```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:05 PM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-level multiple
indicator growth model with categorical
outcomes using multiple imputation data
DATA:           FILE = ex11.8implist.dat;
TYPE = IMPUTATION;
SWMATRIX = ex11.8swlist.dat;
VARIABLE:	NAMES are u11 u21 u31 u12 u22 u32 u13 u23 u33 clus;
CATEGORICAL = u11-u33;
CLUSTER = clus;
ANALYSIS:	TYPE = TWOLEVEL;
ESTIMATOR = WLSMV;
PROCESSORS = 2;
MODEL:	%WITHIN%
f1w BY u11
u21 (1)
u31 (2);
f2w BY u12
u22 (1)
u32 (2);
f3w BY u13
u23 (1)
u33 (2);
iw sw | f1w@0 f2w@1 f3w@2;
%BETWEEN%
f1b BY u11
u21 (1)
u31 (2);
f2b BY u12
u22 (1)
u32 (2);
f3b BY u13
u23 (1)
u33 (2);
[u11\$1 u12\$1 u13\$1] (3);
[u21\$1 u22\$1 u23\$1] (4);
[u31\$1 u32\$1 u33\$1] (5);
u11-u33;
ib sb | f1b@0 f2b@1 f3b@2;
[f1b-f3b@0 ib@0 sb];
f1b-f3b (6);
OUTPUT:	TECH1 TECH8;

INPUT READING TERMINATED NORMALLY

this is an example of a two-level multiple
indicator growth model with categorical
outcomes using multiple imputation data

SUMMARY OF ANALYSIS

Number of groups                                                 1
Average number of observations                                1000

Number of replications
Requested                                                    5
Completed                                                    5

Number of dependent variables                                    9
Number of independent variables                                  0
Number of continuous latent variables                           10

Observed dependent variables

Binary and ordered categorical (ordinal)
U11         U21         U31         U12         U22         U32
U13         U23         U33

Continuous latent variables
F1W         F2W         F3W         IW          SW          F1B
F2B         F3B         IB          SB

Variables with special functions

Cluster variable      CLUS

Estimator                                                    WLSMV
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                1000
Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations                                 500
Convergence criteria
Loglikelihood change                                 0.100D-02
Relative loglikelihood change                        0.100D-05
Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            10
Minimum value for logit thresholds                           -10
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                          FS
Integration Specifications
Type                                                    STANDARD
Number of integration points                                   7
Dimensions of numerical integration                            0
Adaptive quadrature                                           ON
Link                                                        PROBIT
Cholesky                                                        ON

Input data file(s)
Multiple data files from
ex11.8implist.dat
Input data format  FREE

SUMMARY OF DATA FOR THE FIRST DATA SET

Number of clusters                         20

Average cluster size       50.000

Estimated Intraclass Correlations for the Y Variables

Intraclass              Intraclass              Intraclass
Variable  Correlation   Variable  Correlation   Variable  Correlation

U11          0.292      U21          0.344      U31          0.318
U12          0.426      U22          0.437      U32          0.335
U13          0.318      U23          0.219      U33          0.224

UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES

NOTE:  These are average results over 5 data sets.

U11
Category 1    0.511
Category 2    0.489
U21
Category 1    0.460
Category 2    0.540
U31
Category 1    0.602
Category 2    0.398
U12
Category 1    0.292
Category 2    0.708
U22
Category 1    0.221
Category 2    0.779
U32
Category 1    0.365
Category 2    0.635
U13
Category 1    0.228
Category 2    0.772
U23
Category 1    0.156
Category 2    0.844
U33
Category 1    0.317
Category 2    0.683

SAMPLE STATISTICS

NOTE:  These are average results over 5 data sets.

