LGM with two groups
Message/Author
 daniel posted on Tuesday, August 19, 2003 - 5:06 am
I ran the following model and obtained the following results. How would I compare specific path coefficients for significant differences between the two groups? FOr instance, I am interested in knowing whether the values for the path from rlevel to slevel are significantly different between the two groups. How would I do that given my data is ordered-categorical?

variable: names are id race gender
smoke9 smoke10f smoke10s smoke11
soma9 depaff9 posaff9 interp9
soma10 depaff10 posaff10 interp10
soma11 depaff11 posaff11 interp11
totdep9 totdep10 totdep11
recep9 recep10 recep11 expose9;
missing are .;
idvariable is id;
grouping totdep9 (0=low 1=high);
usevariables are smoke9-smoke11
recep9-recep11 gender race expose9;
categorical are smoke9-smoke11
recep9-recep11;
define: cut smoke9-smoke11 (0 2);
cut totdep9 (16);
Analysis: Type=meanstructure;
iterations = 20000;
model: slevel by smoke9-smoke11@1;
strend by smoke9@0 smoke10f@1
smoke10s@1.422 smoke11@2.099;
rlevel by recep9-recep11@1;
rtrend by recep9@0 recep10@1 recep11@2;
strend on slevel rlevel rtrend;
slevel on rlevel;
rtrend on slevel;
strend rtrend on gender-expose9;
slevel rlevel on gender-expose9;
[smoke9\$1 smoke10f\$1 smoke10s\$1 smoke11\$1] (4);
[smoke9\$2 smoke10f\$2 smoke10s\$2 smoke11\$2] (5);
[slevel@0 strend];
{smoke9@1 smoke10f smoke10s smoke11};
[recep9\$1 recep10\$1 recep11\$1] (1);
[recep9\$2 recep10\$2 recep11\$2] (2);
[recep9\$3 recep10\$3 recep11\$3] (3);
[rlevel@0 rtrend];
{recep9@1 recep10 recep11};
model high: strend@.067;

output: tech4 standardized cinterval;

SUMMARY OF ANALYSIS

Number of groups 2
Number of observations
Group LOW 668
Group HIGH 290

Number of y-variables 7
Number of x-variables 3
Number of continuous latent variables 4

Observed variables in the analysis
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11 GENDER RACE EXPOSE9

Grouping variable TOTDEP9
ID variable ID

Categorical variables
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11

Continuous latent variables in the analysis
SLEVEL STREND RLEVEL RTREND

Estimator WLSMV
Maximum number of iterations 20000
Convergence criterion 0.500D-04
Parameterization DELTA

Input data file(s)

Input data format FREE

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 72.855*
Degrees of Freedom 22**
P-Value 0.0000

* The chi-square value for MLM, MLR, MLMV, MUMLM, MUMLMV, WLSM and WLSMV
cannot be used for chi-square difference tests. MLM and MLR chi-square
difference testing is described on page 360 in the Mplus User's Guide.

** The degrees of freedom for MLMV and WLSMV are estimated according to
formula 110 (page 358) in the Mplus User's Guide.

Chi-Square Test of Model Fit for the Baseline Model

Value 19692.277
Degrees of Freedom 31
P-Value 0.0000

CFI/TLI

CFI 0.997
TLI 0.996

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.069

WRMR (Weighted Root Mean Square Residual)

Value 1.267

MODEL RESULTS

Estimates S.E. Est./S.E. Std StdYX

Group LOW

SLEVEL BY
SMOKE9 1.000 0.000 0.000 1.093 0.988
SMOKE10F 1.000 0.000 0.000 1.093 1.001
SMOKE10S 1.000 0.000 0.000 1.093 1.005
SMOKE11 1.000 0.000 0.000 1.093 1.013

STREND BY
SMOKE9 0.000 0.000 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000 0.202 0.185
SMOKE10S 1.422 0.000 0.000 0.287 0.264
SMOKE11 2.099 0.000 0.000 0.424 0.393

RLEVEL BY
RECEP9 1.000 0.000 0.000 0.762 0.732
RECEP10 1.000 0.000 0.000 0.762 0.733
RECEP11 1.000 0.000 0.000 0.762 0.734

RTREND BY
RECEP9 0.000 0.000 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000 0.209 0.201
RECEP11 2.000 0.000 0.000 0.418 0.402

STREND ON
SLEVEL -0.058 0.025 -2.362 -0.315 -0.315
RLEVEL 0.039 0.040 0.975 0.149 0.149
RTREND 0.380 0.251 1.514 0.393 0.393

SLEVEL ON
RLEVEL 0.463 0.094 4.920 0.323 0.323

RTREND ON
SLEVEL -0.013 0.030 -0.429 -0.067 -0.067

STREND ON
GENDER 0.037 0.040 0.929 0.183 0.091
RACE -0.060 0.045 -1.340 -0.298 -0.138
EXPOSE9 -0.004 0.043 -0.089 -0.019 -0.010

RTREND ON
GENDER -0.025 0.049 -0.508 -0.118 -0.059
RACE 0.051 0.051 0.990 0.244 0.113
EXPOSE9 -0.028 0.057 -0.486 -0.132 -0.066

SLEVEL ON
GENDER 0.051 0.107 0.474 0.046 0.023
RACE 0.074 0.110 0.673 0.067 0.031
EXPOSE9 0.738 0.115 6.419 0.675 0.338

RLEVEL ON
GENDER -0.411 0.082 -4.997 -0.539 -0.270
RACE -0.081 0.087 -0.932 -0.106 -0.049
EXPOSE9 0.425 0.083 5.139 0.557 0.279

