Session 8: Running Group-Comparison of CFA using AMOS

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Running a General SEM controlling for Clustering and Nonequal
Sampling Weights with Mplus
Note: This example employs the National Survey of Child and Adolescent Well-Being
(NSCAW) data. Because this is not a publically released data, we cannot include the
data file in the Website.
In this example, you will learn: (1) basic features of Mplus, (2) how to run a general SEM to
control for clustering effects using Huber’s robust estimator, (3) how to run a general SEM
that is based on different sampling weights, (4) how to conduct multiple group comparison
for a general SEM, and (5) how to conduct the Satorra-Bentler scaled chi-square difference
test.
Overview of Mplus
Nice features:
 Very quick and helpful response from Linda Muthen ([email protected])
 Handle categorical variable
 Do missing data imputation
 Non-linear function
 Allow you to run Mixture modeling (latent class model: categorical latent variable but
continuous indicator variables)
 Growth curve modeling
 Monte Carlo
 Allow you to use sampling weights and correct for clustering effects (marginal model
adjust S.E.)
 And many more!!
Ten commands of Mplus:
 TITLE
 DATA (Required)
 VARIABLE (Required)
 DEFINE
 ANALYSIS
 MODEL
 OUTPUT
 SAVEDATA
 PLOT
 MONTECARLO
Key words: ON, BY, WITH, *, @.
[Example] NSCAW – Change of well-being from baseline to 18 months (Aged 6-10 compared
to Aged 11+)
Mplus for Bowen & Guo SEM
page 1
Why Mplus? - Need to Run SEM With Complex Sample Data
The NSCAW employed a stratified two-stage sampling design, with the Primary Sampling
Units (PSUs) being county CPS agencies (92 agencies) and the Secondary Sampling Units being
selected from lists of closed investigations or assessments from the sampled agencies (NSCAW
Research Group, 2002). This design requires that analysis of NSCAW data should: (1) employ
weights so that we can generalize findings from the sample to the target population; and (2) control
for non-independence within PSU or clustering when performing tests of statistical significance.
Among popular software programs specially designed for SEM analysis (i.e., AMOS,
LISREL, EQS, and Mplus), Mplus is the only one that can partially meet our needs. This software
package takes clustering into consideration by computing standard errors using the sandwich
estimator - know as Taylor expansion of Huber-White (Muthen & Satorra, 1995), as well as allows
users to incorporate sampling weights into statistical inference.
Research question:
Same question as that for Session 10: whether children from different age groups share the same
structural change of well-being over time? That is, whether age moderates the structural change of
well-being?
Descriptive statistics and variable transformation:
___________________________________________________________________________________________________________________
Statistics Before Transformation
Variable
_____________________________Transformation
Name
Description
Mean
Range
Variance
Method
______________
______________________________________________________ ________ ________ ________ _____________
Ages 6-10
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Y13
Academic achivement math - MBA Baseline
Social skills - SSRS Baseline
Behavior - CBCL Total Baseline
Caregiver physical health - SF12 Baseline
Caregiver mental health - SF12 Baseline
Risk assessment on caregiver Baseline: 1=low, 2, 3=high
Income as % of poverty threshold Baseline: 1=poverty line
% time in Out-of-home (OOH) care baseline to 18-months
Ever received outpatient mental service: 1=Yes, 2=No
Ever received inpatient mental service: 1=Yes, 2=No
Academic achivement math - MBA 18-months
Social skills - SSRS 18-months
Behavior - CBCL Total 18-months
93.26
87.92
59.18
47.47
47.76
2.01
1.42
0.17
1.68
1.95
92.53
90.21
57.28
0 - 180
42 - 130
24 - 91
14 - 67
13 - 69
1-3
0.08 - 6.32
0-1
1-2
1-2
0 -164
42 - 130
24 - 91
619.20
261.60
152.10
123.91
132.19
0.70
1.42
0.13
0.22
0.05
489.70
273.47
163.93
Original / 10
Original / 10
Original / 10
Original / 10
Original / 10
No
No
No
ln (Original)
ln (Original)
