 (OBSERVED MATRIX is nonexistent for raw data) EXPECTED COVARIANCE MATRIX TWINA TWINB TWINA 1.0000 TWINB 0.5312 1.0000 Function value of this group: 635.6429 Where the fit function is -2 * Log-likelihood of raw ordinal

  30. GROUP NUMBER: 2 Analysis of ordinal alcohol tolerance and dependence data: DZm MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.6482 MATRIX N This is a FULL matrix of order 1 by 1 1 1 1.2687 MATRIX R This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.3518 MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 11.0000 MATRIX V This is a computed FULL matrix of order 1 by 1 [=R+E] 1 1 1.0000

  31. MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.5931 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.8051 Matrix of EXPECTED thresholds TWINA TWINB Threshold 1 1.2687 1.2687 Threshold 2 1.0000 1.4487 (OBSERVED MATRIX is nonexistent for raw data) EXPECTED COVARIANCE MATRIX TWINA TWINB TWINA 1.0000 TWINB 0.3518 1.0000 Function value of this group: 572.2531 Where the fit function is -2 * Log-likelihood of raw ordinal

  32. MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.8051 Your model has 6 estimated parameters and 18 Observed statistics Observed statistics include 2 constraints. -2 times log-likelihood of data >>> 1207.896 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 0.5312 0.3367 0.6903 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 0.3518 0.1190 0.5558 0 0 0 0 This problem used 0.2% of my workspace Task Time elapsed (DD:HH:MM:SS) Reading script & data 0: 0: 0: 0.11 Execution 0: 0: 0: 3.41 TOTAL 0: 0: 0: 3.52 Total number of warnings issued: 0

  33. ESTIMATED TETRACHORIC CORRELATIONS (estimating separate thresholds for each zygosity group)

  34. TEST FOR ZYGOSITY DIFFERENCE IN PREVALENCE (takes into account non-independence!) 1 1

  35. This approach extends naturally to fitting univariate genetic models.

  36. ! univariate.mx! fitting a univariate genetic model to 2x2 data#define nvar 1#define maxthresf 1 ! number of thresholdsAnalysis of depression data: fitting ACE model data NI=3 NG=3LAbels twina twinb countmzOrdinal fi=depmzf.rec! Count is a definition variable that we use to tell MX the frequency count! for each element of the 2x2 table!Definition_variables countmz /Begin matrices;W LO nvar nvar fr ! additive genetic path (A=w*w')X LO nvar nvar fr ! shared environmental path (C=x*x') Y LO nvar nvar fr ! non-shared environmental path (E=y*y') Z LO nvar nvar fi ! non-additive genetic path (D=z*z')M FU maxthresf nvar fi ! matrix of thresholdsS DI nvar nvar ! Matrix that will store weight variableend matrices;SP M4 MATRIX M 1.5487! This tells MX to store the definition variable count in SSP S-1 mat w 0.5mat x 0.5 mat y 0.7

  37. Begin algebra;A=W*W';C=X*X';E=Y*Y';D=Z*Z';V=A+C+D+E;end algebra;FREQ S; ! tells MX that S contains the weight (frequency) variableTH M|M; ! tells MX that row and column thresholds contained in M|MCO V|A+D+C_ A'+D'+C'|V; ! formula for correlation matrix!bo 0.001 1.0 y(1,1) bo 0.0001 0.999 w(1,1) x(1,1)bo -5.0 5.0 m(1,1)interval a(1,1) c(1,1) e(1,1) ! compute 95% confidence interval for correlation OPT func=1.E-12OPT RSEND

  38. Analysis of depression data: DZmdata NI=3 NO=4LAbels twina twinb countdzOR fi=depdzf.recDefinition_variables countdz /Begin matrices = group 1; S DI nvar nvar ! Matrix that will store weight variableg DI 1 1 ! constant (=0.5) for coefficient of additive genetic componenth DI 1 1 ! constant (=0.25) for coefficient of dominance genetic component n FU maxthresf nvar fi ! matrix of thresholdsend matrices;SP N5 MATRIX N 1.4487MAT g 0.5MAT h 0.25SP S-1 FREQ S;TH N|N;CO V|g@A+h@D+C_ g@A'+h@D'+C'|V; ! formula for correlation matrix!bo -5.0 5.0 n(1,1)OPT RSEND

  39. Constraint function - constrain variance to unity CO NI=1Begin matrices = group 1;U unit 1 nvarend matrices;CO \d2v(V) = u;end

  40. ** Mx startup successful ** **MX-Sunos version 1.49** ! univariate.mx ! fitting a univariate genetic model to 2x2 data The following MX script lines were read for group 1 #DEFINE NVAR 1 #DEFINE MAXTHRESF 1 ! NUMBER OF THRESHOLDS ANALYSIS OF DEPRESSION DATA: FITTING ACE MODEL DATA NI=3 NO=2 NG=3 LABELS TWINA TWINB COUNTMZ ORDINAL FI=DEPMZF.REC Ordinal data read initiated NOTE: Rectangular file contained 4 records with data ! 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 ! ADDITIVE GENETIC PATH (A=W*W') X LO NVAR NVAR FR ! SHARED ENVIRONMENTAL PATH (C=X*X') Y LO NVAR NVAR FR ! NON-SHARED ENVIRONMENTAL PATH (E=Y*Y') Z LO NVAR NVAR FI ! NON-ADDITIVE GENETIC PATH (D=Z*Z') M FU MAXTHRESF NVAR FI ! MATRIX OF THRESHOLDS S DI NVAR NVAR ! MATRIX THAT WILL STORE WEIGHT VARIABLE END MATRICES;