ESTIMATED SAMPLE STATISTICS

MEANS/INTERCEPTS/THRESHOLDS
U11\$1         U21\$1         U31\$1         U12\$1         U22\$1
________      ________      ________      ________      ________
0.031        -0.148         0.329        -0.725        -1.035

MEANS/INTERCEPTS/THRESHOLDS
U32\$1         U13\$1         U23\$1         U33\$1
________      ________      ________      ________
-0.416        -0.887        -1.139        -0.571

WITHIN LEVEL VARIANCE/COVARIANCE
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            1.000
U21            0.610         1.000
U31            0.487         0.568         1.000
U12            0.346         0.439         0.384         1.000
U22            0.287         0.386         0.303         0.576         1.000
U32            0.297         0.368         0.331         0.619         0.598
U13            0.291         0.307         0.392         0.531         0.574
U23            0.178         0.244         0.245         0.550         0.533
U33            0.248         0.322         0.322         0.477         0.549

WITHIN LEVEL VARIANCE/COVARIANCE
U32           U13           U23           U33
________      ________      ________      ________
U32            1.000
U13            0.574         1.000
U23            0.527         0.751         1.000
U33            0.525         0.746         0.706         1.000

WITHIN LEVEL CORRELATION
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            1.000
U21            0.610         1.000
U31            0.487         0.568         1.000
U12            0.346         0.439         0.384         1.000
U22            0.287         0.386         0.303         0.576         1.000
U32            0.297         0.368         0.331         0.619         0.598
U13            0.291         0.307         0.392         0.531         0.574
U23            0.178         0.244         0.245         0.550         0.533
U33            0.248         0.322         0.322         0.477         0.549

WITHIN LEVEL CORRELATION
U32           U13           U23           U33
________      ________      ________      ________
U32            1.000
U13            0.574         1.000
U23            0.527         0.751         1.000
U33            0.525         0.746         0.706         1.000

BETWEEN LEVEL VARIANCE/COVARIANCE
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            0.412
U21            0.226         0.524
U31            0.243         0.051         0.467
U12            0.305         0.311         0.351         0.613
U22            0.271         0.225         0.273         0.423         0.774
U32            0.136         0.095         0.152         0.279         0.221
U13            0.171         0.227         0.147         0.216         0.275
U23            0.176         0.129         0.116         0.156         0.291
U33            0.169         0.150         0.082         0.064         0.230

BETWEEN LEVEL VARIANCE/COVARIANCE
U32           U13           U23           U33
________      ________      ________      ________
U32            0.477
U13            0.017         0.446
U23            0.099         0.258         0.279
U33            0.070         0.266         0.249         0.385

BETWEEN LEVEL CORRELATION
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            1.000
U21            0.486         1.000
U31            0.553         0.104         1.000
U12            0.607         0.549         0.656         1.000
U22            0.480         0.353         0.454         0.614         1.000
U32            0.307         0.190         0.322         0.517         0.364
U13            0.399         0.468         0.322         0.413         0.469
U23            0.519         0.337         0.322         0.377         0.625
U33            0.424         0.334         0.194         0.132         0.420

BETWEEN LEVEL CORRELATION
U32           U13           U23           U33
________      ________      ________      ________
U32            1.000
U13            0.036         1.000
U23            0.273         0.731         1.000
U33            0.163         0.643         0.761         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       25

Chi-Square Test of Model Fit

Degrees of freedom                      65

Mean                                57.060
Std Dev                              1.635
Number of successful computations        5

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000           41.444         55.581
0.980       1.000           43.779         55.581
0.950       1.000           47.450         55.581
0.900       1.000           50.883         55.581
0.800       1.000           55.262         55.581
0.700       0.200           58.573         55.581
0.500       0.000           64.335         55.937
0.300       0.000           70.462         56.544
0.200       0.000           74.351         57.072
0.100       0.000           79.973         57.072
0.050       0.000           84.821         57.072
0.020       0.000           90.501         57.072
0.010       0.000           94.422         57.072

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.000
Std Dev                              0.000
Number of successful computations        5

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       1.000
0.050       1.000
0.020       1.000
0.010       1.000

CFI/TLI

CFI

Mean                                 1.000
Std Dev                              0.000
Number of successful computations        5

Cumulative Distribution Function
Value    Function Value
0.990       0.000
0.980       0.000
0.950       0.000
0.900       0.000
0.800       0.000
0.700       0.000
0.500       0.000
0.300       0.000
0.200       0.000
0.100       0.000
0.050       0.000
0.020       0.000
0.010       0.000

TLI

Mean                                 1.011
Std Dev                              0.002
Number of successful computations        5

Cumulative Distribution Function
Value    Function Value
0.990       0.000
0.980       0.000
0.950       0.000
0.900       0.000
0.800       0.000
0.700       0.000