Intercepts
SLEVEL 0.000 0.000 0.000 0.000 0.000
STREND 0.000 0.000 0.000 0.000 0.000
RLEVEL 0.000 0.000 0.000 0.000 0.000
RTREND 0.000 0.000 0.000 0.000 0.000

Thresholds
SMOKE9\$1 0.561 0.072 7.772 0.561 0.561
SMOKE9\$2 2.061 0.092 22.427 2.061 2.061
SMOKE10F\$1 0.561 0.072 7.772 0.561 0.561
SMOKE10F\$2 2.061 0.092 22.427 2.061 2.061
SMOKE10S\$1 0.561 0.072 7.772 0.561 0.561
SMOKE10S\$2 2.061 0.092 22.427 2.061 2.061
SMOKE11\$1 0.561 0.072 7.772 0.561 0.561
SMOKE11\$2 2.061 0.092 22.427 2.061 2.061
RECEP9\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP9\$2 0.111 0.058 1.917 0.111 0.111
RECEP9\$3 0.444 0.059 7.481 0.444 0.444
RECEP10\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP10\$2 0.111 0.058 1.917 0.111 0.111
RECEP10\$3 0.444 0.059 7.481 0.444 0.444
RECEP11\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP11\$2 0.111 0.058 1.917 0.111 0.111
RECEP11\$3 0.444 0.059 7.481 0.444 0.444

Residual Variances
SLEVEL 0.865 0.051 17.125 0.724 0.724
STREND 0.030 0.013 2.250 0.727 0.727
RLEVEL 0.498 0.030 16.435 0.857 0.857
RTREND 0.042 0.015 2.770 0.974 0.974

Scales
SMOKE9 1.000 0.000 0.000 1.000 1.000
SMOKE10F 1.000 0.000 0.000 1.000 1.000
SMOKE10S 1.000 0.000 0.000 1.000 1.000
SMOKE11 1.000 0.000 0.000 1.000 1.000
RECEP9 1.000 0.000 0.000 1.000 1.000
RECEP10 1.000 0.000 0.000 1.000 1.000
RECEP11 1.000 0.000 0.000 1.000 1.000

Group HIGH

SLEVEL BY
SMOKE9 1.000 0.000 0.000 1.073 0.944
SMOKE10F 1.000 0.000 0.000 1.073 0.859
SMOKE10S 1.000 0.000 0.000 1.073 0.793
SMOKE11 1.000 0.000 0.000 1.073 0.688

STREND BY
SMOKE9 0.000 0.000 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000 0.355 0.284
SMOKE10S 1.422 0.000 0.000 0.505 0.373
SMOKE11 2.099 0.000 0.000 0.745 0.478

RLEVEL BY
RECEP9 1.000 0.000 0.000 0.804 0.785
RECEP10 1.000 0.000 0.000 0.804 0.625
RECEP11 1.000 0.000 0.000 0.804 0.719

RTREND BY
RECEP9 0.000 0.000 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000 0.356 0.276
RECEP11 2.000 0.000 0.000 0.711 0.636

STREND ON
SLEVEL 0.197 0.094 2.101 0.596 0.596
RLEVEL -0.149 0.076 -1.968 -0.336 -0.336
RTREND 0.532 0.246 2.162 0.533 0.533

SLEVEL ON
RLEVEL 0.550 0.099 5.555 0.412 0.412

RTREND ON
SLEVEL -0.065 0.050 -1.299 -0.197 -0.197

STREND ON
GENDER 0.121 0.089 1.359 0.340 0.164
RACE -0.120 0.094 -1.280 -0.339 -0.163
EXPOSE9 -0.041 0.115 -0.354 -0.114 -0.055

RTREND ON
GENDER -0.110 0.073 -1.502 -0.309 -0.149
RACE 0.109 0.078 1.401 0.305 0.147
EXPOSE9 0.199 0.089 2.223 0.559 0.271

SLEVEL ON
GENDER -0.435 0.143 -3.042 -0.406 -0.196
RACE 0.305 0.162 1.888 0.285 0.137
EXPOSE9 0.769 0.188 4.098 0.717 0.348

RLEVEL ON
GENDER -0.104 0.134 -0.771 -0.129 -0.062
RACE -0.211 0.131 -1.604 -0.262 -0.126
EXPOSE9 0.411 0.131 3.125 0.511 0.248

Intercepts
SLEVEL 0.000 0.000 0.000 0.000 0.000
STREND -0.010 0.117 -0.087 -0.029 -0.029
RLEVEL 0.000 0.000 0.000 0.000 0.000
RTREND -0.058 0.076 -0.754 -0.162 -0.162

Thresholds
SMOKE9\$1 0.561 0.072 7.772 0.561 0.561
SMOKE9\$2 2.061 0.092 22.427 2.061 2.061
SMOKE10F\$1 0.561 0.072 7.772 0.561 0.561
SMOKE10F\$2 2.061 0.092 22.427 2.061 2.061
SMOKE10S\$1 0.561 0.072 7.772 0.561 0.561
SMOKE10S\$2 2.061 0.092 22.427 2.061 2.061
SMOKE11\$1 0.561 0.072 7.772 0.561 0.561
SMOKE11\$2 2.061 0.092 22.427 2.061 2.061
RECEP9\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP9\$2 0.111 0.058 1.917 0.111 0.111
RECEP9\$3 0.444 0.059 7.481 0.444 0.444
RECEP10\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP10\$2 0.111 0.058 1.917 0.111 0.111
RECEP10\$3 0.444 0.059 7.481 0.444 0.444
RECEP11\$1 -0.872 0.059 -14.677 -0.872 -0.872
RECEP11\$2 0.111 0.058 1.917 0.111 0.111
RECEP11\$3 0.444 0.059 7.481 0.444 0.444

