```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:06 PM

INPUT INSTRUCTIONS

TITLE:	this is an example of a Monte Carlo
simulation study for a linear growth model
for a continuous outcome with missing data
where attrition is	predicted by time-
invariant covariates (MAR)
MONTECARLO:
NAMES ARE y1-y4 x1 x2;
NOBSERVATIONS = 500;
NREPS = 500;
SEED = 4533;
CUTPOINTS = x2(1);
MISSING = y1-y4;
MODEL POPULATION:
x1-x2@1;
[x1-x2@0];
i s | y1@0 y2@1 y3@2 y4@3;
[i*1 s*2];
i*1; s*.2; i WITH s*.1;
y1-y4*.5;
i ON x1*1 x2*.5;
s ON x1*.4 x2*.25;
MODEL MISSING:
[y1-y4@-1];
y1 ON x1*.4 x2*.2;
y2 ON x1*.8 x2*.4;
y3 ON x1*1.6 x2*.8;
y4 ON x1*3.2 x2*1.6;
MODEL:	i s | y1@0 y2@1 y3@2 y4@3;
[i*1 s*2];
i*1; s*.2; i WITH s*.1;
y1-y4*.5;
i ON x1*1 x2*.5;
s ON x1*.4 x2*.25;
OUTPUT:	TECH9;

this is an example of a Monte Carlo
simulation study for a linear growth model
for a continuous outcome with missing data
where attrition is predicted by time-
invariant covariates (MAR)

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
Requested                                                  500
Completed                                                  500
Value of seed                                                 4533

Number of dependent variables                                    4
Number of independent variables                                  2
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Y1          Y2          Y3          Y4

Observed independent variables
X1          X2

Continuous latent variables
I           S

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03

SUMMARY OF DATA FOR THE FIRST REPLICATION

Number of missing data patterns            15

SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION

MISSING DATA PATTERNS (x = not missing)

1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
Y1        x  x  x  x  x  x  x  x
Y2        x  x  x  x              x  x  x  x
Y3        x  x        x  x        x  x        x  x
Y4        x     x     x     x     x     x     x     x
X1        x  x  x  x  x  x  x  x  x  x  x  x  x  x  x
X2        x  x  x  x  x  x  x  x  x  x  x  x  x  x  x

MISSING DATA PATTERN FREQUENCIES

Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
1         139           6          30          11          13
2          40           7          11          12          20
3          27           8          32          13          10
4          42           9          45          14          15
5          45          10          25          15           6

COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT

Covariance Coverage
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1             0.732
Y2             0.496         0.702
Y3             0.508         0.498         0.698
Y4             0.444         0.448         0.478         0.592
X1             0.732         0.702         0.698         0.592         1.000
X2             0.732         0.702         0.698         0.592         1.000

Covariance Coverage
X2
________
X2             1.000

SAMPLE STATISTICS FOR THE FIRST REPLICATION

ESTIMATED SAMPLE STATISTICS

Means
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
1.110         3.078         5.038         7.107        -0.018

Means
X2
________
0.126

Covariances
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1             2.681
Y2             2.575         3.781
Y3             3.060         4.011         5.425
Y4             3.631         4.938         6.321         8.586
X1             0.920         1.248         1.561         2.022         0.880
X2             0.012         0.005         0.024         0.040        -0.027

Covariances
X2
________
X2             0.110

Correlations
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1             1.000
Y2             0.809         1.000
Y3             0.802         0.886         1.000
Y4             0.757         0.867         0.926         1.000
X1             0.599         0.684         0.714         0.736         1.000
X2             0.022         0.008         0.031         0.042        -0.087

Correlations
X2
________
X2             1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -2958.775

MODEL FIT INFORMATION

Number of Free Parameters                       13

Loglikelihood

H0 Value

Mean                             -2156.302
Std Dev                             41.768
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.990        -2253.466      -2262.670
0.980       0.980        -2242.080      -2247.081
0.950       0.950        -2225.005      -2225.327
0.900       0.886        -2209.831      -2211.278
0.800       0.790        -2191.453      -2194.399
0.700       0.692        -2178.205      -2179.344
0.500       0.540        -2156.302      -2152.975
0.300       0.308        -2134.399      -2132.892
0.200       0.202        -2121.150      -2120.652
0.100       0.106        -2102.773      -2101.748
0.050       0.038        -2087.598      -2092.016
0.020       0.016        -2070.524      -2079.359
0.010       0.008        -2059.138      -2066.564

H1 Value

Mean                             -2151.696
Std Dev                             41.802
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.988        -2248.938      -2257.355
0.980       0.980        -2237.543      -2241.302
0.950       0.948        -2220.455      -2221.494
0.900       0.894        -2205.268      -2206.349
0.800       0.792        -2186.876      -2190.004
0.700       0.688        -2173.616      -2174.889
0.500       0.540        -2151.696      -2148.003
0.300       0.308        -2129.775      -2129.445