Original / 10
Original / 10
Original / 10
Ages 11+
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Y13
Academic achivement math - MBA Baseline
Social skills - SSRS Baseline
Behavior - CBCL Total Baseline
Caregiver physical health - SF12 Baseline
Caregiver mental health - SF12 Baseline
Risk assessment on caregiver Baseline: 1=low, 2, 3=high
Income as % of poverty threshold Baseline
% time in Out-of-home (OOH) care baseline to 18-months
Ever received outpatient mental service: 1=Yes, 2=No
Ever received inpatient mental service: 1=Yes, 2=No
Academic achivement math - MBA 18-months
Social skills - SSRS 18-months
Behavior - CBCL Total 18-months
90.62
91.24
60.73
47.37
47.50
1.97
1.51
0.18
1.67
1.89
91.01
92.53
58.84
0 - 171
54 - 130
23 - 89
13 - 65
13 - 70
1-3
0.07 - 6.32
0-1
1-2
1-2
21 - 171
54 - 130
23 - 87
393.62
252.81
149.95
120.34
130.31
0.65
1.55
0.12
0.22
0.10
349.16
257.13
144.81
Original / 10
Original / 10
Original / 10
Original / 10
Original / 10
No
No
No
ln (Original)
ln (Original)
Original / 10
Original / 10
Original / 10
Mplus for Bowen & Guo SEM
page 2
[Step 1]: The baseline model to test the hypothesis about “same form”:
The Mplus syntax:
TITLE: Group comparison Run 1 - Same Form
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON C_SVS*-2;
CHILD_3 ON CHILD_B*.41;
CHILD_3 ON CG_B*-.02;
C_SVS ON CHILD_B*-.042;
CHILD_B WITH CG_B*.107;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
CHILD_3 ON C_SVS*-2 CHILD_B*.41 CG_B*-.02;
C_SVS ON CHILD_B*-.042;
CHILD_B WITH CG_B*.06;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
____________________________________________________________________________________
Notes about Mplus syntax:
 “GROUPING IS age11 (0=g1 1=g2)” specifies that AGE11 is the grouping variable with
0=group1(age 6-10) and 1=group2 (age11+). The data file stack the two group data in one
file with one variable “AGE11” indicates group membership.
 “CLUSTER IS nscawpsu; WEIGHT IS w;” specifies the variable indicating PSU membership
and the variable indicating sampling weights.
 “ANALYSIS: TYPE IS COMPLEX;” requires the control of clustering effects using “sandwich”;
Mplus for Bowen & Guo SEM
page 3






BY: a latent variable points to an indicator variable;
WITH: correlational relation (similar to a two double-headed curve line);
ON: An endogenous variable regresses on one or more exogenous variables;
@: fixes the value to a given number;
*: specifies starting value.
“Model g2:…” relaxes equality constraints to allow the group has its own effects on the
specified parameters.
Same Form Model
Group 1: Children Aged 6-10 at Baseline
Selected Coefficients Are Shown
(+p<.1,*p<.05,**p<.01,***p<.001)
d1
d2
1
y1
d8
d3
1
y2
d9
1
1
d10
d1
d2
1
1
1
1
y8
y3
Same Form Model
Group 2: Children Aged 11+ at Baseline
Selected Coefficients Are Shown
(+p<.1,*p<.05,**p<.01,***p<.001)
y9
y10
y1
1
1
Child Well-being
Baseline
Child Service Use
Baseline to 18 Months
.853***
1
d4
1
y9
y10
1
z1
1
-0.031
Child Service Use
Baseline to 18 Months
.387*
-4.868
-4.049
0.012
1
y4
d10
1
y8
y3
Child Well-being
Baseline
.118*
1
y2
d9
1
1
1
z1
1
-0.033
d8
d3
Caregiver's
Characteristics
at Baseline
-0.141
z2
1
Child Well-being
18 Months
1
1
y5
1
d5
y6
1
d6
y7
1
d7
y11
y12
y13
1
1
1
d11
d12
d13
y4
Caregiver's
Characteristics
at Baseline
-.100
z2
Child Well-being
18 Months
1
y5
1
1
d4
d5
y6
1
d6
y7
y11
y12
y13
1
1
1
d11
d12
d13
1
d7
Results show that we can accept the “same form” hypothesis, because the model has a
reasonably good fit to data: 2M (125) = 298.405, p<.001, Normed Chi-square = 2.39,
CGI=.910, RMSEA=.041.
The Satorra-Bentler scaled chi-square difference test (TRD)
Mplus prints out the following chi-square information with a warning message:
Chi-Square Test of Model Fit
Value
298.405*
Degrees of Freedom
125
P-Value
0.0000
Scaling Correction Factor
2.647
for MLR
*
The chi-square value for MLM, MLMV, MLR, WLSM and WLSMV cannot be used for
chi-square difference tests. MLM, MLR and WLSM chi-square difference
testing is described in the Mplus Technical Appendices at www.statmodel.com.
Mplus for Bowen & Guo SEM
page 4
See chi-square difference testing in the index of the Mplus User's Guide.