Residual Variances
SLEVEL 0.679 0.065 10.433 0.590 0.590
STREND 0.067 0.000 0.000 0.532 0.532
RLEVEL 0.598 0.072 8.285 0.926 0.926
RTREND 0.115 0.051 2.272 0.909 0.909

Scales
SMOKE9 1.000 0.000 0.000 1.000 1.000
SMOKE10F 0.919 0.061 15.134 0.919 0.919
SMOKE10S 0.841 0.068 12.448 0.841 0.841
SMOKE11 0.717 0.071 10.133 0.717 0.717
RECEP9 1.000 0.000 0.000 1.000 1.000
RECEP10 0.796 0.080 9.923 0.796 0.796
RECEP11 0.940 0.072 13.084 0.940 0.940

R-SQUARE

Group LOW

Observed Residual
Variable Variance R-Square

SMOKE9 0.028 0.977
SMOKE10F 0.093 0.922
SMOKE10S 0.097 0.918
SMOKE11 0.074 0.936
RECEP9 0.502 0.536
RECEP10 0.465 0.569
RECEP11 0.343 0.682

Latent
Variable R-Square

SLEVEL 0.276
STREND 0.273
RLEVEL 0.143
RTREND 0.026

Group HIGH

Observed Residual
Variable Variance R-Square

SMOKE9 0.140 0.892
SMOKE10F 0.023 0.985
SMOKE10S 0.053 0.971
SMOKE11 0.177 0.927
RECEP9 0.402 0.617
RECEP10 0.906 0.453
RECEP11 0.145 0.884

Latent
Variable R-Square

SLEVEL 0.410
STREND 0.468
RLEVEL 0.074
RTREND 0.091

CONFIDENCE INTERVALS OF MODEL RESULTS

Lower 1% Lower 5% Estimates Upper 5% Upper 1%

Group LOW

SLEVEL BY
SMOKE9 1.000 1.000 1.000 1.000 1.000
SMOKE10F 1.000 1.000 1.000 1.000 1.000
SMOKE10S 1.000 1.000 1.000 1.000 1.000
SMOKE11 1.000 1.000 1.000 1.000 1.000

STREND BY
SMOKE9 0.000 0.000 0.000 0.000 0.000
SMOKE10F 1.000 1.000 1.000 1.000 1.000
SMOKE10S 1.422 1.422 1.422 1.422 1.422
SMOKE11 2.099 2.099 2.099 2.099 2.099

RLEVEL BY
RECEP9 1.000 1.000 1.000 1.000 1.000
RECEP10 1.000 1.000 1.000 1.000 1.000
RECEP11 1.000 1.000 1.000 1.000 1.000

RTREND BY
RECEP9 0.000 0.000 0.000 0.000 0.000
RECEP10 1.000 1.000 1.000 1.000 1.000
RECEP11 2.000 2.000 2.000 2.000 2.000

STREND ON
SLEVEL -0.122 -0.107 -0.058 -0.010 0.005
RLEVEL -0.065 -0.040 0.039 0.119 0.143
RTREND -0.266 -0.112 0.380 0.871 1.026

SLEVEL ON
RLEVEL 0.221 0.279 0.463 0.648 0.706

RTREND ON
SLEVEL -0.090 -0.071 -0.013 0.046 0.064

STREND ON
GENDER -0.065 -0.041 0.037 0.115 0.139
RACE -0.176 -0.148 -0.060 0.028 0.056
EXPOSE9 -0.116 -0.089 -0.004 0.081 0.108

RTREND ON
GENDER -0.150 -0.120 -0.025 0.071 0.101
RACE -0.082 -0.050 0.051 0.152 0.184
EXPOSE9 -0.174 -0.139 -0.028 0.084 0.119

SLEVEL ON
GENDER -0.225 -0.159 0.051 0.261 0.327
RACE -0.209 -0.141 0.074 0.289 0.356
EXPOSE9 0.442 0.513 0.738 0.963 1.034

RLEVEL ON
GENDER -0.623 -0.572 -0.411 -0.250 -0.199
RACE -0.304 -0.251 -0.081 0.089 0.142
EXPOSE9 0.212 0.263 0.425 0.587 0.638

Intercepts
SLEVEL 0.000 0.000 0.000 0.000 0.000
STREND 0.000 0.000 0.000 0.000 0.000
RLEVEL 0.000 0.000 0.000 0.000 0.000
RTREND 0.000 0.000 0.000 0.000 0.000