0.500       0.000
0.300       0.000
0.200       0.000
0.100       0.000
0.050       0.000
0.020       0.000
0.010       0.000

SRMR (Standardized Root Mean Square Residual) for the WITHIN level

Mean                                 0.048
Std Dev                              0.005
Number of successful computations        5

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       1.000
0.050       0.600
0.020       0.000
0.010       0.000

SRMR (Standardized Root Mean Square Residual) for the BETWEEN level

Mean                                 0.140
Std Dev                              0.012
Number of successful computations        5

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       0.000
0.050       0.000
0.020       0.000
0.010       0.000

MODEL RESULTS

Two-Tailed   Rate of
Estimate       S.E.  Est./S.E.    P-Value    Missing

Within Level

IW       |
F1W                1.000      0.000    999.000    999.000      0.000
F2W                1.000      0.000    999.000    999.000      0.000
F3W                1.000      0.000    999.000    999.000      0.000

SW       |
F1W                0.000      0.000    999.000    999.000      0.000
F2W                1.000      0.000    999.000    999.000      0.000
F3W                2.000      0.000    999.000    999.000      0.000

F1W      BY
U11                1.000      0.000    999.000    999.000      0.000
U21                1.057      0.162      6.522      0.000      0.309
U31                0.912      0.137      6.680      0.000      0.190

F2W      BY
U12                1.000      0.000    999.000    999.000      0.000
U22                1.057      0.162      6.522      0.000      0.309
U32                0.912      0.137      6.680      0.000      0.190

F3W      BY
U13                1.000      0.000    999.000    999.000      0.000
U23                1.057      0.162      6.522      0.000      0.309
U33                0.912      0.137      6.680      0.000      0.190

SW       WITH
IW                 0.003      0.162      0.017      0.986      0.467

Variances
IW                 0.851      0.315      2.699      0.007      0.284
SW                 0.456      0.195      2.340      0.019      0.293

Residual Variances
F1W                0.406      0.263      1.543      0.123      0.362
F2W                0.237      0.297      0.797      0.425      0.194
F3W                0.315      0.457      0.689      0.491      0.526

Between Level

IB       |
F1B                1.000      0.000    999.000    999.000      0.000
F2B                1.000      0.000    999.000    999.000      0.000
F3B                1.000      0.000    999.000    999.000      0.000

SB       |
F1B                0.000      0.000    999.000    999.000      0.000
F2B                1.000      0.000    999.000    999.000      0.000
F3B                2.000      0.000    999.000    999.000      0.000

F1B      BY
U11                1.000      0.000    999.000    999.000      0.000
U21                1.057      0.162      6.522      0.000      0.309
U31                0.912      0.137      6.680      0.000      0.190

F2B      BY
U12                1.000      0.000    999.000    999.000      0.000
U22                1.057      0.162      6.522      0.000      0.309
U32                0.912      0.137      6.680      0.000      0.190

F3B      BY
U13                1.000      0.000    999.000    999.000      0.000
U23                1.057      0.162      6.522      0.000      0.309
U33                0.912      0.137      6.680      0.000      0.190

SB       WITH
IB                 0.099      0.132      0.752      0.452      0.043

Means
IB                 0.000      0.000    999.000    999.000      0.000
SB                 0.942      0.151      6.253      0.000      0.074

Intercepts
F1B                0.000      0.000    999.000    999.000      0.000
F2B                0.000      0.000    999.000    999.000      0.000
F3B                0.000      0.000    999.000    999.000      0.000

Thresholds
U11\$1              0.024      0.237      0.102      0.919      0.001
U21\$1             -0.407      0.227     -1.791      0.073      0.006
U31\$1              0.428      0.201      2.127      0.033      0.037
U12\$1              0.024      0.237      0.102      0.919      0.001
U22\$1             -0.407      0.227     -1.791      0.073      0.006
U32\$1              0.428      0.201      2.127      0.033      0.037
U13\$1              0.024      0.237      0.102      0.919      0.001
U23\$1             -0.407      0.227     -1.791      0.073      0.006
U33\$1              0.428      0.201      2.127      0.033      0.037

Variances
IB                 0.239      0.227      1.051      0.293      0.073
SB                -0.038      0.109     -0.352      0.725      0.063

Residual Variances
U11                0.455      0.345      1.320      0.187      0.001
U21                0.731      0.603      1.211      0.226      0.003
U31                0.561      0.317      1.769      0.077      0.001
U12                0.918      0.841      1.092      0.275      0.052
U22                1.400      0.903      1.550      0.121      0.051
U32                0.560      0.358      1.564      0.118      0.014
U13                1.062      0.514      2.065      0.039      0.108
U23                0.417      0.370      1.126      0.260      0.085
U33                0.766      0.555      1.381      0.167      0.261
F1B                0.236      0.212      1.111      0.266      0.020
F2B                0.236      0.212      1.111      0.266      0.020
F3B                0.236      0.212      1.111      0.266      0.020

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.348E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

TAU
U11\$1         U21\$1         U31\$1         U12\$1         U22\$1
________      ________      ________      ________      ________
0             0             0             0             0

TAU
U32\$1         U13\$1         U23\$1         U33\$1
________      ________      ________      ________
0             0             0             0

NU