0.200       0.210        -2116.515      -2114.266
0.100       0.104        -2098.123      -2097.787
0.050       0.036        -2082.936      -2087.567
0.020       0.016        -2065.848      -2074.406
0.010       0.006        -2054.453      -2062.106

Information Criteria

Akaike (AIC)

Mean                              4338.604
Std Dev                             83.535
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         4144.276       4156.429
0.980       0.984         4167.048       4179.672
0.950       0.962         4201.197       4208.183
0.900       0.894         4231.545       4228.779
0.800       0.798         4268.300       4265.444
0.700       0.692         4294.798       4291.709
0.500       0.460         4338.604       4331.444
0.300       0.308         4382.409       4384.098
0.200       0.210         4408.907       4414.276
0.100       0.114         4445.662       4447.893
0.050       0.050         4476.010       4475.704
0.020       0.020         4510.160       4500.917
0.010       0.010         4532.931       4530.484

Bayesian (BIC)

Mean                              4393.393
Std Dev                             83.535
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         4199.066       4211.219
0.980       0.984         4221.838       4234.462
0.950       0.962         4255.987       4262.973
0.900       0.894         4286.335       4283.569
0.800       0.798         4323.090       4320.233
0.700       0.692         4349.588       4346.498
0.500       0.460         4393.393       4386.234
0.300       0.308         4437.199       4438.888
0.200       0.210         4463.697       4469.066
0.100       0.114         4500.452       4502.683
0.050       0.050         4530.800       4530.494
0.020       0.020         4564.949       4555.707
0.010       0.010         4587.721       4585.273

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              4352.131
Std Dev                             83.535
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         4157.803       4169.957
0.980       0.984         4180.575       4193.199
0.950       0.962         4214.724       4221.710
0.900       0.894         4245.072       4242.307
0.800       0.798         4281.828       4278.971
0.700       0.692         4308.325       4305.236
0.500       0.460         4352.131       4344.972
0.300       0.308         4395.936       4397.625
0.200       0.210         4422.434       4427.803
0.100       0.114         4459.189       4461.420
0.050       0.050         4489.537       4489.231
0.020       0.020         4523.687       4514.444
0.010       0.010         4546.458       4544.011

Chi-Square Test of Model Fit

Degrees of freedom                       9

Mean                                 9.213
Std Dev                              4.538
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992            2.088          2.304
0.980       0.986            2.532          2.723
0.950       0.956            3.325          3.361
0.900       0.896            4.168          4.087
0.800       0.812            5.380          5.474
0.700       0.726            6.393          6.506
0.500       0.510            8.343          8.460
0.300       0.328           10.656         11.034
0.200       0.208           12.242         12.431
0.100       0.100           14.684         14.626
0.050       0.068           16.919         18.364
0.020       0.034           19.679         21.149
0.010       0.012           21.666         21.826

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.012
Std Dev                              0.016
Number of successful computations      500

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       0.968
0.020       0.680
0.010       0.586

CFI/TLI

CFI

Mean                                 0.999
Std Dev                              0.002
Number of successful computations      500

Cumulative Distribution Function
Value    Function Value
0.990       0.006
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                                 0.998
Std Dev                              0.003
Number of successful computations      500

Cumulative Distribution Function
Value    Function Value
0.990       0.040
0.980       0.004
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)

Mean                                 0.016
Std Dev                              0.006
Number of successful computations      500

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       0.772
0.010       0.106

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff

I        |
Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

S        |
Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
Y4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

I        ON
X1                  1.000     1.0013     0.0571     0.0578     0.0033 0.956 1.000
X2                  0.500     0.5003     0.1578     0.1566     0.0249 0.950 0.886

S        ON
X1                  0.400     0.3996     0.0346     0.0348     0.0012 0.954 1.000
X2                  0.250     0.2475     0.0844     0.0873     0.0071 0.952 0.844

I        WITH
S                   0.100     0.1030     0.0417     0.0434     0.0017 0.956 0.682

Intercepts
Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y4                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
I                   1.000     0.9980     0.0648     0.0612     0.0042 0.924 1.000
S                   2.000     2.0009     0.0339     0.0341     0.0011 0.948 1.000

Residual Variances
Y1                  0.500     0.5038     0.0805     0.0843     0.0065 0.952 1.000