Thresholds
SMOKE9\$1 0.375 0.419 0.561 0.702 0.747
SMOKE9\$2 1.824 1.881 2.061 2.241 2.297
SMOKE10F 0.375 0.419 0.561 0.702 0.747
SMOKE10F 1.824 1.881 2.061 2.241 2.297
SMOKE10S 0.375 0.419 0.561 0.702 0.747
SMOKE10S 1.824 1.881 2.061 2.241 2.297
SMOKE11\$ 0.375 0.419 0.561 0.702 0.747
SMOKE11\$ 1.824 1.881 2.061 2.241 2.297
RECEP9\$1 -1.025 -0.988 -0.872 -0.755 -0.719
RECEP9\$2 -0.038 -0.003 0.111 0.224 0.259
RECEP9\$3 0.291 0.328 0.444 0.561 0.597
RECEP10\$ -1.025 -0.988 -0.872 -0.755 -0.719
RECEP10\$ -0.038 -0.003 0.111 0.224 0.259
RECEP10\$ 0.291 0.328 0.444 0.561 0.597
RECEP11\$ -1.025 -0.988 -0.872 -0.755 -0.719
RECEP11\$ -0.038 -0.003 0.111 0.224 0.259
RECEP11\$ 0.291 0.328 0.444 0.561 0.597

Residual Variances
SLEVEL 0.735 0.766 0.865 0.964 0.995
STREND -0.004 0.004 0.030 0.055 0.064
RLEVEL 0.420 0.439 0.498 0.557 0.576
RTREND 0.003 0.012 0.042 0.072 0.082

Scales
SMOKE9 1.000 1.000 1.000 1.000 1.000
SMOKE10F 1.000 1.000 1.000 1.000 1.000
SMOKE10S 1.000 1.000 1.000 1.000 1.000
SMOKE11 1.000 1.000 1.000 1.000 1.000
RECEP9 1.000 1.000 1.000 1.000 1.000
RECEP10 1.000 1.000 1.000 1.000 1.000
RECEP11 1.000 1.000 1.000 1.000 1.000

Group HIGH

SLEVEL BY
SMOKE9 1.000 1.000 1.000 1.000 1.000
SMOKE10F 1.000 1.000 1.000 1.000 1.000
SMOKE10S 1.000 1.000 1.000 1.000 1.000
SMOKE11 1.000 1.000 1.000 1.000 1.000

STREND BY
SMOKE9 0.000 0.000 0.000 0.000 0.000
SMOKE10F 1.000 1.000 1.000 1.000 1.000
SMOKE10S 1.422 1.422 1.422 1.422 1.422
SMOKE11 2.099 2.099 2.099 2.099 2.099

RLEVEL BY
RECEP9 1.000 1.000 1.000 1.000 1.000
RECEP10 1.000 1.000 1.000 1.000 1.000
RECEP11 1.000 1.000 1.000 1.000 1.000

RTREND BY
RECEP9 0.000 0.000 0.000 0.000 0.000
RECEP10 1.000 1.000 1.000 1.000 1.000
RECEP11 2.000 2.000 2.000 2.000 2.000

STREND ON
SLEVEL -0.045 0.013 0.197 0.381 0.439
RLEVEL -0.343 -0.297 -0.149 -0.001 0.046
RTREND -0.102 0.050 0.532 1.013 1.165

SLEVEL ON
RLEVEL 0.295 0.356 0.550 0.744 0.805

RTREND ON
SLEVEL -0.195 -0.164 -0.065 0.033 0.064

STREND ON
GENDER -0.108 -0.053 0.121 0.295 0.350
RACE -0.362 -0.304 -0.120 0.064 0.122
EXPOSE9 -0.336 -0.265 -0.041 0.184 0.255

RTREND ON
GENDER -0.298 -0.253 -0.110 0.033 0.079
RACE -0.091 -0.043 0.109 0.261 0.308
EXPOSE9 -0.032 0.024 0.199 0.374 0.429

SLEVEL ON
GENDER -0.804 -0.715 -0.435 -0.155 -0.067
RACE -0.111 -0.012 0.305 0.622 0.722
EXPOSE9 0.286 0.401 0.769 1.137 1.253

RLEVEL ON
GENDER -0.450 -0.367 -0.104 0.160 0.243
RACE -0.549 -0.468 -0.211 0.047 0.128
EXPOSE9 0.072 0.153 0.411 0.668 0.749

Intercepts
SLEVEL 0.000 0.000 0.000 0.000 0.000
STREND -0.312 -0.240 -0.010 0.220 0.292
RLEVEL 0.000 0.000 0.000 0.000 0.000
RTREND -0.254 -0.207 -0.058 0.092 0.139

Thresholds
SMOKE9\$1 0.375 0.419 0.561 0.702 0.747
SMOKE9\$2 1.824 1.881 2.061 2.241 2.297
SMOKE10F 0.375 0.419 0.561 0.702 0.747
SMOKE10F 1.824 1.881 2.061 2.241 2.297
SMOKE10S 0.375 0.419 0.561 0.702 0.747
SMOKE10S 1.824 1.881 2.061 2.241 2.297
SMOKE11\$ 0.375 0.419 0.561 0.702 0.747
SMOKE11\$ 1.824 1.881 2.061 2.241 2.297
RECEP9\$1 -1.025 -0.988 -0.872 -0.755 -0.719
RECEP9\$2 -0.038 -0.003 0.111 0.224 0.259
RECEP9\$3 0.291 0.328 0.444 0.561 0.597
RECEP10\$ -1.025 -0.988 -0.872 -0.755 -0.719
RECEP10\$ -0.038 -0.003 0.111 0.224 0.259
RECEP10\$ 0.291 0.328 0.444 0.561 0.597
RECEP11\$ -1.025 -0.988 -0.872 -0.755 -0.719
RECEP11\$ -0.038 -0.003 0.111 0.224 0.259
RECEP11\$ 0.291 0.328 0.444 0.561 0.597

Residual Variances
SLEVEL 0.512 0.552 0.679 0.807 0.847
STREND 0.067 0.067 0.067 0.067 0.067
RLEVEL 0.412 0.457 0.598 0.740 0.784
RTREND -0.015 0.016 0.115 0.214 0.245

