icpsr general structural equation models
DESCRIPTION
ICPSR General Structural Equation Models. Week 4 # 3 Panel Data (including Growth Curve Models). Causal models:. Cross-lagged panel coefficients [Reduced form of model on next slide]. Causal models:. Reciprocal effects, using lagged values to achieve model identification. Causal models:. - PowerPoint PPT PresentationTRANSCRIPT
ICPSR General Structural Equation Models
Week 4 # 3
Panel Data
(including Growth Curve Models)
Causal models:
Ksi-1
Ksi-2 Eta-2
ga2,1
Eta-1
ga1,2
1
1
Cross-lagged panel coefficients
[Reduced form of model on next slide]
Causal models:
Reciprocal effects, using lagged values to achieve model identification
Ksi-1
Ksi-2 Eta-2
Eta-1
1
1
Causal models:
TV Use
PoliticalTrust
Pol TrustTime 2
gamma 1,1 gamma2,1
Beta 2,1
A variant
Issue: what does ga(1,1) mean given concern over causal direction?
Lagged and contemporaneous effects
1
1
This model is underidentified
Lagged effects model
ksi-2 eta-1 eta-2
ksi-1
Ksi-1 could be an “event”
1/0 dummy variable
First order model for three wave data(univariate)
1
1 1 1
1
1 1 1
1
1 1 1
Time 1 Time 2 Time 3
First order model for three wave data(univariate)
1
1 1 1
1
1 1 1
1
1 1 1
b1 b1
Tests: Equivalent of stability coefficients (b1)
Mean differences (see earlier slide)
Second order model for three wave data(univariate)
1
1 1 11
1 1 1
1
1 1 1
b1 b1
No longer comparable to b1 (t1 t2)
Second order model for three wave data(univariate)
1
1 1 11
1 1 1
1
1 1 1
b1 b1
Issue: adding appropriate error terms (2nd order)
Multivariate Model for Three-wave panel data: cross-lagged effects (first order)
1
1
1
1
Multivariate Model for Three-wave panel data: cross-lagged effects (first order)
1
1
1
1
Equivalence of parameters:
T1 T2
T2 T3
Multivariate Model for Three-wave panel data: cross-lagged effects (second order)
Multivariate Model for Four-wave panel data: cross-lagged effects (second order)
Lagged and contemporaneous effectsThree wave model with constraints:
a
e f
b
d
c
1
1
a
b
e f
1
1
d
c
Under many circumstances, there will be an empirical under-ident. problem, though in theory this model is identified
Example:
• Canada, Quality of Life data
• In directory \Panel in
Week4Examples
Panel Data model
Model for attitudes about labour unions, 1977-1979
Items: 5-pt. agree/disagree199D QD6B Unions too much power Q156C QK16F Scabs (gov’t prohibit
strikebreakers)Q156D QK16G Workers on BoardsQ156B QK16E Teachers should not have
right to strike
Source: Cdn. Quality of life panel study, 1977-1979 waves
Union Atts1977
1
1111
Union atts1979
1
1111
1
Panel Data model
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
LABOR77 LABOR79 -------- -------- Q199D 1.000 - - Q156C -1.803 - - (0.141) -12.796 Q156D -1.148 - - (0.101) -11.350 Q156B 0.789 - - (0.098) 8.040 QD7B - - 1.000 QK16F - - -1.352 (0.109) -12.355 QK16G - - -0.755 (0.072) -10.479 QK16E - - 0.709 (0.084) 8.427
Panel Data model
BETA
LABOR77 LABOR79 -------- -------- LABOR77 - - - - LABOR79 1.420 - - (0.138) 10.318
PSI Note: This matrix is diagonal.
