1. LISREL matrices, LISREL programming
ICPSR General Structural Equations
Week 2 Class #4

2. Class Exercise
(from previous class notes:)

3. Class exercise BETA 2 x 2 0 BE(1,2) BE(2,1) 0 PHI 2 X 2 PHI(1,1)
GAMMA 2 X 2
GA(1,1) 0
0 GA(2,2)
PSI 2 x 2
PS(1,1)
PS(2,1) PS(2,2)

4. LAMBDA-X
1 0
LX(2,1) 0
LX(3,1) LX(3,2)
0 1
0 LX(5,2)
LAMBDA-Y
1 0
LY(2,1) 0
LY(3,1) 0
0 1
0 LY(5,2)
0 LY(6,2)

5. MO NY=6 NX=5 NK=2 NE=2 LX=FU,FI LY=FU,FI C
PH=SY BE=FU,FI GA=FU,FI TD=SY TE=SY PS=SY,FR
VA 1.0 LX 1 1 LX 4 2 LY 1 1 LY 4 2
FR LX 2 1 LX 3 1 LX 3 2 LX 5 2 LY 2 1 LY 3 1 LY 5 2 LY 6 2
FR GA 1 1 GA 2 2
FR BE 2 1 BE 1 2

6. Exercise 2:A (PANEL) MODEL WITH CORRELATED ERRORS

7. Exercise 2:A (PANEL) MODEL WITH CORRELATED ERRORS
Beta 2 x 2
0 0
BE(2,1) 0
PSI 2 x 2
PS(1,1)
0 PS(2,2)
Not shown: zeta1
Theta-eps
TE(1,1)
0 TE(2,2)
0 0 TE(3,3)
TE(4,1) 0 0 TE(4,4)
0 TE(5,2) 0 0 TE(5,5)
TE(6,6)

8. Exercise 2:A (PANEL) MODEL WITH CORRELATED ERRORS
MO NY=6 NE=2 LY=FU,FI PS=SY TE=SY BE=FU,FI
VA 1.0 LY 1 1 LY 4 2
FR LY 2 1 LY 3 1 LY 5 2 LY 6 2
FR BE 2 1
FR TE 4 1 TE 5 2
Notes: PS=SY specification  free diagonals (PS(1,1) and PS(2,2), fixed off-diagonals [ps(2,1)=0 in this model].

9. Exercise 3

10. Exercise 3 BETA 2 X 2 0 0 BE(2,1) 0 LAMBDA-Y 1 0 LY(2,1) 0 Gamma 2 x 1
0 0
BE(2,1) 0
LAMBDA-Y
1 0
LY(2,1) 0
LY(3,1) LY(3,2)
0 1
0 LY(5,2)
Gamma 2 x 1
GA(1,1)
LAMBDA-X 1 X 1 1

11. Exercise 3 MO NX=1 NY=5 NK=1 NE=2 LX=ID LY=FU,FI C
PS=SY PH=SY TD=ZE TE=SY BE=FU,FI GA=FU,FI
VA 1.0 LY 1 1 LY 4 2
FR LY 2 1 LY 3 1 LY 3 2 LY 5 2
FR GA 1 1 BE 2 1

12. Exercise 4
This is a non-standard model.

13. Exercise 4
This parameter cannot be estimated in LISREL; must re-express the model (to an equivalent that CAN be estimated)

14. RE-EXPRESSED MODEL LAMBDA – Y BETA 1 0 0 BE(1,2) LY(2,1) 0 0 0
1 0
LY(2,1) 0
LY(3,1) 0
LY(4,1) 0
0 1
BETA
0 BE(1,2)
0 0

15. RE-EXPRESSED MODEL Now X1,X2
MO NY=5 NX=2 NK=1 NE=2 LY=FU,FI LX=FU,FR C
GA=FU,FR PS=SY PH=SY TD=SY TE=SY
VA 1.0 LX 1 1 LY 1 1 LY 5 2
FR LX 2 1 LY 2 1 LY 3 1 LY 4 1
FI TE  SINGLE INDICATOR, CANNOT ESTIMATE ERROR

16. Re-expressed as: e3 variance=0 Same variance as e3 in previous model
Same as lambda parameter in previous model

17. The same sort of principle can be used for other purposes too:
Imposing an inequality constraint.
Example: We wish to impose a constraint such that VAR(e3) > 0 (don’t allow negative error variance).

18. Lambda 2, lambda 3: same parm’s
Variance of ksi-2 fixed to 1.0
X3 = lambda3 KSI1 + lambda4 KSI2
VAR(X3) = lambda32*VAR(Ksi-1) + lambda42 *VAR(KSI-2) Since…..VAR(ksi-2) = 1.0
[expression lambda42 replaces VAR(e3)
Regardless of estimate of lambda4, variance >0.