Scales
SMOKE9 1.000 1.000 1.000 1.000 1.000
SMOKE10F 0.762 0.800 0.919 1.038 1.075
SMOKE10S 0.667 0.708 0.841 0.973 1.015
SMOKE11 0.535 0.578 0.717 0.855 0.899
RECEP9 1.000 1.000 1.000 1.000 1.000
RECEP10 0.589 0.638 0.796 0.953 1.002
RECEP11 0.755 0.799 0.940 1.081 1.125
 Linda K. Muthen posted on Tuesday, August 19, 2003 - 7:07 am
You can use the WLS estimator and do a chi-square difference test between the model with the path constrained and the mode with the path not constrained.
 Daniel posted on Monday, August 25, 2003 - 7:31 am
In the above analysis, there was a significant effect for strend on rtrend in the high but not the low depression group. However, when I constrained the paths to equality and compared the model with constrained paths to the model above with freely estimated path coefficients for each group, the WLS chi-square difference was not significant. DOes that mean that there is no interaction? How meaningful are the above results, given there are significant differences within each group? Or is this finding completely invalidated because the chi-square difference was not significant?
 Linda K. Muthen posted on Monday, August 25, 2003 - 10:42 am
If the chi-square difference was not significant, this means there is not an interaction. The fact that the path was significant in one group and not the other could be a matter of power. Was the sample size smaller in the group without significance? Also, was the constrained path significant?
 daniel posted on Monday, August 25, 2003 - 11:32 am
The sample size was smaller for the group with significance.
Group LOW 668 (not significant)
Group HIGH 290 (significant)

The constrained path was significant.
 Linda K. Muthen posted on Tuesday, August 26, 2003 - 10:22 am
This can occur. I would need to see full outputs from the constrained and not constraied runs to comment further.
 daniel posted on Tuesday, August 26, 2003 - 11:18 am
This is the unconstrained model with WLS estimation

INPUT INSTRUCTIONS

variable: names are id race gender
smoke9 smoke10f smoke10s smoke11
soma9 depaff9 posaff9 interp9
soma10 depaff10 posaff10 interp10
soma11 depaff11 posaff11 interp11
totdep9 totdep10 totdep11
recep9 recep10 recep11 expose9;
missing are .;
idvariable is id;
grouping is totdep9 (0=low 1=high);
usevariables are smoke9-smoke11
recep9-recep11 gender race expose9;
categorical are smoke9-smoke11
recep9-recep11;
define: cut smoke9-smoke11 (0 2);
define: cut totdep9 (16);
Analysis: Type=meanstructure;
estimator=wls;
iterations = 20000;
model: slevel by smoke9-smoke11@1;
strend by smoke9@0 smoke10f@1
smoke10s@1.422 smoke11@2.099;
rlevel by recep9-recep11@1;
rtrend by recep9@0 recep10@1 recep11@2;
strend on slevel;
strend on rlevel;
strend on rtrend;
slevel on rlevel;
rtrend on slevel;
strend rtrend on gender-expose9;
slevel on gender race;
slevel on expose9;
rlevel on gender race;
rlevel on expose9;
[smoke9\$1 smoke10f\$1 smoke10s\$1 smoke11\$1] (4);
[smoke9\$2 smoke10f\$2 smoke10s\$2 smoke11\$2] (5);
[slevel@0 strend];
{smoke9@1 smoke10f smoke10s smoke11};
[recep9\$1 recep10\$1 recep11\$1] (1);
[recep9\$2 recep10\$2 recep11\$2] (2);
[recep9\$3 recep10\$3 recep11\$3] (3);
[rlevel@0 rtrend];
{recep9@1 recep10 recep11};
model high: strend@.067;

SUMMARY OF ANALYSIS

Number of groups 2
Number of observations
Group LOW 668
Group HIGH 290

Number of y-variables 7
Number of x-variables 3
Number of continuous latent variables 4

Observed variables in the analysis
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11 GENDER RACE EXPOSE9

Grouping variable TOTDEP9
ID variable ID

Categorical variables
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11

Continuous latent variables in the analysis
SLEVEL STREND RLEVEL RTREND

Estimator WLS
Maximum number of iterations 20000
Convergence criterion 0.500D-04
Parameterization DELTA

Input data file(s)

Input data format FREE

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 211.479
Degrees of Freedom 65
P-Value 0.0000

Chi-Square Test of Model Fit for the Baseline Model

Value 43883.996
Degrees of Freedom 84
P-Value 0.0000

CFI/TLI

CFI 0.997
TLI 0.996

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.069

MODEL RESULTS

Estimates S.E. Est./S.E.

