General Structural Equation (LISREL) Models

1
General Structural Equation (LISREL) Models

• Week 3 1
• Multiple Group Models
• An extended multiple-group model Religiosity
  Sexual Morality in 2 countries (LISREL example)
• Computer programming for multiple-group models
  a) LISREL b) AMOS
• See Week3Examples

2
MOST IMPORTANT FORM OF CONSTRAINT INVOLVES
CONSTRAINING PARAMETERS ACROSS GROUPS
Group 1
Group 2
Constraint b1group1 b1group2
3
Multiple Group Models
Group 2 (female)
Group 1 (male)
Equivalence of measurement coefficients H0 ?1
?2 lambda 1 1 lambda 1
2 df2 lambda 2 1 lambda 2 2
4
Multiple Group Models

• Other equivalence tests possible
• Equivalence of variances of latent variables
• H0 PSI-11 PSI-12
• This test will depend upon which ref. indicator
  used
• Equivalence of error variances
• H0 Theta-eps1 Theta-eps2 entire
  matrix
• df3 and covariances if there are correlated
  errors

5
Multiple Group Models

• Measurement model equivalence does not imply same
  mean levels
• Measurement model for Group 1 can be identical to
  Group 2, yet the two groups can differ radically
  in terms of level.
• Example Group 1 Group 2
• Load mean Load mean
• Always trust govt .80 2.3 .78 3.9
• Govern. Corrupt -.75 3.8 -.80 2.3
• Politicians dont
• care
• (where 1agree strongly through 10disagree
  strongly)

6
Multiple Group Models

• It is possible to have multiple group models
  with both common and unique items
• Example
• Y1 Both countries We should always trust our
  elected leaders
• Y2 Both countries If my government told me to
  go to war, Id go
• Y3 Both countries We need more respect for
  government authority
• Y4 (US) George Bush commands my respect because
  he is our President
• Y4 (Canada) Paul Martin commands my respect
  because he is our Prime Minister

We might expect (if measurement equivalence
holds) lambda11 lambda12 lambda21
lambda22 BUT lambda31 ? lambda32
7
Multiple Group Models

• Should be careful with the use of reference
  indicators (and/or sensitive to the fact that
  apparently non-equivalent models might appear to
  be so simply because of a single (reference)
  indicator
• Example
• Group 1 Group 2
• Lambda-1 1.0 1.0
• Lambda-2 .50 1.0
• Lambda-3 .75 1.5
• Lambda-4 1.0 2.0
• These two groups appear to have measurement
  models that are very different, but.

8
Multiple Group Models

• Group 1 Group 2
• Lambda-1 1.0 1.0
• Lambda-2 .50 1.0
• Lambda-3 .75 1.5
• Lambda-4 1.0 2.0
• These two groups appear to have measurement
  models that are very different, but.
• If we change the reference indicator to Y2, we
  find

Gr 1 Gr 2 Lambda1 2.0 1.0 Lambda2 1.0 1.0 Lamb
da3 1.5 1.5 Lambda4 2.0 2.0
9
Multiple Group Models
Modification Indices and what they mean in
multiple-group models Assuming LY1 LY2
(entire matrix)
Example MODIFICATION INDICES Group 1 Group
2 Eta 1 Eta 1 Y1 --- Y1 --- Y2 .382 Y2 .38
2 Y3 1.24 Y3 1.24 Y4 45.23 Y4 45.23
10
Multiple Group Models
Modification Indices and what they mean in
multiple-group models Assuming LY1 LY2
(entire matrix)
Example MODIFICATION INDICES Group 1 Group
2 Eta 1 Eta 1 Y1 --- Y1 --- Y2 .382 Y2 .38
2 Y3 1.24 Y3 1.24 Y4 45.23 Y4 45.23
Improvement in chi-square if equality constraint
released
11
Multiple Group Models Modification Indices
MODIFICATION Group 1 Group 2 INDICES eta1
eta2 eta1 eta2 Y1 --- 2.42 --- 3.89 Y2 1.42
3.44 1.42 1.01 Y3 0.43 2.11 0.43
40.89 Y4 0.11 --- 0.98 --- Y5 2.32 1.49 1.
22 1.49 Y6 1.01 29.23 3.21 29.23
Tests equality constraint lambda51lambda52
12
Multiple Group Models Modification Indices
MODIFICATION Group 1 Group 2 INDICES eta1
eta2 eta1 eta2 Y1 --- 2.42 --- 3.89 Y2 1.42
3.44 1.42 1.01 Y3 0.43 2.11 0.43
40.89 Y4 0.11 --- 0.98 --- Y5 2.32 1.49 1.
22 1.49 Y6 1.01 29.23 3.21 29.23
Tests equality constraint lambda51lambda52
Wald test (MI) for adding parameter LY(3,3) to
the model in group 2 only
13
MULTIPLE GROUP MODELS parameter significance
tests

