Session 8: Running Group-Comparison of CFA using AMOS
Running a General SEM controlling for Clustering and Nonequal
Sampling Weights with MplusNote: 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 Hubers 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+)
Why Mplus? - Need to Run SEM With Complex Sample DataThe 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:
[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 y1@1 y2*2.564 y3*-.916;
CG_B BY y4@1 y5*.351 y6*-.451 y7*1.101;
C_SVS BY y8@1 y9*-5 y10*-3;
CHILD_3 BY y11@1 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 y1@1 y2*2.399 y3*-.768;
CG_B BY y4@1 y5*1.9 y6*-.4 y7*-.5;
C_SVS BY y8@1 y9*-3.7 y10*-3;
CHILD_3 BY y11@1 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;
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.
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