Group LOW

SLEVEL BY
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000

STREND BY
SMOKE9 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.422 0.000 0.000
SMOKE11 2.099 0.000 0.000

RLEVEL BY
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

RTREND BY
RECEP9 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 2.000 0.000 0.000

STREND ON
SLEVEL -0.009 0.020 -0.458
RLEVEL 0.014 0.040 0.358
RTREND 0.171 0.282 0.608

SLEVEL ON
RLEVEL 0.484 0.085 5.667

RTREND ON
SLEVEL -0.007 0.029 -0.230

SLEVEL ON
GENDER -0.051 0.097 -0.523
RACE -0.036 0.105 -0.342
EXPOSE9 0.577 0.100 5.744

STREND ON
GENDER 0.133 0.034 3.972
RACE 0.046 0.039 1.169
EXPOSE9 0.042 0.031 1.374

RTREND ON
GENDER -0.030 0.040 -0.742
RACE 0.024 0.047 0.502
EXPOSE9 -0.014 0.049 -0.297

RLEVEL ON
GENDER -0.403 0.075 -5.387
RACE -0.085 0.081 -1.040
EXPOSE9 0.414 0.076 5.415

Intercepts
SLEVEL 0.000 0.000 0.000
STREND 0.000 0.000 0.000
RLEVEL 0.000 0.000 0.000
RTREND 0.000 0.000 0.000

Thresholds
SMOKE9\$1 0.570 0.066 8.583
SMOKE9\$2 1.803 0.080 22.456
SMOKE10F\$1 0.570 0.066 8.583
SMOKE10F\$2 1.803 0.080 22.456
SMOKE10S\$1 0.570 0.066 8.583
SMOKE10S\$2 1.803 0.080 22.456
SMOKE11\$1 0.570 0.066 8.583
SMOKE11\$2 1.803 0.080 22.456
RECEP9\$1 -0.839 0.057 -14.766
RECEP9\$2 0.133 0.055 2.424
RECEP9\$3 0.478 0.057 8.430
RECEP10\$1 -0.839 0.057 -14.766
RECEP10\$2 0.133 0.055 2.424
RECEP10\$3 0.478 0.057 8.430
RECEP11\$1 -0.839 0.057 -14.766
RECEP11\$2 0.133 0.055 2.424
RECEP11\$3 0.478 0.057 8.430

Residual Variances
SLEVEL 0.835 0.048 17.370
STREND 0.005 0.010 0.529
RLEVEL 0.529 0.029 17.975
RTREND 0.035 0.014 2.466

Scales
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

Group HIGH

SLEVEL BY
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000

STREND BY
SMOKE9 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.422 0.000 0.000
SMOKE11 2.099 0.000 0.000

RLEVEL BY
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

RTREND BY
RECEP9 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 2.000 0.000 0.000

STREND ON
SLEVEL 0.201 0.087 2.315
RLEVEL -0.095 0.072 -1.311
RTREND 0.525 0.194 2.712

SLEVEL ON
RLEVEL 0.599 0.091 6.580

RTREND ON
SLEVEL -0.033 0.044 -0.763

SLEVEL ON
GENDER -0.416 0.125 -3.326
RACE 0.299 0.149 2.000
EXPOSE9 0.523 0.120 4.375

STREND ON
GENDER 0.112 0.081 1.378
RACE -0.125 0.082 -1.516
EXPOSE9 0.060 0.088 0.683

RTREND ON
GENDER -0.109 0.070 -1.543
RACE 0.047 0.076 0.622
EXPOSE9 0.233 0.074 3.147

RLEVEL ON
GENDER 0.030 0.102 0.294
RACE -0.128 0.117 -1.088
EXPOSE9 0.398 0.107 3.709

Intercepts
SLEVEL 0.000 0.000 0.000
STREND -0.022 0.077 -0.284
RLEVEL 0.000 0.000 0.000
RTREND -0.124 0.066 -1.875

Thresholds
SMOKE9\$1 0.570 0.066 8.583
SMOKE9\$2 1.803 0.080 22.456
SMOKE10F\$1 0.570 0.066 8.583
SMOKE10F\$2 1.803 0.080 22.456
SMOKE10S\$1 0.570 0.066 8.583
SMOKE10S\$2 1.803 0.080 22.456
SMOKE11\$1 0.570 0.066 8.583
SMOKE11\$2 1.803 0.080 22.456
RECEP9\$1 -0.839 0.057 -14.766
RECEP9\$2 0.133 0.055 2.424
RECEP9\$3 0.478 0.057 8.430
RECEP10\$1 -0.839 0.057 -14.766
RECEP10\$2 0.133 0.055 2.424
RECEP10\$3 0.478 0.057 8.430
RECEP11\$1 -0.839 0.057 -14.766
RECEP11\$2 0.133 0.055 2.424
RECEP11\$3 0.478 0.057 8.430

Residual Variances
SLEVEL 0.744 0.063 11.745
STREND 0.067 0.000 0.000
RLEVEL 0.586 0.058 10.079
RTREND 0.136 0.046 2.983

Scales
SMOKE9 1.000 0.000 0.000
SMOKE10F 0.844 0.049 17.384
SMOKE10S 0.773 0.056 13.872
SMOKE11 0.672 0.061 11.030
RECEP9 1.000 0.000 0.000
RECEP10 0.940 0.061 15.458
RECEP11 0.870 0.060 14.507