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
0             0             0             0             0

NU
U32           U13           U23           U33
________      ________      ________      ________
0             0             0             0

LAMBDA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
U11                0             0             0             0             0
U21                1             0             0             0             0
U31                2             0             0             0             0
U12                0             0             0             0             0
U22                0             1             0             0             0
U32                0             2             0             0             0
U13                0             0             0             0             0
U23                0             0             1             0             0
U33                0             0             2             0             0

THETA
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11                0
U21                0             0
U31                0             0             0
U12                0             0             0             0
U22                0             0             0             0             0
U32                0             0             0             0             0
U13                0             0             0             0             0
U23                0             0             0             0             0
U33                0             0             0             0             0

THETA
U32           U13           U23           U33
________      ________      ________      ________
U32                0
U13                0             0
U23                0             0             0
U33                0             0             0             0

ALPHA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
0             0             0             0             0

BETA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
F1W                0             0             0             0             0
F2W                0             0             0             0             0
F3W                0             0             0             0             0
IW                 0             0             0             0             0
SW                 0             0             0             0             0

PSI
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
F1W                3
F2W                0             4
F3W                0             0             5
IW                 0             0             0             6
SW                 0             0             0             7             8

PARAMETER SPECIFICATION FOR BETWEEN

TAU
U11\$1         U21\$1         U31\$1         U12\$1         U22\$1
________      ________      ________      ________      ________
23            24            25            23            24

TAU
U32\$1         U13\$1         U23\$1         U33\$1
________      ________      ________      ________
25            23            24            25

NU
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
0             0             0             0             0

NU
U32           U13           U23           U33
________      ________      ________      ________
0             0             0             0

LAMBDA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
U11                0             0             0             0             0
U21                1             0             0             0             0
U31                2             0             0             0             0
U12                0             0             0             0             0
U22                0             1             0             0             0
U32                0             2             0             0             0
U13                0             0             0             0             0
U23                0             0             1             0             0
U33                0             0             2             0             0

THETA
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11                9
U21                0            10
U31                0             0            11
U12                0             0             0            12
U22                0             0             0             0            13
U32                0             0             0             0             0
U13                0             0             0             0             0
U23                0             0             0             0             0
U33                0             0             0             0             0

THETA
U32           U13           U23           U33
________      ________      ________      ________
U32               14
U13                0            15
U23                0             0            16
U33                0             0             0            17

ALPHA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
0             0             0             0            18

BETA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
F1B                0             0             0             0             0
F2B                0             0             0             0             0
F3B                0             0             0             0             0
IB                 0             0             0             0             0
SB                 0             0             0             0             0

PSI
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
F1B               19
F2B                0            19
F3B                0             0            19
IB                 0             0             0            20
SB                 0             0             0            21            22

STARTING VALUES FOR WITHIN

TAU
U11\$1         U21\$1         U31\$1         U12\$1         U22\$1
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

TAU
U32\$1         U13\$1         U23\$1         U33\$1