LABOR77 LABOR79 -------- -------- 0.125 -0.066 (0.017) (0.018) 7.529 -3.611
Squared Multiple Correlations for Structural Equations
LABOR77 LABOR79 -------- -------- - - 1.356
W_A_R_N_I_N_G: PSI is not positive definite
Panel Data model
Completely Standardized Solution
LAMBDA-Y
LABOR77 LABOR79 -------- -------- Q199D 0.425 - - Q156C -0.559 - - Q156D -0.436 - - Q156B 0.262 - - QD7B - - 0.409 QK16F - - -0.524 QK16G - - -0.382 QK16E - - 0.277
BETA
LABOR77 LABOR79 -------- -------- LABOR77 - - - - LABOR79 1.165 - -
What is the problem here?
Panel Data model
Theta-epsilon was specified as diagonal
Modification Indices for THETA-EPS
Q199D Q156C Q156D Q156B QD7B QK16F -------- -------- -------- -------- -------- -------- Q199D - - Q156C 2.845 - - Q156D 3.439 20.324 - - Q156B 17.009 5.334 13.004 - - QD7B 83.881 42.939 10.988 4.108 - - QK16F 10.361 108.940 28.775 23.541 2.034 - - QK16G 19.366 28.336 141.658 5.494 0.242 7.172 QK16E 0.158 7.133 14.031 169.430 25.246 6.019
Panel Data model
Union Atts1977
1
1111
Union atts1979
1
1111
1
Panel Data model
Added error covariances:
FR TE 5 1 TE 6 2 TE 7 3 TE 8 4
BETA
LABOR77 LABOR79 -------- -------- LABOR77 - - - - LABOR79 1.094 - - (0.115) 9.547
Covariance Matrix of ETA
LABOR77 LABOR79 -------- -------- LABOR77 0.116 LABOR79 0.127 0.199
Panel Data model
Added error covariances:
FR TE 5 1 TE 6 2 TE 7 3 TE 8 4
PSI Note: This matrix is diagonal.
LABOR77 LABOR79 -------- -------- 0.116 0.060 (0.020) (0.016) 5.935 3.721
Squared Multiple Correlations for Structural Equations
LABOR77 LABOR79 -------- -------- - - 0.698
Panel Data model
Panel data model Cdn. Quality of Life 1977-81! Model for mean differencesSY='H:\QOL3WAVE\imputed_data.dsf'SE Q199D Q156C Q156D Q156B QD7B QK16F QK16G QK16E /MO NY=8 NE=2 LY=FU,FI PS=SY,FR TE=SY BE=FU,FI TY=FR AL=FILE LABOR77 LABOR79VA 1.0 LY 1 1 LY 5 2FR LY 2 1 LY 3 1 LY 4 1FR LY 6 2 LY 7 2 LY 8 2 FR TE 5 1 TE 6 2 TE 7 3 TE 8 4EQ TY 5 TY 1EQ TY 6 TY 2EQ TY 7 TY 3EQ TY 8 TY 4EQ LY 2 1 LY 6 2EQ LY 3 1 LY 7 2EQ LY 4 1 LY 8 2FR AL 2OU ME=ML MI SC ND=3
Alternative specification with stability coefficient:
PS=SY BE=SD
[or BE=FU,FI then FR BE 2 1]
Panel Data
ALPHA
LABOR77 LABOR79
-------- --------
- - 0.043
(0.014)
3.051
Higher score = pro-union (ref. indicator: too much/too little power… too little=5 too much=1
Panel Data
Panel data model Cdn. Quality of Life 1977-81
! Impact of TV newspapers on labor union attitudesSY='H:\QOL3WAVE\imputed_data.dsf'SE Q258 Q260 Q261 Q199D Q156C Q156D Q156B QD7B QK16F QK16G QK16E /MO NY=11 NE=4 LY=FU,FI PS=SY TE=SY BE=FU,FILE NEWSP TV LABOR77 LABOR79VA 1.0 LY 2 1 VA 1.0 LY 3 2FR LY 1 1 FI TE 3 3 VA 1.0 LY 4 3 LY 8 4FR LY 5 3 LY 6 3 LY 7 3FR LY 9 4 LY 10 4 LY 11 4 FR BE 4 3FR BE 3 2 BE 3 1FR BE 4 2 BE 4 1FR PS 2 1 FR TE 11 7 TE 10 6 TE 9 5 TE 8 4OU ME=ML MI SC ND=3