THis is the constrained model

INPUT INSTRUCTIONS

variable: names are id race gender
smoke9 smoke10f smoke10s smoke11
soma9 depaff9 posaff9 interp9
soma10 depaff10 posaff10 interp10
soma11 depaff11 posaff11 interp11
totdep9 totdep10 totdep11
recep9 recep10 recep11 expose9;
missing are .;
idvariable is id;
grouping is totdep9 (0=low 1=high);
usevariables are smoke9-smoke11
recep9-recep11 gender race expose9;
categorical are smoke9-smoke11
recep9-recep11;
define: cut smoke9-smoke11 (0 2);
define: cut totdep9 (16);
Analysis: Type=meanstructure;
estimator=wls;
iterations = 20000;
model: slevel by smoke9-smoke11@1;
strend by smoke9@0 smoke10f@1
smoke10s@1.422 smoke11@2.099;
rlevel by recep9-recep11@1;
rtrend by recep9@0 recep10@1 recep11@2;
strend on slevel;
strend on rlevel;
strend on rtrend (6);
slevel on rlevel;
rtrend on slevel;
strend rtrend on gender-expose9;
slevel on gender race;
slevel on expose9;
rlevel on gender race;
rlevel on expose9;
[smoke9\$1 smoke10f\$1 smoke10s\$1 smoke11\$1] (4);
[smoke9\$2 smoke10f\$2 smoke10s\$2 smoke11\$2] (5);
[slevel@0 strend];
{smoke9@1 smoke10f smoke10s smoke11};
[recep9\$1 recep10\$1 recep11\$1] (1);
[recep9\$2 recep10\$2 recep11\$2] (2);
[recep9\$3 recep10\$3 recep11\$3] (3);
[rlevel@0 rtrend];
{recep9@1 recep10 recep11};
model high: strend@.067;

SUMMARY OF ANALYSIS

Number of groups 2
Number of observations
Group LOW 668
Group HIGH 290

Number of y-variables 7
Number of x-variables 3
Number of continuous latent variables 4

Observed variables in the analysis
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11 GENDER RACE EXPOSE9

Grouping variable TOTDEP9
ID variable ID

Categorical variables
SMOKE9 SMOKE10F SMOKE10S SMOKE11 RECEP9 RECEP10
RECEP11

Continuous latent variables in the analysis
SLEVEL STREND RLEVEL RTREND

Estimator WLS
Maximum number of iterations 20000
Convergence criterion 0.500D-04
Parameterization DELTA

Input data file(s)

Input data format FREE

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 212.558
Degrees of Freedom 66
P-Value 0.0000

Chi-Square Test of Model Fit for the Baseline Model

Value 43883.996
Degrees of Freedom 84
P-Value 0.0000

CFI/TLI

CFI 0.997
TLI 0.996

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.068

MODEL RESULTS

Estimates S.E. Est./S.E.

Group LOW

SLEVEL BY
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000

STREND BY
SMOKE9 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.422 0.000 0.000
SMOKE11 2.099 0.000 0.000

RLEVEL BY
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

RTREND BY
RECEP9 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 2.000 0.000 0.000

STREND ON
SLEVEL 0.004 0.024 0.167
RLEVEL -0.006 0.036 -0.160
RTREND 0.477 0.162 2.936

SLEVEL ON
RLEVEL 0.499 0.082 6.085

RTREND ON
SLEVEL -0.017 0.028 -0.620

SLEVEL ON
GENDER -0.049 0.097 -0.501
RACE -0.030 0.105 -0.289
EXPOSE9 0.572 0.100 5.708

STREND ON
GENDER 0.137 0.038 3.620
RACE 0.040 0.045 0.876
EXPOSE9 0.047 0.037 1.269

RTREND ON
GENDER -0.032 0.040 -0.799
RACE 0.023 0.047 0.489
EXPOSE9 -0.006 0.048 -0.117

RLEVEL ON
GENDER -0.402 0.075 -5.373
RACE -0.086 0.081 -1.063
EXPOSE9 0.412 0.076 5.389

Intercepts
SLEVEL 0.000 0.000 0.000
STREND 0.000 0.000 0.000
RLEVEL 0.000 0.000 0.000
RTREND 0.000 0.000 0.000

Thresholds
SMOKE9\$1 0.572 0.066 8.609
SMOKE9\$2 1.803 0.080 22.489
SMOKE10F\$1 0.572 0.066 8.609
SMOKE10F\$2 1.803 0.080 22.489
SMOKE10S\$1 0.572 0.066 8.609
SMOKE10S\$2 1.803 0.080 22.489
SMOKE11\$1 0.572 0.066 8.609
SMOKE11\$2 1.803 0.080 22.489
RECEP9\$1 -0.841 0.057 -14.821
RECEP9\$2 0.132 0.055 2.407
RECEP9\$3 0.478 0.057 8.436
RECEP10\$1 -0.841 0.057 -14.821
RECEP10\$2 0.132 0.055 2.407
RECEP10\$3 0.478 0.057 8.436
RECEP11\$1 -0.841 0.057 -14.821
RECEP11\$2 0.132 0.055 2.407
RECEP11\$3 0.478 0.057 8.436

Residual Variances
SLEVEL 0.824 0.049 16.963
STREND -0.001 0.011 -0.088
RLEVEL 0.540 0.028 18.954
RTREND 0.029 0.013 2.253

Scales
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

Group HIGH

SLEVEL BY
SMOKE9 1.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.000 0.000 0.000
SMOKE11 1.000 0.000 0.000

STREND BY
SMOKE9 0.000 0.000 0.000
SMOKE10F 1.000 0.000 0.000
SMOKE10S 1.422 0.000 0.000
SMOKE11 2.099 0.000 0.000

RLEVEL BY
RECEP9 1.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 1.000 0.000 0.000