As the warning message indicates, you cannot perform chi-square difference test as you normally
would do. You must instead use the Satorra-Bentler scaled chi-square difference test (TRD). The
formula for calculating TRD can be expressed below (for details, see
http://www.statmodel.com/chidiff.shtl):
d 0 * c0  d1 * c1
T 0  T1
, TRD 
d 0  d1
cd
where 0 indicates the nested model, and 1 indicates the comparison model, or:
cd 
For the nested model:
d0 – degree of freedom;
c0 – the scaling correction factor;
T0 – the chi-square value;
For the comparison model:
d1 – degree of freedom
c1 – the scaling correction factor;
T1 – the chi-square value.
[Step 2]: Test the “same gamma” hypothesis by constraining the gamma coefficients to be equal
between the two groups.
The Mplus syntax:
TITLE: Group comparison Run 2 - Same Gamma
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON C_SVS*-2;
CHILD_3 ON CHILD_B*.41 (1);
CHILD_3 ON CG_B*-.02 (2);
C_SVS ON CHILD_B*-.042 (3);
CHILD_B WITH CG_B*.107;
Y1 WITH Y11;
Y2 WITH Y12;
Mplus for Bowen & Guo SEM
page 5
Y3 WITH Y13;
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
CHILD_3 ON C_SVS*-2;
CHILD_B WITH CG_B*.06;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
_____________________________________________________________________________________
Note:
The following commands equalize parameters between groups:
CHILD_3 ON CHILD_B*.41 (1);
CHILD_3 ON CG_B*-.02 (2);
C_SVS ON CHILD_B*-.042 (3);
Mplus prints out the following chi-square information:
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
Scaling Correction Factor
for MLR
302.735*
128
0.0000
2.644
When compare Model 2 (same gamma) with Model 1 (same form), Model 2 is the nested model
(with T0, d0, c0) and Model 1 is the comparison model (with T1, d1, c1). We can calculate TRD
as follows:
cd 
d 0 * c0  d1 * c1 128 * 2.644  125 * 2.647 338.432  330.875


 2.519
d 0  d1
128  125
3
T 0  T 1 302.735  298.405 4.33


 1.7189 , the p-value of TRD can be obtained
cd
2.519
2.519
through the Excel function “=chidist(1.7189,3)”, which returns a value of 0.632732. Since this is
not significant, we can accept the “same gamma” hypothesis.
and TRD 
Repeating the above procedure, we can sequentially accept a series of hypotheses.
[Step 3]: Test the “same beta” hypothesis by constraining the beta coefficient to be equal between
the two groups.
The Mplus syntax:
TITLE: Group comparison Run 3 Same Beta
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
Mplus for Bowen & Guo SEM
page 6
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON C_SVS*-2 (1);
CHILD_3 ON CHILD_B*.41;
CHILD_3 ON CG_B*-.02;
C_SVS ON CHILD_B*-.042;
CHILD_B WITH CG_B*.107;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
CHILD_3 ON CHILD_B*.41;
CHILD_3 ON CG_B*-.02;
C_SVS ON CHILD_B*-.042;
CHILD_B WITH CG_B*.06;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
_____________________________________________________________________________________
[Step 4]: Test the “same gamma & same beta” hypothesis by constraining the gamma and beta
coefficients to be equal between the two groups.
The Mplus syntax:
TITLE: Group comparison Run 4 - Same Gamma & Beta
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
Mplus for Bowen & Guo SEM
page 7
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON CHILD_B*.41 (1);
CHILD_3 ON CG_B*-.02 (2);
C_SVS ON CHILD_B*-.042 (3);
CHILD_3 ON C_SVS*-2 (4);
CHILD_B WITH CG_B*.107;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
CHILD_B WITH CG_B*.06;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
_____________________________________________________________________________________
[Step 5]: Test the “same gamma, same beta, and same psi” hypothesis by constraining the gamma,
beta coefficients and the variances of the structural disturbance terms to be equal
between the two groups.
The Mplus syntax:
TITLE: Group comparison Run 5 - Same Gamma, Beta, & Psi
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON CHILD_B*.41 (1);
Mplus for Bowen & Guo SEM
page 8
CHILD_3 ON CG_B*-.02 (2);
C_SVS ON CHILD_B*-.042 (3);
CHILD_3 ON C_SVS*-2 (4);
CHILD_B WITH CG_B*.107;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
C_SVS (5);
CHILD_3 (6);
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
CHILD_B WITH CG_B*.06;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
_____________________________________________________________________________________
[Step 6]: Test the “same gamma, same beta, same psi, and same phi” hypothesis by constraining
the gamma, beta coefficients, the variances of the structural disturbance terms, and the
variances-covariances of the exogenous factors to be equal between the two groups.