________      ________      ________      ________
0.000         0.000         0.000         0.000

NU
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
U32           U13           U23           U33
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
U11            1.000         0.000         0.000         0.000         0.000
U21            1.000         0.000         0.000         0.000         0.000
U31            1.000         0.000         0.000         0.000         0.000
U12            0.000         1.000         0.000         0.000         0.000
U22            0.000         1.000         0.000         0.000         0.000
U32            0.000         1.000         0.000         0.000         0.000
U13            0.000         0.000         1.000         0.000         0.000
U23            0.000         0.000         1.000         0.000         0.000
U33            0.000         0.000         1.000         0.000         0.000

THETA
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            1.000
U21            0.000         1.000
U31            0.000         0.000         1.000
U12            0.000         0.000         0.000         1.000
U22            0.000         0.000         0.000         0.000         1.000
U32            0.000         0.000         0.000         0.000         0.000
U13            0.000         0.000         0.000         0.000         0.000
U23            0.000         0.000         0.000         0.000         0.000
U33            0.000         0.000         0.000         0.000         0.000

THETA
U32           U13           U23           U33
________      ________      ________      ________
U32            1.000
U13            0.000         1.000
U23            0.000         0.000         1.000
U33            0.000         0.000         0.000         1.000

ALPHA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

BETA
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
F1W            0.000         0.000         0.000         1.000         0.000
F2W            0.000         0.000         0.000         1.000         1.000
F3W            0.000         0.000         0.000         1.000         2.000
IW             0.000         0.000         0.000         0.000         0.000
SW             0.000         0.000         0.000         0.000         0.000

PSI
F1W           F2W           F3W           IW            SW
________      ________      ________      ________      ________
F1W            0.050
F2W            0.000         0.050
F3W            0.000         0.000         0.050
IW             0.000         0.000         0.000         0.050
SW             0.000         0.000         0.000         0.000         0.050

STARTING VALUES FOR BETWEEN

TAU
U11\$1         U21\$1         U31\$1         U12\$1         U22\$1
________      ________      ________      ________      ________
-0.377        -0.567        -0.164        -0.377        -0.567

TAU
U32\$1         U13\$1         U23\$1         U33\$1
________      ________      ________      ________
-0.164        -0.377        -0.567        -0.164

NU
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
U32           U13           U23           U33
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
U11            1.000         0.000         0.000         0.000         0.000
U21            1.000         0.000         0.000         0.000         0.000
U31            1.000         0.000         0.000         0.000         0.000
U12            0.000         1.000         0.000         0.000         0.000
U22            0.000         1.000         0.000         0.000         0.000
U32            0.000         1.000         0.000         0.000         0.000
U13            0.000         0.000         1.000         0.000         0.000
U23            0.000         0.000         1.000         0.000         0.000
U33            0.000         0.000         1.000         0.000         0.000

THETA
U11           U21           U31           U12           U22
________      ________      ________      ________      ________
U11            1.000
U21            0.000         1.000
U31            0.000         0.000         1.000
U12            0.000         0.000         0.000         1.000
U22            0.000         0.000         0.000         0.000         1.000
U32            0.000         0.000         0.000         0.000         0.000
U13            0.000         0.000         0.000         0.000         0.000
U23            0.000         0.000         0.000         0.000         0.000
U33            0.000         0.000         0.000         0.000         0.000

THETA
U32           U13           U23           U33
________      ________      ________      ________
U32            1.000
U13            0.000         1.000
U23            0.000         0.000         1.000
U33            0.000         0.000         0.000         1.000

ALPHA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

BETA
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
F1B            0.000         0.000         0.000         1.000         0.000
F2B            0.000         0.000         0.000         1.000         1.000
F3B            0.000         0.000         0.000         1.000         2.000
IB             0.000         0.000         0.000         0.000         0.000
SB             0.000         0.000         0.000         0.000         0.000

PSI
F1B           F2B           F3B           IB            SB
________      ________      ________      ________      ________
F1B            0.050
F2B            0.000         0.050
F3B            0.000         0.000         0.050
IB             0.000         0.000         0.000         0.050
SB             0.000         0.000         0.000         0.000         0.050

TECHNICAL 8 OUTPUT

Beginning Time:  23:05:57
Ending Time:  23:05:59
Elapsed Time:  00:00:02

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Fax: (310) 391-8971
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Support: Support@StatModel.com

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