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LISREL matrices, LISREL programming. ICPSR General Structural Equations Week 2 Class #4. Class Exercise. (from previous class notes:). Class exercise. BETA 2 x 2 0 BE(1,2) BE(2,1) 0 PHI 2 X 2 PHI(1,1) 0 PHI(2,2) GAMMA 2 X 2 GA(1,1) 0 0 GA(2,2). PSI 2 x 2 PS(1,1)

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Lisrel matrices lisrel programming

LISREL matrices, LISREL programming

ICPSR General Structural Equations

Week 2 Class #4


Class Exercise

(from previous class notes:)


Class exercise
Class exercise

BETA 2 x 2

0 BE(1,2)

BE(2,1) 0

PHI 2 X 2

PHI(1,1)

0 PHI(2,2)

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)


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)


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


Exercise 2 a panel model with correlated errors
Exercise 2:A (PANEL) MODEL WITH CORRELATED ERRORS


Exercise 2 a panel model with correlated errors1
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)

0 0 0 0 0 TE(6,6)


Exercise 2 a panel model with correlated errors2
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].



Exercise 31
Exercise 3

BETA 2 X 2

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)

0

LAMBDA-X 1 X 1

1


Exercise 32
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


Exercise 4
Exercise 4

This is a non-standard model.


Exercise 41
Exercise 4

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


Re expressed model
RE-EXPRESSED MODEL

LAMBDA – Y

1 0

LY(2,1) 0

LY(3,1) 0

LY(4,1) 0

0 1

BETA

0 BE(1,2)

0 0


Re expressed model1
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 5 5  SINGLE INDICATOR, CANNOT ESTIMATE ERROR


Re-expressed as:

e3 variance=0

Same variance as e3 in previous model

Same as lambda parameter in previous model


The same sort of principle can be used for other purposes too
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).


Lambda 2, lambda 3: same parm’s too:

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.


The lisrel program
The LISREL PROGRAM: too:

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


The lisrel program1
The LISREL PROGRAM: too:

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)


The lisrel program2
The LISREL PROGRAM too::

! 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)


Lisrel output
LISREL Output: too:

Parameter Specifications

LAMBDA-Y

ETA 1

--------

REDUCE 0

NEVHAPP 1

NEW_GOAL 2

IMPROVE 3

ACHIEVE 4

CONTENT 5

PSI

ETA 1

--------

6

THETA-EPS

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

7 8 9 10 11 12

Reference indicator is “fixed” All fixed parameters represented by 0.

Theta-eps is diagonal


Lisrel output1
LISREL Output too:

LISREL Estimates (Maximum Likelihood)

LAMBDA-Y

ETA 1

--------

REDUCE 1.00

NEVHAPP 2.14

(0.37)

5.72

NEW_GOAL -2.76

(0.46)

-6.00

IMPROVE -4.23

(0.70)

-6.01

ACHIEVE -2.64

(0.45)

-5.87

CONTENT 2.66

(0.46)

5.78


Lisrel output2
LISREL Output too:

Covariance Matrix of ETA

ETA 1

--------

0.01

PSI

ETA 1

--------

0.01

(0.00)

3.08

THETA-EPS

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

0.53 0.38 0.19 0.21 0.36 0.50

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)

38.84 36.44 28.79 18.92 34.53 35.92

Squared Multiple Correlations for Y - Variables

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

0.02 0.11 0.29 0.46 0.17 0.13


Lisrel output3
LISREL Output too:

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 323.45 - -

NEW_GOAL 24.46 4.29 - -

IMPROVE 92.13 52.90 87.29 - -

ACHIEVE 19.12 48.71 0.97 33.31 - -

CONTENT 170.74 243.43 58.94 21.28 1.82 - -

Expected Change for THETA-EPS

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

REDUCE - -

NEVHAPP 0.15 - -

NEW_GOAL 0.03 0.01 - -

IMPROVE 0.08 0.06 0.10 - -

ACHIEVE 0.04 0.05 0.01 0.06 - -

CONTENT 0.13 0.14 0.06 0.05 0.01 - -

Completely Standardized Expected Change for THETA-EPS

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

REDUCE - -

NEVHAPP 0.32 - -

NEW_GOAL 0.09 0.04 - -

IMPROVE 0.18 0.15 0.29 - -

ACHIEVE 0.08 0.12 0.02 0.14 - -

CONTENT 0.23 0.27 0.14 0.10 0.02 - -

Maximum Modification Index is 323.45 for Element ( 2, 1) of THETA-EPS


Lisrel program input
Lisrel program input too:

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

2 3 6 9 8 7 /

Selection: corresponds to order in which variables located on input covariance matrix (3rd variable on the matrix is now Y2).


