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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 0BE(1,2) BE(2,1) 0 PHI 2 X 2 PHI(1,1) 0PHI(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

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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

0BE(1,2)

BE(2,1) 0

PHI 2 X 2

PHI(1,1)

0PHI(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

10

LX(2,1)0

LX(3,1)LX(3,2)

01

0LX(5,2)

LAMBDA-Y

10

LY(2,1)0

LY(3,1)0

01

0LY(5,2)

0LY(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

Beta 2 x 2

00

BE(2,1)0

PSI 2 x 2

PS(1,1)

0PS(2,2)

Not shown: zeta1

Theta-eps

TE(1,1)

0TE(2,2)

00TE(3,3)

TE(4,1)00TE(4,4)

0TE(5,2)00TE(5,5)

00000TE(6,6)


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 3


Exercise 3

BETA 2 X 2

00

BE(2,1)0

LAMBDA-Y

10

LY(2,1)0

LY(3,1) LY(3,2)

01

0LY(5,2)

Gamma 2 x 1

GA(1,1)

0

LAMBDA-X 1 X 1

1


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

This is a non-standard model.


Exercise 4

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


RE-EXPRESSED MODEL

LAMBDA – Y

10

LY(2,1)0

LY(3,1)0

LY(4,1)0

01

BETA

0BE(1,2)

00


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:

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

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:

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 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)


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)


LISREL Output:

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 Output

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 Output

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 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 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

If reading in a covariance matrix generated by PRELIS instead of a .dsf file:

DANO=# 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:

! 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)

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)

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

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 output)

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

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

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


Manifest variables only


Manifest variables only


Manifest variables only

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


Manifest variables only

With Beta matrix:


Manifest variables only


Manifest variables only


Manifest variables only


Manifest variables only


Latent variables included

Measurement model only


Latent variables included


δ


(last slide)


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