• When a parameter is constrained to equality
  across 2 (or more) groups, pooled significance
  test (more power)
• Possible to have a coefficient non-signif. in
  each of 2 groups yet significant when equality
  constraint imposed
• Possible to have a coefficient that is not
  significant in each of two groups (e.g., ve
  coefficient, NS, in one group, -ve, NS, in
  another) yet the difference between the groups is
  statistically significant

14
Tests in 3 groups

• 2-group model can be extended to m groups (in
  theory, infinite number as long as minimum sample
  size requirements met in each group in practice,
  some software packages have limits)
• Models
• Group1Group2Group3
• Group1Group2?Group3
• Group1 ? Group2?Group3
• Must be careful about interpretation of
  Modification Indices
• In a model with 123 ? 0, then a MI will
  provide an indication of how much the model
  improve if the parameter constraint is removed in
  the mth group only (e.g., MI in group 2 would
  test against a model in which the group 1 group
  3 same parameter are constrained to equality
  but the group 2 is allowed to differ)

15
MULTIPLE GROUP MODELS Modification Indices
(again)
Model LY1LY2LY3
Group 1 MOD INDICES Lambda 1 3.01 Lambda
2 1.52 Lambda 3 3.22 Group 2 MOD INDICES Lambda
1 4.22 Lambda 2 3.99 Lambda 3 5.22 Group 3 MOD
INDICES Lambda 1 89.22 Lambda 2 6.11 Lambda 3 1.22
Free LY(2,1) in group 3 but LY(2,1) in group 1
LY(2,1) in group 2
16
When do we have measurement equivalence

• STRONG equivalence
• all matrices identical, all groups
• (might possibly exclude variance of LVs from
  this i.e., the PHI or PSI matrices)
• WEAKER equivalence (usually accepted)
• Lambda matices identical, all groups
• Theta matrices could be different (and probably
  are), either having the same form or not
• WEAKER YET
• Lambda matrices have the same form, some
  identical coefficients

17
Measurement coefficients, construct equation
coefficients in multiple group models

• We usually need the measurement equation
  coefficients to be equivalent in order to proceed
  with comparison of construct equation coefficients

18
Measurement coefficients, construct equation
coefficients in multiple group models

• We usually need the measurement equation
  coefficients to be equivalent in order to proceed
  with comparison of construct equation
  coefficients
• For this reason, tests for measurement
  equivalence are usually not as rigorous as the
  substantive tests for construct equation
  coefficient equivalence (though instances of poor
  fit should be noted in any report of results)

19
LISREL PROGRAMMING FOR MULTIPLE GROUP MODELS

• Basics
• Stack the groups (one program after the next)
• In DA statement of first group, specify total
  number of groups e.g., DA NG2 NI23 NO1246
• NI specification ( of input vars) applies only
• to group 1
• NO specification ( of observations) applies
  only to group 1

20
LISREL PROGRAMMING FOR MULTIPLE GROUP MODELS

• DA NG2
• Specify group 1 model as usual
• Title for Group 2
• DA statement group 2 NI NO
• CM FI location of group 2 cov mtx
• SE
• 1 3 4 6 8 /
• LABELS optional
• MO NY NX NK NE special options for matrix
  specification
• OU (as usual)

21
LISREL PROGRAMMING MULTIPLE GROUPS

• MO specification
• LYPS same pattern as prev. group
• - for example, if group 1 specifies 2 LVs with
  first three indicators on LV1, next 6 on LV2,
  this same specification will be copied to group 2
• LY IN invariant
• - same pattern and all free coefficients in
  this matrix constrained to equality with
  corresponding coefficients in previous group

22
LISREL PROGRAMMING MULTIPLE GROUPS

• Adding equality constraints to a matrix that is
  otherwise allowed to differ from the same matrix
  in a previous group
• Group 1 (e.g.) LYFU,FI
• VA 1.0 LY 2 1
• FR LY 2 1 LY 3 1 LY 4 1
• Group 2 LYPS
• EQ LY 1 2 1 LY 2 2 1
• EQ LY 1 3 1 LY 3 1