19. The LISREL PROGRAM: MO modelparameters statement FR free a parameter
FI fix a parameter
VA set a parameter to a value (if the parameter is free, this is the “start value” to override program default estimate; otherwise, it is the value to which a parameter is constrained

20. The LISREL PROGRAM:
If reading in a “system” .dsf file created by prelis:
Title
SY= input file if LISREL .dsf
DA - dataparameters
SE selection of variables
MO – modelparameters
… various FI and FR statements
OU – outputparameters (see handout)

21. The LISREL PROGRAM: ! Achievement Values Program #1
SY='z:\baer\Week2Examples\LISREL\Achieve1.dsf' SE
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT /
MO NY=6 NE=1 LY=FU,FR PS=SY TE=SY
FI LY 1 1
VA 1.0 LY 1 1
OU ME=ML SC MI
SE statement lists variables to be used (always specify Y variables first)
can change order on SE statement. Here, REDUCE is Y1, NEVHAPP is Y2, etc. LY 1 1 refers to REDUCE.
OU : ME=ML (maximum likelihood) SC (standardized solution) MI (provide modification indices)

22. LISREL Output:
Parameter Specifications
LAMBDA-Y
ETA 1
REDUCE
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
PSI 6
THETA-EPS
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT
Reference indicator is “fixed” All fixed parameters represented by 0.
Theta-eps is diagonal

23. LISREL Output LISREL Estimates (Maximum Likelihood) LAMBDA-Y ETA 1
REDUCE
NEVHAPP
(0.37)
5.72
NEW_GOAL
(0.46)
-6.00
IMPROVE
(0.70)
-6.01
ACHIEVE
(0.45)
-5.87
CONTENT
5.78

24. LISREL Output Covariance Matrix of ETA ETA 1 -------- 0.01 PSI (0.00)
3.08
THETA-EPS
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Squared Multiple Correlations for Y - Variables

25. LISREL Output Modification Indices and Expected Change
No Non-Zero Modification Indices for LAMBDA-Y
No Non-Zero Modification Indices for PSI
Modification Indices for THETA-EPS
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT
REDUCE
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
Expected Change for THETA-EPS
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
Completely Standardized Expected Change for THETA-EPS
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
Maximum Modification Index is for Element ( 2, 1) of THETA-EPS

26. Lisrel program input SE 2 3 6 9 8 7 /
If reading in a covariance matrix generated by PRELIS instead of a .dsf file:
DA NO=# cases NI=# of input var’s MA=CM
{MA = type of matrix to be analyzed; default = CM, or a covariance matrix}
CM FI=‘c:\file1.cov’
input file specification(cov) SE /
Selection: corresponds to order in which variables located on input covariance matrix (3rd variable on the matrix is now Y2).

27. Another LISREL example:
! Achievement Values Program #8: Adding One Extra Measurement Model Path
SY='z:\baer\Week2Examples\LISREL\Achieve1.dsf' SE
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT
GENDER AGE EDUC INCOME/
MO NX=4 NK=4 NY=6 NE=2 LX=ID PH=SY,FR TD=ZE LY=FU,FI C
PS=SY,FR TE=SY GA=FU,FR
FI LY 2 1
FI LY 3 2
VA 1.0 LY 2 1 LY 3 2
FR LY 1 1 LY 6 1 LY 4 2 LY 5 2
FR LY 1 2 PD
OU ME=ML SE TV SC MI

28. (from output listing) Parameter Specifications LAMBDA-Y ETA 1 ETA 2
REDUCE
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
GAMMA
GENDER AGE EDUC INCOME
ETA
ETA
PHI
GENDER
AGE
EDUC
INCOME
PSI
ETA
ETA
THETA-EPS
REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

29. (output) LISREL Estimates (Maximum Likelihood) LAMBDA-Y ETA 1 ETA 2
REDUCE
(0.07) (0.08)
NEVHAPP
NEW_GOAL
IMPROVE
(0.12)
16.00
ACHIEVE
(0.06)
15.95
CONTENT
19.84
GAMMA
GENDER AGE EDUC INCOME
ETA
(0.02) (0.00) (0.00) (0.00)
ETA
(0.01) (0.00) (0.00) (0.00)

30. Squared Multiple Correlations for Structural Equations
Covariance Matrix of ETA and KSI
ETA ETA GENDER AGE EDUC INCOME
ETA
ETA
GENDER
AGE
EDUC
INCOME
Squared Multiple Correlations for Structural Equations
ETA ETA 2

31. (LISREL output) Modification Indices and Expected Change
Modification Indices for LAMBDA-Y
ETA ETA 2
REDUCE
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT

32. Completely Standardized Solution
LAMBDA-Y
ETA ETA 2
REDUCE
NEVHAPP
NEW_GOAL
IMPROVE
ACHIEVE
CONTENT
GAMMA
GENDER AGE EDUC INCOME
ETA
ETA
(could have used LA (labels) statement to provide labels for these latent variables)

33. Reproduced covariances in matrix form
First examples are for SEM models that are “manifest variable only” – no latent variables.

34. Manifest variables only

35. Manifest variables only

36. Manifest variables only
Previous example had no paths connecting endogenous y-variables (no “Beta” matrix). A bit more complicated with these included:

37. Manifest variables only
With Beta matrix:

38. Manifest variables only

39. Manifest variables only

40. Manifest variables only

41. Manifest variables only

42. Latent variables included
Measurement model only

43. Latent variables included

44. δ

47. (last slide)