Union Atts1977
1
1111
Union atts1979
1
1111
1
Newsp11
1
TV1
Panel Data
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
NEWSP TV LABOR77 LABOR79 -------- -------- -------- -------- Q258 0.917 - - - - - - (0.176) 5.212 Q260 1.000 - - - - - - Q261 - - 1.000 - - - - Q199D - - - - 1.000 - - Q156C - - - - -1.891 - - (0.214) -8.819
Panel Data
BETA
NEWSP TV LABOR77 LABOR79 -------- -------- -------- -------- NEWSP - - - - - - - - TV - - - - - - - - LABOR77 0.061 -0.005 - - - - (0.026) (0.011) 2.325 -0.406 LABOR79 0.047 -0.017 1.081 - - (0.030) (0.014) (0.113) 1.584 -1.216 9.564
Panel Data
Panel data model Cdn. Quality of Life 1977-81! Impact of TV newspapers on labor union attitudes! Controls: education sex union membership SY='H:\QOL3WAVE\imputed_data.dsf'SE Q258 Q260 Q261 Q199D Q156C Q156D Q156B QD7B QK16F QK16G QK16E Q63 SEX Q201 RAGE Q157/MO NY=11 NE=4 LY=FU,FI PS=SY TE=SY BE=FU,FI NX=5 NK=5 FIXEDXLE NEWSP TV LABOR77 LABOR79LKMEMBER SEX EDUC AGE INCOMEVA 1.0 LY 2 1 VA 1.0 LY 3 2FR LY 1 1 FI TE 3 3 VA 1.0 LY 4 3 LY 8 4FR LY 5 3 LY 6 3 LY 7 3FR LY 9 4 LY 10 4 LY 11 4 FR BE 4 3FR BE 3 2 BE 3 1FR BE 4 2 BE 4 1FR PS 2 1 FR TE 11 7 TE 10 6 TE 9 5 TE 8 4OU ME=ML MI SC ND=3
Panel Data BETA
NEWSP TV LABOR77 LABOR79 -------- -------- -------- -------- NEWSP - - - - - - - - TV - - - - - - - - LABOR77 -0.025 -0.012 - - - - (0.034) (0.011) -0.738 -1.157 LABOR79 0.068 -0.010 1.033 - - (0.042) (0.013) (0.115) 1.622 -0.751 8.970
GAMMA
MEMBER SEX EDUC AGE INCOME -------- -------- -------- -------- -------- NEWSP -0.017 0.011 -0.097 -0.014 -0.014 (0.039) (0.035) (0.009) (0.001) (0.005) -0.422 0.311 -11.303 -13.496 -2.898 TV -0.013 -0.150 0.025 -0.017 0.001 (0.070) (0.062) (0.015) (0.002) (0.009) -0.182 -2.408 1.685 -9.807 0.113 LABOR77 0.286 -0.056 -0.039 -0.005 -0.010 (0.036) (0.026) (0.008) (0.001) (0.004) 7.880 -2.131 -5.158 -5.331 -2.557 LABOR79 0.045 0.114 0.001 0.001 -0.006 (0.042) (0.033) (0.009) (0.001) (0.004) 1.082 3.487 0.069 0.966 -1.436
Another model (panel7)
BETA
INEQ77 LABOR77 INEQ79 LABOR79 -------- -------- -------- -------- INEQ77 - - - - - - - - LABOR77 - - - - - - - - INEQ79 0.704 0.012 - - - - (0.069) (0.110) 10.214 0.105 LABOR79 -0.106 0.819 - - - - (0.044) (0.124) -2.400 6.622
Re-expressing parameters:GROWTH CURVE MODELS
Intercept & linear (& sometimes quadratic) terms
• Suitable for panel models with >2 waves
• Best for panel models with >3 waves
Linear Growth Model
Two Factor LGM
Parm1,
Intercept
Parm2,
Slope
0
V1 - t1
0
V2 - t2
10
1
1
0, 01
0, 01
LISREL:
2 manifest variable, 2 latent variable model
LY matrix
INT Slope
V1 1 0
V2 1 1
TE matrix = elements equal
PS matrix = SY,FR
(parm1 in model = variance of INT, parm2 = variance of Slope)
TY zero
AL free (“parm1” and “parm2” above)
