Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016   5:16 PM

INPUT INSTRUCTIONS

title:
hypothetical potential outcome example data

data:
file = potential.txt;

variable:
names = x m y;
usev = x m y mx;
categorical = m;

define:
mx = m*x;

analysis:
estimator = mlr;

model:
y on m x mx;
m on x;

model indirect:
y mod m mx x;

output:
sampstat tech1 tech8 cinterval;

hypothetical potential outcome example data

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                           6

Number of dependent variables                                    2
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

Continuous
Y

Binary and ordered categorical (ordinal)
M

Observed independent variables
X           MX

Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                 100
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                            15
Minimum value for logit thresholds                           -15
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                  15
Dimensions of numerical integration                            0
Cholesky                                                       OFF

Input data file(s)
potential.txt
Input data format  FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

M
Category 1    0.500            3.000
Category 2    0.500            3.000

SAMPLE STATISTICS

SAMPLE STATISTICS

Means
Y             X             MX
________      ________      ________
1             10.167         0.500         0.333

Covariances
Y             X             MX
________      ________      ________
Y              7.806
X              0.583         0.250
MX             0.778         0.167         0.222

Correlations
Y             X             MX
________      ________      ________
Y              1.000
X              0.418         1.000
MX             0.591         0.707         1.000

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

Y                    10.167      -0.584       5.000   16.67%       5.000      9.000     10.500
6.000       7.806      -0.423      14.000   16.67%      11.000     12.000
X                     0.500       0.000       0.000   50.00%       0.000      0.000      0.500
6.000       0.250      -2.000       1.000   50.00%       1.000      1.000
MX                    0.333       0.707       0.000   66.67%       0.000      0.000      0.000
6.000       0.222      -1.500       1.000   33.33%       0.000      1.000

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX.  THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION.  THE
CONDITION NUMBER IS       0.259D-15.  PROBLEM INVOLVING THE FOLLOWING PARAMETER:
Parameter 4, Y ON X

NOTE THAT THE NUMBER OF PARAMETERS IS GREATER THAN THE SAMPLE SIZE.

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

H0 Value                         -17.059
H0 Scaling Correction Factor      0.8010
for MLR

Information Criteria

Akaike (AIC)                      48.119
Bayesian (BIC)                    46.661
(n* = (n + 2) / 24)

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Y          ON
M                  1.500      2.475      0.606      0.544
X                  0.500      2.475      0.202      0.840
MX                 2.000      2.693      0.743      0.458

M          ON
X                  1.386      1.732      0.800      0.423

Intercepts
Y                  8.500      2.475      3.435      0.001

Thresholds
M\$1                0.693      1.225      0.566      0.571

Residual Variances
Y                  4.833      2.174      2.224      0.026

LOGISTIC REGRESSION ODDS RATIO RESULTS

M          ON
X                  4.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.259E-15
(ratio of smallest to largest eigenvalue)

TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from X to Y

Tot natural IE       1.167      1.393      0.838      0.402
Pure natural DE      1.167      1.773      0.658      0.511
Total effect         2.333      2.073      1.126      0.260

Other effects

Pure natural IE      0.500      1.007      0.497      0.619
Tot natural DE       1.833      1.215      1.509      0.131
Total effect         2.333      2.073      1.126      0.260

CONFIDENCE INTERVALS OF MODEL RESULTS

Lower .5%  Lower 2.5%    Lower 5%    Estimate    Upper 5%  Upper 2.5%   Upper .5%

Y        ON
M               -4.875      -3.351      -2.571       1.500       5.571       6.351       7.875
X               -5.875      -4.351      -3.571       0.500       4.571       5.351       6.875
MX              -4.936      -3.277      -2.429       2.000       6.429       7.277       8.936

M        ON
X               -3.075      -2.009      -1.463       1.386       4.236       4.781       5.848

Intercepts
Y                2.125       3.649       4.429       8.500      12.571      13.351      14.875

Thresholds
M\$1             -2.462      -1.707      -1.322       0.693       2.708       3.094       3.848

Residual Variances
Y               -0.765       0.573       1.258       4.833       8.409       9.094      10.432

CONFIDENCE INTERVALS FOR THE LOGISTIC REGRESSION ODDS RATIO RESULTS

M        ON
X                0.046       0.134       0.232       4.000      69.097     119.237     346.440

CONFIDENCE INTERVALS OF TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)

Lower .5%  Lower 2.5%    Lower 5%    Estimate    Upper 5%  Upper 2.5%   Upper .5%

Effects from X to Y

Tot natural IE    -2.421      -1.563      -1.124       1.167       3.458       3.896       4.754
Pure natural DE   -3.400      -2.308      -1.750       1.167       4.083       4.642       5.734
Total effect      -3.006      -1.729      -1.076       2.333       5.743       6.396       7.672

Other effects

Pure natural IE   -2.094      -1.474      -1.156       0.500       2.156       2.474       3.094
Tot natural DE    -1.297      -0.549      -0.166       1.833       3.832       4.215       4.964
Total effect      -3.006      -1.729      -1.076       2.333       5.743       6.396       7.672

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

TAU
M\$1
________
1                  7

NU
M             Y             X             MX
________      ________      ________      ________
1                  0             0             0             0

LAMBDA
M             Y             X             MX
________      ________      ________      ________
M                  0             0             0             0
Y                  0             0             0             0
X                  0             0             0             0
MX                 0             0             0             0

THETA
M             Y             X             MX
________      ________      ________      ________
M                  0
Y                  0             0
X                  0             0             0
MX                 0             0             0             0

ALPHA
M             Y             X             MX
________      ________      ________      ________
1                  0             1             0             0

BETA
M             Y             X             MX
________      ________      ________      ________
M                  0             0             2             0
Y                  3             0             4             5
X                  0             0             0             0
MX                 0             0             0             0

PSI
M             Y             X             MX
________      ________      ________      ________
M                  0
Y                  0             6
X                  0             0             0
MX                 0             0             0             0

STARTING VALUES

TAU
M\$1
________
1              0.000

NU
M             Y             X             MX
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

LAMBDA
M             Y             X             MX
________      ________      ________      ________
M              1.000         0.000         0.000         0.000
Y              0.000         1.000         0.000         0.000
X              0.000         0.000         1.000         0.000
MX             0.000         0.000         0.000         1.000

THETA
M             Y             X             MX
________      ________      ________      ________
M              0.000
Y              0.000         0.000
X              0.000         0.000         0.000
MX             0.000         0.000         0.000         0.000

ALPHA
M             Y             X             MX
________      ________      ________      ________
1              0.000        10.167         0.000         0.000

BETA
M             Y             X             MX
________      ________      ________      ________
M              0.000         0.000         0.000         0.000
Y              0.000         0.000         0.000         0.000
X              0.000         0.000         0.000         0.000
MX             0.000         0.000         0.000         0.000

PSI
M             Y             X             MX
________      ________      ________      ________
M              1.000
Y              0.000         3.903
X              0.000         0.000         0.125
MX             0.000         0.000         0.000         0.111

TECHNICAL 8 OUTPUT

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.19757580D+02    0.0000000    0.0000000  EM
2 -0.17059794D+02    2.6977859    0.1365443  EM
3 -0.17059325D+02    0.0004688    0.0000275  EM
4 -0.17059325D+02    0.0000000    0.0000000  EM

DIAGRAM INFORMATION

Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.

Diagram output
c:\users\gryphon\desktop\chapter8\ex8.22.dgm

Beginning Time:  17:16:53
Ending Time:  17:16:53
Elapsed Time:  00:00:00

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