23
LISREL PROGRAMMING MULTIPLE GROUPS

• Releasing equality constraints on a single
  parameter when matrix is otherwise specified as
  Invariant
• Group 2
• LYIN
• FR LY 4 1 ? LY remains invariant
• except for parameter LY(4,1)

24
Examples

• Example (separate handouts)
• (religion sexual morality in 2 countries)

Multiple group example 1 USA DA NO1150 NI19
MACM NG2 CM FIG\CLASSES\ICPSR2005\WEEK3EXAMPL
ES\USA.COV LA A006 F028 F066 F063 F118 F119
F120 F121 GENDER AGE EDUC TOWNSIZE MARR1 MARR2
MARR3 OCC1 OCC2 OCC3 OCC4 SE 1 2 3 4 5 6 7 8/
MO NY8 NE2 LYFU,FI PSSY,FR TESY VA 1.0 LY 2
1 LY 5 2 FR LY 1 1 LY 3 1 LY 4 1 FR LY 6 2 LY 7
2 LY 8 2 FR TE 4 3 OU ND4 SC MI
Basic program
See handout for variable list
25
Multiple group example 1 USA

Number of Input Variables 19
Number of Y - Variables 8
Number of X - Variables 0
Number of ETA -
Variables 2 Number of
KSI - Variables 0
Number of Observations 1150
Number of Groups 2 Group 2
Canada DA NO1763 NI19 MACM CM
FIG\CLASSES\ICPSR2005\WEEK3EXAMPLES\CDN.COV
LA A006 F028 F066 F063 F118 F119 F120 F121
GENDER AGE EDUC TOWNSIZE MARR1 MARR2 MARR3 OCC1
OCC2 OCC3 OCC4 SE 1 2 3 4 5 6 7 8/ MO LYIN
PSPS TEPS OU ND4 SC MI Group 2 Canada

Number of
Input Variables 19
Number of Y - Variables 8
Number of X - Variables 0
Number of ETA - Variables 2
Number of KSI - Variables 0
Number of Observations
1763 Number of Groups
2
Program output TwoGroup1b.ls8, .out
26
Multiple group example 1 USA
Parameter
Specifications LAMBDA-Y EQUALS LAMBDA-Y IN THE
FOLLOWING GROUP PSI
ETA 1 ETA 2 --------
-------- ETA 1 7 ETA 2
8 9 THETA-EPS
A006 F028 F066 F063
F118 F119 -------- --------
-------- -------- -------- --------
A006 10 F028 0 11
F066 0 0 12
F063 0 0 13 14
F118 0 0 0
0 15 F119 0 0
0 0 0 16 F120
0 0 0 0
0 0 F121 0 0
0 0 0 0
THETA-EPS F120 F121
-------- -------- F120
17 F121 0 18
27
Covariance Matrix of ETA
ETA 1 ETA 2 --------
-------- ETA 1 2.4328 ETA 2
1.9415 4.5847 PSI
ETA 1 ETA 2 --------
-------- ETA 1 2.4328
(0.1554) 15.6531 ETA 2
1.9415 4.5847 (0.1464)
(0.3118) 13.2596 14.7036
Group 1
Covariance Matrix of ETA
ETA 1 ETA 2 --------
-------- ETA 1 3.5419 ETA 2
2.3997 5.2741 PSI
ETA 1 ETA 2 --------
-------- ETA 1 3.5419
(0.1924) 18.4093 ETA 2
2.3997 5.2741 (0.1529)
(0.3175) 15.6932 16.6128
Group 2
28
Group Goodness of Fit Statistics (USA)
Contribution to Chi-Square
120.0772 Percentage Contribution
to Chi-Square 51.3912
Root Mean Square Residual (RMR) 0.2698
Standardized RMR 0.04414
Goodness of Fit Index (GFI)
0.9756
Global Goodness of Fit Statistics
Degrees of Freedom 42
Minimum Fit Function Chi-Square 233.6530 (P
0.0) Normal Theory Weighted Least
Squares Chi-Square 229.0169 (P 0.0)
Estimated Non-centrality Parameter (NCP)
187.0169 90 Percent Confidence Interval
for NCP (143.2744 238.2786)
Normed Fit Index (NFI) 0.9840
Non-Normed Fit Index (NNFI) 0.9824
Parsimony Normed Fit Index (PNFI)
0.7380 Comparative Fit
Index (CFI) 0.9868
Incremental Fit Index (IFI) 0.9868
Relative Fit Index (RFI) 0.9787
Group Goodness of Fit Statistics (CANADA)
Contribution to Chi-Square
113.5759 Percentage Contribution
to Chi-Square 48.6088
Root Mean Square Residual (RMR) 0.2222
Standardized RMR 0.03069
Goodness of Fit Index (GFI)
0.9841
29
Multiple group example 1 USA
Modification
Indices and Expected Change
Modification Indices for LAMBDA-Y
ETA 1 ETA 2 --------
-------- A006 5.5766 6.6058
F028 16.2024 26.0322 F066 0.0376
5.6663 F063 1.4466 1.0440
F118 0.5472 4.7638 F119 0.0715
0.0993 F120 2.9330 0.0982
F121 8.8507 2.3763 Group 2 Canada