Linear Growth Model
Two Factor LGM
Parm1,
Intercept
Parm2,
Slope
0
V1 - t1
0
V2 - t2
10
1
1
0, 01
0, 01
Interpretation:
• intercept factor represents initial status
•Slope factor represents difference scores (V2-V1)
With single indicators, cannot estimate error variances (as with any single indicator SEM model)
Parm1 = mean intercept Parm2 = mean slope value
Linear Growth Model
Two Factor LGM
Parm1,
Intercept
Parm2,
Slope
0
V1 - t1
0
V2 - t2
10
1
1
0, 01
0, 01
Parm1 = mean intercept Parm2 = mean slope value
E.g., TV use, adolescents, hours/day
Parm1 = 2.5
Parm2 = 1.0
Increase of 1 hour/day from t1 to t2
We will also get variances for the Intercept and the Slope factors
Some growth curve trajectories:
• Parallel stability
Some growth curve trajectories:
• Strict stability
Single-factor LGM
Curve
V1 V2 V3
1 B1 B1
•Actually nested within 2 factor model
• take 2 factor model, intercept with 0 mean and 0 variance or strictly proportional to slope
Not generally the best model unless assumptions met: (cf. Duncan et al. p. 31: when rank ordering of individuals does not vary across time despite mean level changes)
(can estimate var(e1),(e2),(e3) if we impose constraint v(e1)=v(e2)=v(e3) )
Linear Growth Model
Two Factor LGM
Parm1,
Intercept
Parm2,
Slope
0
LV-t1
0,
1
10,1
0,1
0
LV-t2
0,0,0,
1
111
1
01
1
A bit more complicated with latent variables instead of single manifest variables
… but the same basic principle.
Linear Growth ModelTwo Factor Linear Growth Model
Parm1,
Intercept
Parm2,
Slope
0
t1
0
t2
0
t3
11
1 01 2
0,1
0,1
0,1
LY matrix (LISREL)
Int Slope
V1 1 0
V2 1 1
V3 1 2
Same principle would apply to k time points where k>3
More time points: test of linearity of “growth” (changes in mean)*
*general test: vs. “unspecified growth model”
Unspecified 2 factor Growth Curve Model
Two Factor Unspecified Growth Model
Parm1,
Intercept
Parm2,
Slope
0
t1
0
t2
0
t3
11
1 01 lambda
0,1
0,1
0,1
1 free lambda parameter in LY matrix
In k time-point model, all but first 2 time points are represented by free parameters
3 factor Growth Curve Model
Parm1,
Intercept
Parm2,
Linear
0
t1
0
t2
0
t3
11
10
1
0,1
0,1
0,1
2
0,
Quadratic0
1 4
Non-linear growth
Parm 3
3 factor Growth Curve Model
Parm1,
Intercept
Parm2,
Linear
0
t1
0
t2
0
t3
11
10
1
0,1
0,1
0,1
2
0,
Quadratic0
1 4
LY matrix
INT LIN Quad
V1 1 0 0
V2 1 1 2
V3 1 2 4
TE is constrained to equality across t’s
PS is free
AL is free (parm1-3)
All TY elements 0
parm3
This is a “saturated” model (perfect fit by definition)
Examples:
Z:\baer\Week4Examples\LatentGrowthSingle variable models:LGMProg1.ls8 (output=.out)
intercept modelLGMProg2.ls8 - single factor curve modelLGMProg3.ls8 - intercept + slopeLGMProg4.ls8 – intercept + slope +
quadratic
Where do “growth factors” fit into models?