Y2                  0.500     0.5023     0.0583     0.0559     0.0034 0.938 1.000
Y3                  0.500     0.4974     0.0673     0.0664     0.0045 0.940 1.000
Y4                  0.500     0.4976     0.1199     0.1161     0.0143 0.932 0.992
I                   1.000     0.9929     0.1112     0.1092     0.0124 0.938 1.000
S                   0.200     0.1974     0.0282     0.0288     0.0008 0.958 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.154E-01
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

NU
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
0             0             0             0             0

NU
X2
________
0

LAMBDA
I             S             X1            X2
________      ________      ________      ________
Y1                 0             0             0             0
Y2                 0             0             0             0
Y3                 0             0             0             0
Y4                 0             0             0             0
X1                 0             0             0             0
X2                 0             0             0             0

THETA
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1                 1
Y2                 0             2
Y3                 0             0             3
Y4                 0             0             0             4
X1                 0             0             0             0             0
X2                 0             0             0             0             0

THETA
X2
________
X2                 0

ALPHA
I             S             X1            X2
________      ________      ________      ________
5             6             0             0

BETA
I             S             X1            X2
________      ________      ________      ________
I                  0             0             7             8
S                  0             0             9            10
X1                 0             0             0             0
X2                 0             0             0             0

PSI
I             S             X1            X2
________      ________      ________      ________
I                 11
S                 12            13
X1                 0             0             0
X2                 0             0             0             0

STARTING VALUES

NU
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
X2
________
0.000

LAMBDA
I             S             X1            X2
________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000
Y2             1.000         1.000         0.000         0.000
Y3             1.000         2.000         0.000         0.000
Y4             1.000         3.000         0.000         0.000
X1             0.000         0.000         1.000         0.000
X2             0.000         0.000         0.000         1.000

THETA
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500
Y4             0.000         0.000         0.000         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000

THETA
X2
________
X2             0.000

ALPHA
I             S             X1            X2
________      ________      ________      ________
1.000         2.000        -0.018         0.126

BETA
I             S             X1            X2
________      ________      ________      ________
I              0.000         0.000         1.000         0.500
S              0.000         0.000         0.400         0.250
X1             0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000

PSI
I             S             X1            X2
________      ________      ________      ________
I              1.000
S              0.100         0.200
X1             0.000         0.000         0.880
X2             0.000         0.000        -0.027         0.110

POPULATION VALUES

NU
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
X2
________
0.000

LAMBDA
I             S             X1            X2
________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000
Y2             1.000         1.000         0.000         0.000
Y3             1.000         2.000         0.000         0.000
Y4             1.000         3.000         0.000         0.000
X1             0.000         0.000         1.000         0.000
X2             0.000         0.000         0.000         1.000

THETA
Y1            Y2            Y3            Y4            X1
________      ________      ________      ________      ________
Y1             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500
Y4             0.000         0.000         0.000         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000

THETA
X2
________
X2             0.000

ALPHA
I             S             X1            X2
________      ________      ________      ________
1.000         2.000         0.000         0.000

BETA
I             S             X1            X2
________      ________      ________      ________
I              0.000         0.000         1.000         0.500
S              0.000         0.000         0.400         0.250
X1             0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000

PSI
I             S             X1            X2
________      ________      ________      ________
I              1.000
S              0.100         0.200
X1             0.000         0.000         1.000
X2             0.000         0.000         0.000         1.000

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

Beginning Time:  23:06:26
Ending Time:  23:06:30
Elapsed Time:  00:00:04

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