Modification Indices and Expected
Change Modification Indices for
LAMBDA-Y ETA 1 ETA 2
-------- -------- A006
3.7307 0.3247 F028 16.2027
0.0282 F066 0.0262 3.8083 F063
1.0022 1.3223 F118 18.8935
4.7637 F119 1.4474 0.0831 F120
21.8972 0.0808 F121 5.7255
1.9721
30
LISREL Estimates (Maximum Likelihood)
LAMBDA-Y
ETA 1 ETA 2 --------
-------- A006 0.4590 - -
(0.0119) 38.4181 F028
1.0000 - - F066 0.8854 - -
(0.0257) 34.4187
F063 -1.1710 - - (0.0332)
-35.2593 F118 - -
1.0000 F119 - - 0.7174
(0.0262)
27.3386 F120 - - 1.0684
(0.0326)
32.8141 F121 - - 0.7996
(0.0267)
29.9686
31
Expected Change for LAMBDA-Y (USA)
ETA 1 ETA 2 --------
-------- A006 -0.0334 -0.0296
F028 0.2040 0.1633 F066 0.0041
-0.0492 F063 0.0339 -0.0272
F118 0.0458 0.1229 F119 0.0135
-0.0089 F120 0.0974 -0.0110
F121 -0.1477 -0.0442 Expected Change for
LAMBDA-Y (Canada) ETA 1
ETA 2 -------- --------
A006 0.0150 0.0057 F028 -0.2040
0.0045 F066 -0.0024 -0.0398
F063 -0.0173 -0.0296 F118 -0.1956
-0.1229 F119 0.0444 0.0054
F120 0.1835 0.0059 F121 -0.0842
0.0253
32
Group 2 Canada
Within Group
Completely Standardized Solution
LAMBDA-Y ETA 1 ETA 2
-------- -------- A006
0.8727 - - F028 0.7325 - -
F066 0.7209 - - F063
-0.7439 - - F118 - -
0.6738 F119 - - 0.6078 F120
- - 0.8202 F121 - -
0.6876 Multiple group example 1 USA
Within
Group Completely Standardized Solution
LAMBDA-Y ETA 1 ETA 2
-------- -------- A006
0.8201 - - F028 0.6690 - -
F066 0.7403 - - F063
-0.7512 - - F118 - -
0.6711 F119 - - 0.6047 F120
- - 0.7647 F121 - -
0.6674
33
Multiple group example 1 USA
Common Metric
Completely Standardized Solution
LAMBDA-Y ETA 1 ETA 2
-------- -------- A006
0.8554 - - F028 0.7109 - -
F066 0.7267 - - F063
-0.7461 - - F118 - -
0.6728 F119 - - 0.6067 F120
- - 0.7988 F121 - -
0.6800 Covariance Matrix of ETA
ETA 1 ETA 2
-------- -------- ETA 1 0.7837
ETA 2 0.4927 0.9166 Group 2 Canada

Common Metric Standardized Solution
LAMBDA-Y ETA
1 ETA 2 -------- --------
A006 0.8086 - - F028
1.7618 - - F066 1.5599 - -
F063 -2.0631 - - F118 -
- 2.2365 F119 - - 1.6044
F120 - - 2.3894 F121 - -
1.7883
More variance in Canada
Connection stronger in Canada
Covariance Matrix of ETA
ETA 1 ETA 2 --------
-------- ETA 1 1.1410 ETA 2
0.6090 1.0544
34
Testing measurement equivalence