• Examination of predictors (antecedents) and consequences of change
Two Factor Linear Growth Model
Parm1,
Intercept
Parm2,
Slope
0
t1
0
t2
0
t3
11
1 01 2
0,1
0,1
0,1
Note: Intercept-slope covariance now disturbance covariance
PROGRAM
LGMProg5
ConsequencesTwo Factor Linear Growth Model
Parm1,
Intercept
Parm2,
Slope
0
t1
0
t2
0
t3
11
1 01 2
0,1
0,1
0,1
Model LGMProg6.ls8
Dependent variable: job satisfaction, wave 8.
Multiple indicators for the variable(s) involved in growth
curves
• “factor of curves” LGM
• Intercept term and slope term (e.g.) constructed for each indicator
• if there are 3 variables & 4 waves, we will have an intercept term based on 4 manifest variables representing time x 3 manifest variables per time (3 intercept terms)
“common intercept” variable will have 3 indicators (intercept terms)
“common slope” will have 3 indicators (slope terms)
x1-intercept
x2-t11
x1-t1 x3-t11
x2-t2x1-t2 x3-t21 11 1
x2-t3x1-t3 x3-t31 11
1
x2-Intercept
1 1
x3-intercept
11 1 1
commonintercept
1 lambda2 lambda3
Error variances now estimated (not constrained to equality).. Could include corr. Errors too
x1-intercept
x2-t2x1-t2 x3-t2 x2-t3x1-t3 x3-t3
x2-Intercept
1
x3-intercept
1 1
commonintercept
1 lambda2 lambda3
x3-t1x2-t1x1-t1
1 1
x1-slope x2-slope x3-slope
common slope
0 1 20 1 2
lambda2a
1 lambda3a
1
1 1
11
1
Interactions
Easiest case: X1 is 0/1X2 ix 0/1
Options: 1. Manually construct X3=X1*X2 outside SEM software, estimate model with X1,X2,X3 exogenous. Test for interaction: fix regression coefficient for X3 to 0.2. Create two groups: X1=0 and X1=1. In each group, X2 as exogenous variable. Test for interaction would be H0: gamma[1] = gamma[2].
Extensions for X1, X2 >2 categories straightfoward (more groups/dummy variables)
Interactions
Option 3: Model as a 4-group problem.X11 0
X2 1 gr1 gr20 gr3 gr4
AL[1]=0 al[2], al[3],al[4] parameters to be estimated.
Main effects model (no interaction) would allow for al[2]≠al[3] ≠al[4] but pattern of differences would be constrained such that…..
Interactions
Model as a 4-group problem.X11 0
X2 1 gr1 gr20 gr3 gr4
AL[1]=0 al[2], al[3],al[4] parameters to be estimated.Main effects model (no interaction) would allow for al[2]≠al[3] ≠al[4] but pattern
of differences would be constrained such that…..
The group1 vs. group 2 difference = group 3 vs. group 4 difference(or group 1 vs. 3 difference = group 2 vs. group 4).Programming in LISREL would be:Al[1] – Al[2] = al[3]- al[4]0 – al[2] = al[3] – al[4] Al[2] = al[4]-al[3] LISREL: CO al 2 1 = al 4 1 – al 3 1 Test for interaction: run another model removing this constraint (all AL
completely free except group 1)
… more examples provided in text
Interactions
Interactions involving continuous variables.
Case 1: One continuous (single or multiple indicator) and one categorical variableEASY: categorical variable becomes basis for grouping.
Group 1 Eta = gamma[1] Ksi + zetaGroup 2 Eta = gamma[2] Ksi + zetaTest for interaction: H0: gamma[1] = gamma[2]
Case 2: Two continuous single indicator variablesAlso somewhat straightforward:
Create single-indicator X3 = X2*X1
Case 3: Two continuous multiple indicator latent variablesThis is not so easy! Substantial literature on this question See course outline for extended list. (Schumacker and Mracoulides, eds., Interaction and Nonlinear Effects in Structural Equation Modeling).
