General Structural Equation (LISREL) Models

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General Structural Equation (LISREL) ModelsGeneral Structural Equation (LISREL) Models

Week 3 #1 Week 3 #1 Multiple Group ModelsMultiple Group ModelsAn extended multiple-group model: An extended multiple-group model: Religiosity & Sexual Morality in 2 countries Religiosity & Sexual Morality in 2 countries (LISREL example) (LISREL example) Computer programming for multiple-group Computer programming for multiple-group models: a) LISREL b) AMOSmodels: a) LISREL b) AMOS

–See Week3ExamplesSee Week3Examples

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MOST IMPORTANT FORM OF CONSTRAINT INVOLVES CONSTRAINING PARAMETERS ACROSS GROUPS

1

1 1 1

1

1 1 1

b1

1

1 1 1

1

1 1 1

b1

Group 1

Group 2

Constraint: b1group1 = b1group2

From last Friday 3

Multiple Group Models

Group 1 (male)Group 2 (female)

Equivalence of measurement coefficients

H0: Λ[1] = Λ[2]

lambda 1 [1] = lambda 1 [2] df=2

lambda 2 [1] = lambda 2 [2]

Eta1[1]

y111

y2ly1[1] 1

y3

ly2[1]1

Eta1[2]

y1

y2

y3

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ly1[2] 1

ly2[2]1

From last Friday 4

Multiple Group Models

Eta1[1]

y1 e111

y2 e2ly1[1] 1

y3 e3

ly2[1]1

Eta1[2]

y1 e1

y2 e2

y3 e3

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ly1[2] 1

ly2[2]1

Other equivalence tests possible:

1. Equivalence of variances of latent variables

H0: PSI-1[1] = PSI-1[2]

• This test will depend upon which ref. indicator used

2. Equivalence of error variances *

H0: Theta-eps[1] = Theta-eps[2] {entire matrix}

df=3 *and covariances if there are correlated errors

From last Friday 5

Multiple Group Models

Measurement model equivalence does not imply same mean levelsMeasurement 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 gov’t .80 2.3 .78 3.9 Govern. Corrupt -.75 3.8 -.80 2.3 Politicians don’t

care (where 1=agree strongly through 10=disagree

strongly)

From last Friday 6

Multiple Group Models

Eta1

y11

1

y2lambda-1 1

y3lambda-2 1

y4

lambda-3

1

• 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, I’d 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):

lambda1[1] = lambda1[2]

lambda2[1] = lambda2[2]

BUT

lambda3[1] ≠ lambda3[2]

From last Friday 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….

Eta1

y1lambda-1

1

y2lambda-2 1

y3lambda-3 1

y4

lambda-4

1

From last Friday 8

Multiple Group ModelsGroup 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:

Eta1

y1lambda-1

1

y2lambda-2 1

y3lambda-3 1

y4

lambda-4

1

Gr 1 Gr 2

Lambda1 2.0 1.0

Lambda2 1.0* 1.0*

Lambda3 1.5 1.5

Lambda4 2.0 2.0

From last Friday 9

Multiple Group Models

Modification Indices and what they mean in multiple-group models

Assuming LY[1] = LY[2]

(entire matrix)

Eta1

y11

1

y2lambda-1 1

y3lambda-2 1

y4

lambda-3

1

Example:

MODIFICATION INDICES:

Group 1 Group 2

Eta 1 Eta 1

Y1 --- Y1 ---

Y2 .382 Y2 .382

Y3 1.24 Y3 1.24

Y4 45.23 Y4 45.23

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Multiple Group Models

Modification Indices and what they mean in multiple-group models

Assuming LY[1] = LY[2]

(entire matrix)

Eta1

y11

1

y2lambda-1 1

y3lambda-2 1

y4

lambda-3

1

Example:

MODIFICATION INDICES:

Group 1 Group 2

Eta 1 Eta 1

Y1 --- Y1 ---

Y2 .382 Y2 .382

Y3 1.24 Y3 1.24

Y4 45.23 Y4 45.23

Improvement in chi-square if equality constraint released

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Multiple Group Models : Modification Indices

eta1

y111

y2lambda-2 1

y3lambda-3 1

eta2

y4

y5

y6

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lambda-4 1

lambda-5 1

MODIFICATION Group 1 Group 2

INDICES eta1 eta2 eta1 eta2

Y1 --- 2.42 --- 3.89Y2 1.42 3.44 1.42 1.01Y3 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

lambda5[1]=lambda5[2]

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Multiple Group Models : Modification Indices

eta1

y111

y2lambda-2 1

y3lambda-3 1

eta2

y4

y5

y6

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lambda-4 1

lambda-5 1

MODIFICATION Group 1 Group 2

INDICES eta1 eta2 eta1 eta2

Y1 --- 2.42 --- 3.89Y2 1.42 3.44 1.42 1.01Y3 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

lambda5[1]=lambda5[2]Wald test (MI) for adding

parameter LY(3,3) to the model in group 2 only

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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