• Group 2 Canada
• DA NO1763 NI19 MACM
• CM FIG\CLASSES\ICPSR2005\WEEK3EXAMPLES\CDN.COV
• LA
• A006 F028 F066 F063 F118 F119 F120 F121 GENDER
  AGE EDUC TOWNSIZE MARR1 MARR2 MARR3
• OCC1 OCC2 OCC3 OCC4
• SE
• 1 2 3 4 5 6 7 8 /
• MO LYPS PSPS TEPS
• OU ND4 SC MI

Global Goodness of Fit Statistics
Degrees of Freedom 36
Minimum Fit Function Chi-Square 209.7783 (P
0.0) Normal Theory Weighted Least Squares
Chi-Square 207.3408 (P 0.0)
Estimated Non-centrality Parameter (NCP)
171.3408 90 Percent Confidence Interval
for NCP (129.7727 220.4219) Normed Fit Index
(NFI) 0.9856 Non-Normed
Fit Index (NNFI) 0.9814
Parsimony Normed Fit Index (PNFI) 0.6336
Comparative Fit Index (CFI)
0.9881 Incremental Fit
Index (IFI) 0.9881
Relative Fit Index (RFI) 0.9777
35
Some Model/Test Results Matrices Chi-square d
f IFI TwoGroup1b LYIN 233.653 42 .987 TwoGroup
1c LYPS 209.778 36 .988 TwoGroup1d LYIN
PSIN 272.740 45 .984 TwoGroup1e LYIN PSIN
but 267.472 44 .985 PS 2,1 free
From TwoGroup1d, in Group 2 (Canada) Modificatio
n Indices for PSI ETA
1 ETA 2 -------- --------
ETA 1 31.1069 ETA 2 4.8672
4.0391 Expected Change for PSI
ETA 1 ETA 2
-------- -------- ETA 1 0.3466 ETA
2 -0.1158 0.2188
36
Models with exogenous variables in construct
equations

• Multiple group example 1 USA
• DA NO1150 NI19 MACM NG2
• CM FIG\CLASSES\ICPSR2005\WEEK3EXAMPLES\USA.COV
• LA
• A006 F028 F066 F063 F118 F119 F120 F121 GENDER
  AGE EDUC TOWNSIZE MARR1 MARR2 MARR3
• OCC1 OCC2 OCC3 OCC4
• SE
• 1 2 3 4 5 6 7 8 9 10 11 12/
• MO NY8 NE2 LYFU,FI PSSY,FR TESY NX4 NK4
  LXID C
• PHSY,FR TDZE GAFU,FR
• LE
• RELIG MORAL
• VA 1.0 LY 2 1 LY 5 2
• FR LY 1 1 LY 3 1 LY 4 1
• FR LY 6 2 LY 7 2 LY 8 2
• FR TE 4 3
• OU ND4 SC MI

Group 2 Canada DA NO1763 NI19 MACM CM
FIG\CLASSES\ICPSR2005\WEEK3EXAMPLES\CDN.COV
LA A006 F028 F066 F063 F118 F119 F120 F121
GENDER AGE EDUC TOWNSIZE MARR1 MARR2 MARR3 OCC1
OCC2 OCC3 OCC4 SE 1 2 3 4 5 6 7 8 9 10 11 12/
MO LYIN PSPS TEPS LXIN PHPS TDIN GAPS LE
RELIG MORAL OU ND4 SC MI
37
LAMBDA-Y EQUALS LAMBDA-Y IN THE FOLLOWING GROUP
GAMMA GENDER
AGE EDUC TOWNSIZE --------
-------- -------- -------- RELIG
7 8 9 10 MORAL
11 12 13 14
PHI GENDER AGE
EDUC TOWNSIZE -------- --------
-------- -------- GENDER 15
AGE 16 17 EDUC 18
19 20 TOWNSIZE 21
22 23 24 PSI
RELIG MORAL
-------- -------- RELIG 25
MORAL 26 27
38
Multiple group example 1 USA LISREL
Estimates (Maximum Likelihood)
LAMBDA-Y EQUALS LAMBDA-Y IN THE
FOLLOWING GROUP GAMMA
GENDER AGE EDUC TOWNSIZE
-------- -------- -------- --------
RELIG 0.6772 -0.0169 0.0818
0.0182 (0.1001) (0.0031) (0.0351)
(0.0293) 6.7629 -5.5270
2.3342 0.6194 MORAL 0.0671
-0.0143 0.3045 -0.0218
(0.1451) (0.0045) (0.0515) (0.0428)
0.4623 -3.1968 5.9077
-0.5080 Group 2 Canada
Number of
Iterations 8 LISREL Estimates (Maximum
Likelihood) GAMMA
GENDER AGE EDUC TOWNSIZE
-------- -------- -------- --------
RELIG 0.9517 -0.0292 0.1184
0.0636 (0.0926) (0.0028) (0.0397)
(0.0173) 10.2755 -10.4921
2.9799 3.6641 MORAL -0.0967
-0.0222 0.4775 0.0934
(0.1182) (0.0036) (0.0526) (0.0226)
-0.8176 -6.1962 9.0759 4.1312
39