Case 3A, not talked about much: X1 single indicator Ksi1 (X2, X3,X4)Create: X1X2 , X1X3, X1,X4
Latent variable interactions
Major approaches:• Kenny-Judd• Simplified variants of Kenny-Judd,
modifications, etc. (Joreskog & Yang, 1996; Ping)
• Two-stage least squares (get instrumental variables)
• Use SEM to estimate 2 factor model, save latent variable “scores” (analogous to factor scores), then use these
Latent variable interactions
• Use SEM to estimate 2 factor model, save latent variable “scores” (analogous to factor scores), then use these
In LISREL:
Mo nx=6 nk=2 lx=fu,fi ph-sy,fr td=sy
Va 1.0 lx 1 1 lx 4 2
Fr lx 2 1 lx 3 1 lx 5 2 lx 6 2
PS=Newfile.psf
OU
Latent variable interactions• Use SEM to estimate 2 factor model, save latent variable “scores”
(analogous to factor scores), then use these
In LISREL:
Mo nx=6 nk=2 lx=fu,fi ph-sy,fr td=sy
Va 1.0 lx 1 1 lx 4 2
Fr lx 2 1 lx 3 1 lx 5 2 lx 6 2
PS=Newfile.psf
OU
LISREL documentation suggests that a simple regression can be estimated in PRELIS:
Sy=newfile.psf
ne inter=ksi1*ksi2
rg y on ksi1 ksi2 ksi1 ksi2
ou
Latent variable interactions
LISREL documentation suggests that a simple regression can be estimated in PRELIS:
Sy=newfile.psf
ne inter=ksi1*ksi2
rg y on ksi1 ksi2 ksi1 ksi2
ou
…. But it should also be possible to a) construct “inter” (=ksi1*ksi2) and read the 3 new “single indicator” variables back into LISREL for use with other variables (including those which form the basis of multiple-indicator endogenous variables.
If all else fails, construct a LISREL model for Ksi1, Ksi2, and put FS (factor score regressions) on the OU line:
OU ME=ML FS MI ND=4
.. And use factor score regressions to compute estimated factor scores in any stat package (incl. PRELIS)
Example:INTERACTION MODEL WITH INTERACTION TERM CREATED EXTERNALLY SINGLE INDICATORS FOR EXOGENOUS LVS INVOLVED IN INTERACTION DA NO=1111 NI=10 MA=CM CM FI=G:\ICPSR\INTERACTIONS\INT5b.COV FU FO (10F10.7) LABELS lv1 lv2 interact sex race v217 v216 v125 v127 v130 se 8 9 10 1 2 3 4 5 6 7/ mo ny=3 ne=1 LY=FU,FI PS=SY,FR TE=SY c nx=7 nk=7 fixedx ga=fu,fr va 1.0 ly 1 1 fr ly 2 1 ly 3 1 ou me=ml se tv mi sc
Example:LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
ETA 1 -------- v125 1.00 v127 1.34 (0.24) 5.59 v130 0.65 (0.11) 5.74
GAMMA
lv1 lv2 interact sex race v217 -------- -------- -------- -------- -------- -------- ETA 1 -0.04 -0.21 0.85 0.22 -0.30 0.05 (0.06) (0.08) (0.45) (0.11) (0.13) (0.03) -0.65 -2.57 1.89 2.10 -2.27 1.75
GAMMA
v216 -------- ETA 1 0.09 (0.03) 2.92
Dep var = inequality att’s (high score “more individual effort”)
Lv1=relig. Lv2=econ. status
Kenny-Judd model
Typically, literature (e.g., Kenny-Judd, 1984; Hayduk, 1987) starts with 2-indicator example (2 LV’s each with 2 indicators).
Ksi1
Ksi2 Ksi1*Ksi2 (interaction term)
Indicators: Ksi1: x1
x2
Ksi2: x3
x4
Possible product terms:
x1*x3 x1*x4
x2*X3 X2*x4
Kenny-Judd model use 4 product terms but Joreskog and Yang show that the model can be constructed with 1 product term.
Kenny-Judd model
Typically, literature (e.g., Kenny-Judd, 1984; Hayduk, 1987) starts with 2-indicator example (2 LV’s each with 2 indicators).