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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: Group1=Group2=Group3 Group1=Group2≠Group3 Group1 ≠ Group2≠Group3

Must be careful about interpretation of Modification Indices In a model with [1]=[2]=[3] ≠ 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)

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MULTIPLE GROUP MODELS: Modification Indices (again)

Eta1

y11

1

y2lambda-1 1

y3lambda-2 1

y4

lambda-3

1

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

Model: LY[1]=LY[2]=LY[3]

Free LY(2,1) in group 3 but

LY(2,1) in group 1 = LY(2,1) in group 2

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When do we have measurement equivalence STRONG equivalence:

all matrices identical, all groups (might possibly exclude variance of LV’s 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

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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

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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)

1

1 1 1

1

1 1 1

gamma1[1]

1

1

1 1 1

1

1 1 1

gamma1[2]

1

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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 NG=2 NI=23 NO=1246NI specification (# of input var’s) applies onlyto group 1NO specification (# of observations) applies only to group 1

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LISREL PROGRAMMING FOR MULTIPLE GROUP MODELS

DA NG=2 …Specify group 1 model as usualTitle for Group 2DA statement group 2 NI= NO=CM FI= [location of group 2 cov mtx]SE1 3 4 6 8 / LABELS [optional]MO NY= NX= NK= NE= + special options for matrix

specificationOU (as usual)

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LISREL PROGRAMMING: MULTIPLE GROUPS

MO specification:LY=PS same pattern as prev. group

- for example, if group 1 specifies 2 LV’s 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

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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.) LY=FU,FI

VA 1.0 LY 2 1 FR LY 2 1 LY 3 1 LY 4 1

Group 2 LY=PS EQ LY 1 2 1 LY 2 2 1 EQ LY 1 3 1 LY 3 1

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LISREL PROGRAMMING: MULTIPLE GROUPS

Releasing equality constraints on a single parameter when matrix is otherwise specified as Invariant:

Group 2:LY=INFR LY 4 1 LY remains invariant

except for parameter LY(4,1)

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Examples: Example (separate handouts) (religion & sexual morality in 2 countries)

Multiple group example #1: USA DA NO=1150 NI=19 MA=CM NG=2 CM FI=G:\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/ MO NY=8 NE=2 LY=FU,FI PS=SY,FR TE=SY 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 ND=4 SC MI

Basic program

See handout for variable list

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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 NO=1763 NI=19 MA=CM CM FI=G:\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 LY=IN PS=PS TE=PS OU ND=4 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

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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

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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

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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

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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 2.3763Group #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

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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

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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

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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

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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

Covariance Matrix of ETA

ETA 1 ETA 2 -------- -------- ETA 1 1.1410 ETA 2 0.6090 1.0544

More variance in Canada

Connection stronger in Canada

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Testing measurement equivalence

Group #2: Canada DA NO=1763 NI=19 MA=CM CM FI=G:\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 LY=PS PS=PS TE=PS OU ND=4 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

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Some Model/Test Results:Matrices Chi-square df IFI

TwoGroup1b LY=IN 233.653 42 .987TwoGroup1c LY=PS 209.778 36 .988TwoGroup1d LY=IN PS=IN 272.740 45 .984TwoGroup1e LY=IN PS=IN but 267.472 44 .985

PS 2,1 free

From TwoGroup1d, in Group #2 (Canada):Modification 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

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Models with exogenous variables in construct equations:

Multiple group example #1: USA DA NO=1150 NI=19 MA=CM NG=2 CM FI=G:\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 NY=8 NE=2 LY=FU,FI PS=SY,FR TE=SY NX=4 NK=4 LX=ID C PH=SY,FR TD=ZE GA=FU,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 ND=4 SC MI

Group #2: Canada DA NO=1763 NI=19 MA=CM CM FI=G:\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 LY=IN PS=PS TE=PS LX=IN PH=PS TD=IN GA=PS LE RELIG MORAL OU ND=4 SC MI

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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

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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 -0.5080Group #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

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Models/TestsModel Description Chi-square df CFIGroup2A LY=IN GA=PS 645.0492 90 .968Group2B LY=IN GA=IN 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

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Model Description Chi-square df CFIGroup3AGA=IN 747.942 154 .971Group3BGA=PS 712.264 138 .972Group3C GA=IN 739.907 146 .971

Free occ. in group 2Group3D GA=PS 720.507 146 .972

Occ FI in group 2Group3EGA=PS 731.286 154 .972

Occ Fi both groupsGroup3F GA=PS 715.659 142 .972

Occ coefficients = For 1st Eta variable

Tests: Group3A vs. Group 3B Equality of all GA coefficientsGroup 3A vs Group 3B Equality of occupation GA coefficientsGroup 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.

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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

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(insert AMOS demo here)