Another lisrel example
Another LISREL example: too:

! 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


From output listing
(from output listing) too:

Parameter Specifications

LAMBDA-Y

ETA 1 ETA 2

-------- --------

REDUCE 1 2

NEVHAPP 0 0

NEW_GOAL 0 0

IMPROVE 0 3

ACHIEVE 0 4

CONTENT 5 0

GAMMA

GENDER AGE EDUC INCOME

-------- -------- -------- --------

ETA 1 6 7 8 9

ETA 2 10 11 12 13

PHI

GENDER AGE EDUC INCOME

-------- -------- -------- --------

GENDER 14

AGE 15 16

EDUC 17 18 19

INCOME 20 21 22 23

PSI

ETA 1 ETA 2

-------- --------

ETA 1 24

ETA 2 25 26

THETA-EPS

REDUCE NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT

-------- -------- -------- -------- -------- --------

27 28 29 30 31 32


Output
(output) too:

LISREL Estimates (Maximum Likelihood)

LAMBDA-Y

ETA 1 ETA 2

-------- --------

REDUCE 1.13 0.65

(0.07) (0.08)

17.32 8.53

NEVHAPP 1.00 - -

NEW_GOAL - - 1.00

IMPROVE - - 1.85

(0.12)

16.00

ACHIEVE - - 0.99

(0.06)

15.95

CONTENT 1.16 - -

(0.06)

19.84

GAMMA

GENDER AGE EDUC INCOME

-------- -------- -------- --------

ETA 1 0.02 -0.01 0.03 0.01

(0.02) (0.00) (0.00) (0.00)

1.14 -10.40 10.04 5.67

ETA 2 0.07 0.00 0.01 0.00

(0.01) (0.00) (0.00) (0.00)

  • 4.90 4.81 4.19 -0.79


Covariance Matrix of ETA and KSI too:

ETA 1 ETA 2 GENDER AGE EDUC INCOME

-------- -------- -------- -------- -------- --------

ETA 1 0.15

ETA 2 -0.04 0.07

GENDER -0.01 0.02 0.25

AGE -2.25 0.37 -0.08 269.69

EDUC 0.53 0.06 -0.07 -18.55 13.75

INCOME 0.47 -0.08 -0.98 -15.71 5.55 20.57

Squared Multiple Correlations for Structural Equations

ETA 1 ETA 2

-------- --------

0.22 0.03


Lisrel output4
(LISREL output) too:

Modification Indices and Expected Change

Modification Indices for LAMBDA-Y

ETA 1 ETA 2

-------- --------

REDUCE - - - -

NEVHAPP - - 3.55

NEW_GOAL 4.90 - -

IMPROVE 0.84 - -

ACHIEVE 2.18 - -

CONTENT - - 3.55


Completely Standardized Solution too:

LAMBDA-Y

ETA 1 ETA 2

-------- --------

REDUCE 0.59 0.24

NEVHAPP 0.59 - -

NEW_GOAL - - 0.52

IMPROVE - - 0.79

ACHIEVE - - 0.41

CONTENT 0.59 - -

GAMMA

GENDER AGE EDUC INCOME

-------- -------- -------- --------

ETA 1 0.03 -0.25 0.25 0.15

ETA 2 0.12 0.11 0.10 -0.02

(could have used LA (labels) statement to provide labels for these latent variables)


Reproduced covariances in matrix form
Reproduced covariances in matrix form too:

First examples are for SEM models that are “manifest variable only” – no latent variables.




Manifest variables only2
Manifest variables only too:

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


Manifest variables only3
Manifest variables only too:

With Beta matrix:






Latent variables included
Latent variables included too:

Measurement model only



δ too:



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