Ksi1
Ksi2 Ksi1*Ksi2 (interaction term)
Indicators: Ksi1: x1
x2
Ksi2: x3
x4
Possible product terms:
x1*x3 x1*x4
x2*X3 X2*x4
Kenny-Judd model use 4 product terms but Joreskog and Yang show that the model can be constructed with 1 product term.
Kenny-Judd do not include constant intercept terms (alpha, tau).. But even if dependent variable, Ksi1, Ksi2 and zeta have zero means, alpha will still be nonzero. - means of observed variables functions of other parameters in the model and therefore intercept terms have to be included.
- Nonnormality even if x’s are normal (ADF estimation often recommended if sample size acceptable)
Kenny-Judd model
Kenny-Judd model
alpha=1 term
Kenny-Judd model, mod.INTERACTION MODEL KENNY JUDD MODIFICATION (JORESKOG AND YANG) ONE INTERACTION INDICATOR 3 INDICATORS PER L.V. DA NO=1111 NI=22 CM FI=G:\ICPSR2000\INTERACTIONS\INT5c.COV FU FO (22F20.11) ME FI=G:\ICPSR2000\INTERACTIONS\INT5C.MN FO (22F20.11) LABELS v181 v9 v190 v221 v226 v227 relinc1 relinc2 relinc3 relinc4 relinc5 relinc6 relinc7 relinc8 reling9 sex race v217 v216 v125 v127 v130 se 20 21 22 1 2 3 4 5 6 9 16 17 18 19/ mo ny=3 ne=1 NX=11 NK=7 LY=FU,FI PS=SY,FR C TE=SY TX=FR KA=FI C LX=FU,FI GA=FU,FR PH=SY,FR TD=SY AL=FI TY=FR va 1.0 ly 1 1 fr ly 2 1 ly 3 1 FI PH 3 1 PH 3 2 FR KA 3 VA 1.0 LX 1 1 LX 4 2 LX 7 3 LX 8 4 LX 9 5 LX 10 6 LX 11 7 FR TD 1 1 TD 2 2 TD 3 3 TD 4 4 TD 5 5 TD 6 6 TD 7 7 FR LX 2 1 LX 3 1 LX 5 2 LX 6 2 LX 7 1 LX 7 2 CO LX(7,1)=TX(1) CO LX(7,2)=TX(4) CO KA(3) = PH(2,1) FI PH 3 1 PH 3 2 CO PH(3,3) = PH(1,1)*PH(2,2) + PH(2,1)**2 CO TX(6) = TX(1)*TX(4) FI TD(8,8) TD(9,9) TD(10,10) TD(11,11) CO TD(7,7) = TX(1)**2*TD(3,3) + TX(4)**2*TD(1,1) + PH(1,1)*TX(4) + C PH(2,2)*TX(1) + TD(1,1)*TD(4,4) OU ME=ML SE TV ND=3 AD=off
Kenny-Judd model, modified Joreskog/Yang
Parameter Specifications
LAMBDA-Y
ETA 1 -------- v125 0 v127 1 v130 2
LAMBDA-X
KSI 1 KSI 2 KSI 3 KSI 4 KSI 5 KSI 6 -------- -------- -------- -------- -------- -------- v181 0 0 0 0 0 0 v9 3 0 0 0 0 0 v190 4 0 0 0 0 0 v221 0 0 0 0 0 0 v226 0 5 0 0 0 0 v227 0 6 0 0 0 0 relinc3 Constr'd Constr'd 0 0 0 0 sex 0 0 0 0 0 0 race 0 0 0 0 0 0 v217 0 0 0 0 0 0 v216 0 0 0 0 0 0
Kenny-Judd model, modified Joreskog/Yang
GAMMA
KSI 1 KSI 2 KSI 3 KSI 4 KSI 5 KSI 6 -------- -------- -------- -------- -------- -------- ETA 1 -0.023 -0.003 -0.008 0.209 -0.324 0.051 (0.009) (0.015) (0.004) (0.098) (0.125) (0.024) -2.557 -0.198 -1.984 2.130 -2.593 2.094
GAMMA
KSI 7 -------- ETA 1 0.080 (0.029) 2.735