RTREND BY
RECEP9 0.000 0.000 0.000
RECEP10 1.000 0.000 0.000
RECEP11 2.000 0.000 0.000

STREND ON
SLEVEL 0.191 0.084 2.275
RLEVEL -0.092 0.071 -1.292
RTREND 0.477 0.162 2.936

SLEVEL ON
RLEVEL 0.597 0.091 6.593

RTREND ON
SLEVEL -0.032 0.044 -0.716

SLEVEL ON
GENDER -0.414 0.125 -3.314
RACE 0.301 0.149 2.022
EXPOSE9 0.525 0.119 4.393

STREND ON
GENDER 0.104 0.078 1.327
RACE -0.126 0.080 -1.568
EXPOSE9 0.069 0.085 0.806

RTREND ON
GENDER -0.109 0.071 -1.531
RACE 0.048 0.077 0.625
EXPOSE9 0.236 0.075 3.168

RLEVEL ON
GENDER 0.030 0.102 0.296
RACE -0.130 0.117 -1.104
EXPOSE9 0.400 0.108 3.717

Intercepts
SLEVEL 0.000 0.000 0.000
STREND -0.021 0.075 -0.281
RLEVEL 0.000 0.000 0.000
RTREND -0.125 0.067 -1.886

Thresholds
SMOKE9\$1 0.572 0.066 8.609
SMOKE9\$2 1.803 0.080 22.489
SMOKE10F\$1 0.572 0.066 8.609
SMOKE10F\$2 1.803 0.080 22.489
SMOKE10S\$1 0.572 0.066 8.609
SMOKE10S\$2 1.803 0.080 22.489
SMOKE11\$1 0.572 0.066 8.609
SMOKE11\$2 1.803 0.080 22.489
RECEP9\$1 -0.841 0.057 -14.821
RECEP9\$2 0.132 0.055 2.407
RECEP9\$3 0.478 0.057 8.436
RECEP10\$1 -0.841 0.057 -14.821
RECEP10\$2 0.132 0.055 2.407
RECEP10\$3 0.478 0.057 8.436
RECEP11\$1 -0.841 0.057 -14.821
RECEP11\$2 0.132 0.055 2.407
RECEP11\$3 0.478 0.057 8.436

Residual Variances
SLEVEL 0.741 0.063 11.829
STREND 0.067 0.000 0.000
RLEVEL 0.591 0.058 10.148
RTREND 0.143 0.045 3.148

Scales
SMOKE9 1.000 0.000 0.000
SMOKE10F 0.852 0.047 18.141
SMOKE10S 0.782 0.054 14.456
SMOKE11 0.681 0.060 11.450
RECEP9 1.000 0.000 0.000
RECEP10 0.930 0.059 15.764
RECEP11 0.861 0.059 14.669
 Linda K. Muthen posted on Tuesday, August 26, 2003 - 1:52 pm
You may have been suprised that the weighted average of the two unconstrained estimates is not the estimated value of the constrained estimate. This can come about when you have a model with many degrees of freedom and a certan amount of misfit. For your sample size, the model does not fit very well. If you modify your model to fit better, these estimates are likely to change. When you want to send full outputs, please send them to support@statmodel.com not to the discussion board.
 daniel posted on Wednesday, August 27, 2003 - 4:14 am
Thanks
 anonymous posted on Tuesday, August 05, 2008 - 6:58 pm
Hello,
I'm running an LGM with two groups. In the first group, there is an intercept, linear slope, and quadratic slope. In the second group, there is only an intercept and quadratic slope. In addition, I tested differences between the intercept of the first and second group by constraining: 1) the intercept mean; and 2) the intercept variance. Chi-square difference tests indicated that both parameters differed across groups, so I have left them free. Given this difference in intercepts across groups, is it appropriate to test equivalence of path coefficients from a covariate to the intercepts? Or should these also remain free?
 Bengt O. Muthen posted on Tuesday, August 05, 2008 - 7:08 pm
A regression coefficient can be the same across classes even if the mean and variance of the dependent variable differ, but it is more likely that it also is different.
 gibbon lab posted on Tuesday, October 11, 2011 - 7:20 pm
I am running a two group analysis on LGM with binary endogenous variables. The proportions of the higher category increase in both groups. My code is:

categorical are t3smklast3bin t4smk3cat t5smk3cat t6smk3bin;

grouping=drd4bin (0=nonrisk 1=risk);

analysis:parameterization is theta;

MODEL:
smk_i by t3smklast3bin@1 t4smk3cat@1 t5smk3cat@1 t6smk3bin@1;
smk_s by t3smklast3bin@0 t4smk3cat@3 t5smk3cat@6 t6smk3bin@8;
[t3smklast3bin\$1 t4smk3cat\$1 t5smk3cat\$1 t6smk3bin\$1] (1);

The output says:
...
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN GROUP RISK IS NOT POSITIVE DEFINITE. PROBLEM INVOLVING VARIABLE T6SMK3BI.
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 13. THE CONDITION NUMBER IS 0.419D-18.

However, when I run the exactly same model separately in each group, it worked in both groups. What to do? Thanks a lot.
 Bengt O. Muthen posted on Tuesday, October 11, 2011 - 8:39 pm
You should use the bar (|) language to set up your growth model correctly.
 Melinda Gonzales-Backen posted on Thursday, February 19, 2015 - 8:03 am
I am running a multiple group latent growth curve model. I have two groups and three time points.

The model fit is poor so I examined the modification indices. One suggestion is to add [affw1] for one group. affw1 is the observed variable for the first time point of the growth model. The intercept is set to the first time point and is free to vary between groups.

So my question is -- what is happening in the model if I request this group mean? I thought it was already estimated since I am estimating different intercepts for each group.
Thank you!
 Linda K. Muthen posted on Thursday, February 19, 2015 - 10:01 am
The intercepts for the outcomes must be fixed at zero. This is part of the growth model parametrization. I would suggest fitting the growth model in each group separately as a first step. If the same growth model does not fit in each group, you should not proceed to a multiple group analysis.