  41. MX PARAMETER ESTIMATES GROUP NUMBER: 1Analysis of depression data: fitting ACE model MATRIX A This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.4250 MATRIX C This is a computed FULL matrix of order 1 by 1 [=X*X'] 1 1 1.0000E-08 MATRIX D This is a computed FULL matrix of order 1 by 1 [=Z*Z'] 1 1 0.0000 MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.5750 MATRIX M This is a FULL matrix of order 1 by 1 1 1 0.5493

  42. 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 [=A+C+D+E] 1 1 1.0000 MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.6519 MATRIX X This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 1.0000E-04 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.7583 MATRIX Z This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.0000

  43. Matrix of EXPECTED thresholds TWINA TWINB Threshold 1 0.5493 0.5493 Threshold 2 1.0000 1.5487 (OBSERVED MATRIX is nonexistent for raw data) EXPECTED COVARIANCE MATRIX TWINA TWINB TWINA 1.0000 TWINB 0.4250 1.0000 Function value of this group: 1383.2782 Where the fit function is -2 * Log-likelihood of raw ordinal

  44. Your model has 5 estimated parameters and 17 Observed statistics Observed statistics include 1 constraints. -2 times log-likelihood of data >>> 2509.788 Degrees of freedom >>>>>>>>>>>>>>>> 12 3 Confidence intervals requested in group 1 Matrix Element Int. Estimate Lower Upper Lfail Ufail A 1 1 1 95.0 0.4250 0.1045 0.5325 0 0 0 0 C 1 1 1 95.0 0.0000 0.0000 0.2609 0 0 0 1 E 1 1 1 95.0 0.5750 0.4675 0.6940 0 0 0 0 This problem used 0.1% of my workspace Task Time elapsed (DD:HH:MM:SS) Reading script & data 0: 0: 0: 0.10 Execution 0: 0: 0:15.76 TOTAL 0: 0: 0:15.86 Total number of warnings issued: 1 ______________________________________________________________________________ ______________________________________________________________________________

  45. ** Mx startup successful ** **MX-Sunos version 1.49** ! univar2.mx ! fitting a univariate genetic model to 2x2 data The following MX script lines were read for group 1 #DEFINE NVAR 1 #DEFINE MAXTHRESF 1 ! NUMBER OF THRESHOLDS ANALYSIS OF ALCOHOL DEPENDENCE DATA: FITTING ACE MODEL DATA NI=3 NO=2 NG=3 LABELS TWINA TWINB COUNTMZ ORDINAL FI=ALCMZF.REC Ordinal data read initiated NOTE: Rectangular file contained 4 records with data ! 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

  46. MX PARAMETER ESTIMATES GROUP NUMBER: 1Analysis of alcohol dependence data: fitting ACE model MATRIX A This is a computed FULL matrix of order 1 by 1 [=W*W'] 1 1 0.3588 MATRIX C This is a computed FULL matrix of order 1 by 1 [=X*X'] 1 1 0.1724 MATRIX D This is a computed FULL matrix of order 1 by 1 [=Z*Z'] 1 1 0.0000 MATRIX E This is a computed FULL matrix of order 1 by 1 [=Y*Y'] 1 1 0.4688

  47. MATRIX M This is a FULL matrix of order 1 by 1 1 1 1.4017 MATRIX S This is a DIAGONAL matrix of order 1 by 1 1 1 15.0000 MATRIX V This is a computed FULL matrix of order 1 by 1 [=A+C+D+E] 1 1 1.0000 MATRIX W This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.5990 MATRIX X This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.4152 MATRIX Y This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.6847 MATRIX Z This is a LOWER TRIANGULAR matrix of order 1 by 1 1 1 0.0000

  48. Matrix of EXPECTED thresholds TWINA TWINB Threshold 1 1.4017 1.4017 Threshold 2 1.0000 1.5487 (OBSERVED MATRIX is nonexistent for raw data) EXPECTED COVARIANCE MATRIX TWINA TWINB TWINA 1.0000 TWINB 0.5312 1.0000 Function value of this group: 635.6429 Where the fit function is -2 * Log-likelihood of raw ordinal

  49. Your model has 5 estimated parameters and 17 Observed statistics Observed statistics include 1 constraints. -2 times log-likelihood of data >>> 1207.896 Degrees of freedom >>>>>>>>>>>>>>>> 12 3 Confidence intervals requested in group 1 Matrix Element Int. Estimate Lower Upper Lfail Ufail A 1 1 1 95.0 0.3588 0.0000 0.6902 0 0 0 0 C 1 1 1 95.0 0.1724 0.0000 0.5542 0 0 0 0 E 1 1 1 95.0 0.4688 0.3097 0.6628 0 1 0 0 This problem used 0.1% of my workspace Task Time elapsed (DD:HH:MM:SS) Reading script & data 0: 0: 0: 0.10 Execution 0: 0: 0: 7.55 TOTAL 0: 0: 0: 7.65 Total number of warnings issued: 1 ______________________________________________________________________________ ______________________________________________________________________________

  50. VIRGINIA TWIN STUDY: Female Like-Sex Pairs Summary Model-Fitting Results

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