The Mplus syntax:
TITLE: Group comparison Run 6 - Same Gamma, Beta, Psi, & Phi
DATA:
FILE IS C:C:\Documents and Settings\SGUO\Desktop\NSEM\gcomp.dat;
FORMAT IS 2F8.0, F14.6, 14F8.2;
VARIABLE:
NAMES ARE nscawid nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
USEVARIABLES ARE nscawpsu w y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 age11;
GROUPING IS age11 (0 = g1 1 = g2);
CLUSTER IS nscawpsu;
WEIGHT IS w;
ANALYSIS:
TYPE IS COMPLEX;
ITERATIONS = 10000;
CONVERGENCE = 0.00005;
OUTPUT: SAMPSTAT STANDARDIZED tech1;
MODEL:
CHILD_B BY [email protected] y2*2.564 y3*-.916;
CG_B BY [email protected] y5*.351 y6*-.451 y7*1.101;
C_SVS BY [email protected] y9*-5 y10*-3;
CHILD_3 BY [email protected] y12*4.62 y13*-.079;
CHILD_3 ON CHILD_B*.41 (1);
CHILD_3 ON CG_B*-.02 (2);
C_SVS ON CHILD_B*-.042 (3);
CHILD_3 ON C_SVS*-2 (4);
CHILD_B WITH CG_B*.107 (9);
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
Mplus for Bowen & Guo SEM
page 9
C_SVS (5);
CHILD_3 (6);
CHILD_B (7);
CG_B (8);
MODEL g2:
CHILD_B BY [email protected] y2*2.399 y3*-.768;
CG_B BY [email protected] y5*1.9 y6*-.4 y7*-.5;
C_SVS BY [email protected] y9*-3.7 y10*-3;
CHILD_3 BY [email protected] y12*3 y13*-1.5;
Y1 WITH Y11;
Y2 WITH Y12;
Y3 WITH Y13;
[email protected];
[email protected];
_____________________________________________________________________________________
Mplus for Bowen & Guo SEM
page 10
The above tests are summarized by the following table:
Step
1
2
3
4
5
6
Hypothesis
Same form
Same gamma
Same beta
Same gamma & beta
Same gamma, beta, & psi
Same gamma, beta, psi, & phi
Chi-square df
298.405
302.735
298.948
303.153
307.177
313.485
Comparison
2 vs 1
3 vs 1
4 vs 1
5 vs 4
6 vs 5
d0*c0
d1*c1
d0-d1 cd
338.432 330.875
3
2.519
333.018 330.875
1
2.143
340.689 330.875
4
2.4535
345.447 340.689
2
2.379
357.512 345.447
3 4.021667
125
128
126
129
131
134
Correction
2.647
2.644
2.643
2.641
2.637
2.668
TRD
1.718936
0.253383
1.935195
1.691467
1.568504
p-value
0.632732
0.614703
0.747677
0.429242
0.666552
Decision
Accepted
Accepted
Accepted
Accepted
Accepted
Thus, we have obtained our final model:
Same Form, Gamma, Beta, Psi, & Phi
Bothe Groups
Selected Coefficients Are Shown
(+p<.1,*p<.05,**p<.01,***p<.001)
d1
d2
1
1
y1
d8
d3
1
y2
d9
1
y8
y3
d10
1
1
y9
y10
1
1
Child Well-being
Baseline
z1
1
-.033*
Child Service Use
Baseline to 18 Months
.604***
-4.490+
.036*
1
1
y4
1
d4
Caregiver's
Characteristics
at Baseline
-0.102
z2
Child Well-being
18 Months
1
y5
1
d5
y6
1
d6
y7
1
d7
y11
y12
y13
1
1
1
d11
d12
d13
Conclusion: The multiple-group comparison about children’s change of well-being over time
confirms that young children (aged 6-10) did not follow a different pattern than old children (aged
Mplus for Bowen & Guo SEM
page 11
11+0). In other words, age does not moderate relationships among variables describing children’s
change of well-being.
The correction of Mplus on clustering effects and on using sampling weights resulted in very
different findings from those of AMOS (See Session 10.doc). This illustrates the importance of
using special software when analyzing survey data with a complex design of sampling!
Reference
Muthen, B., & Satorra, A. (1995). “Complex sample data in structural equation modeling”, in P.V.
Marsden (Ed.), Sociological Methodology (pp. 267-316). Washington D.C.: The American
Sociological Association.
Mplus for Bowen & Guo SEM
page 12
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