• Models/Tests
• Model Description Chi-square df CFI
• Group2A LYIN GAPS 645.0492 90 .968
• Group2B LYIN GAIN 675.2567 98 .966
• From Model Group2B (Group 2, Canada)
• Modification Indices for GAMMA
• GENDER AGE EDUC
  TOWNSIZE
• -------- -------- --------
  --------
• RELIG 7.8388 7.6672 -0.0001
  0.0965
• MORAL 3.1242 0.0477 41.6948
  1.3675
• Modification Indices for GAMMA (Group 1, USA)
  
• GENDER AGE EDUC
  TOWNSIZE
• -------- -------- --------
  --------
• RELIG 7.7220 7.4528 0.0002
  0.2770
• MORAL 3.0729 0.0516 5.5255
  4.2116

40
Model Description Chi-square df CFI Group3A
GAIN 747.942 154 .971 Group3B GAPS 712.264
138 .972 Group3C GAIN 739.907 146 .971 Fre
e occ. in group 2 Group3D GAPS 720.507 146 .97
2 Occ FI in group 2 Group3E GAPS 731.286 154
.972 Occ Fi both groups Group3F GAPS 715.65
9 142 .972 Occ coefficients For 1st Eta
variable Tests Group3A vs. Group 3B Equality
of all GA coefficients Group 3A vs Group
3B Equality of occupation GA coefficients Group
3B vs. Group 3D Is occupation stat. significant
in group 2 (Canada)? Group 3B vs. Group
3E Is occupation stat. sign. in both
groups? Group 3D vs. Group 3E Is occupation
stat. sign. in group 1? Group 3B vs. Group
3F Equality of occupation effect for First
eta variable.
41
GAMMA USA GENDER AGE
EDUC TOWNSIZE OCC1 OCC2
-------- -------- -------- --------
-------- -------- RELIG 0.6576
-0.0165 0.1054 0.0189 0.3237
0.1832 (0.1023) (0.0031) (0.0382)
(0.0293) (0.3118) (0.3063)
6.4303 -5.3480 2.7565 0.6438
1.0382 0.5982 MORAL 0.1103
-0.0147 0.2874 -0.0247 -0.0462
0.1877 (0.1484) (0.0045) (0.0561)
(0.0429) (0.4558) (0.4479)
0.7435 -3.2723 5.1225 -0.5766
-0.1013 0.4192 GAMMA
CANADA GENDER AGE EDUC
TOWNSIZE OCC1 OCC2
-------- -------- -------- --------
-------- -------- RELIG 0.9358
-0.0287 0.1329 0.0640 -0.2922
-0.2209 (0.0944) (0.0029)
(0.0465) (0.0174) (0.3589) (0.3319)
9.9177 -10.0111 2.8594 3.6850
-0.8143 -0.6655 MORAL -0.0903
-0.0239 0.4201 0.0927 0.2387
0.2938 (0.1206) (0.0037) (0.0610)
(0.0226) (0.4668) (0.4317)
-0.7488 -6.4577 6.8844 4.0967
0.5112 0.6805
GAMMA OCC3 OCC4
-------- -------- RELIG
0.4312 0.3988 (0.3019)
(0.3000) 1.4285 1.3290
MORAL -0.0230 0.2741 (0.4412)
(0.4386)
GAMMA OCC3 OCC4
-------- -------- RELIG
-0.1334 -0.2529 (0.3125)
(0.3123) -0.4269 -0.8097
MORAL -0.0750 0.0260 (0.4065)
(0.4063) -0.1846 0.0640
42
(insert AMOS demo here)