```Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016   5:15 PM

INPUT INSTRUCTIONS

title: Hayes ESTRESS example, cont's X

data:
file = estress.txt;

variable:
names = tenure estress affect withdraw sex age ese;
usev = affect estress u y;
categorical = u;

define:
withdraw = withdraw - 1;

data twopart:
names = withdraw;
binary = u;
continuous = y;
cutpoint = 0;

analysis:
estimator = ml;
bootstrap = 1000;

model:
y on affect (beta1)
estress (beta2);
[y] (beta0);
y (v);
affect on estress (gamma1);
[affect] (gamma0);
affect (sig);
u on affect (kappa1)
estress (kappa2);
[u\$1] (kappa0);

model indirect:
u IND affect estress (6.04 4.62);

model constraint:
new(x1 x0
ey1 ey0 mum1 mum0 ay1 ay0 bym11 bym10 bym01 bym00
eym11 eym10 eym01 eym00 tnie pnde total pnie beta3
sd pi11 pi10 pi01 pi00);
beta3 = 0;
x1=6.04;
x0=4.62;
ey1=exp(v/2)*exp(beta0+beta2*x1);
ey0=exp(v/2)*exp(beta0+beta2*x0);
mum1=gamma0+gamma1*x1;
mum0=gamma0+gamma1*x0;
ay1=sig*(beta1+beta3*x1);
ay0=sig*(beta1+beta3*x0);
bym11=(ay1/mum1+1);
bym10=(ay1/mum0+1);
bym01=(ay0/mum1+1);
bym00=(ay0/mum0+1);
sd=sqrt(kappa1*kappa1*sig+1);
pi11=phi((-kappa0+kappa2*x1+kappa1*bym11*(gamma0+gamma1*x1))/sd);
pi10=phi((-kappa0+kappa2*x1+kappa1*bym10*(gamma0+gamma1*x0))/sd);
pi01=phi((-kappa0+kappa2*x0+kappa1*bym11*(gamma0+gamma1*x1))/sd);
pi00=phi((-kappa0+kappa2*x0+kappa1*bym00*(gamma0+gamma1*x0))/sd);
eym11=exp((bym11*bym11-1)*mum1*mum1/(2*sig));
eym10=exp((bym10*bym10-1)*mum0*mum0/(2*sig));
eym01=exp((bym01*bym01-1)*mum1*mum1/(2*sig));
eym00=exp((bym00*bym00-1)*mum0*mum0/(2*sig));
tnie=pi11*ey1*eym11-pi10*ey1*eym10;
pnde=pi10*ey1*eym10-pi00*ey0*eym00;
total=pi11*ey1*eym11-pi00*ey0*eym00;
pnie=pi01*ey0*eym01-pi00*ey0*eym00;

plot:
type = plot3;

output:
sampstat tech1 tech8 cinterval(bootstrap);

Hayes ESTRESS example, cont's X

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         262

Number of dependent variables                                    3
Number of independent variables                                  1
Number of continuous latent variables                            0

Observed dependent variables

Continuous
AFFECT      Y

Binary and ordered categorical (ordinal)
U

Observed independent variables
ESTRESS

Estimator                                                       ML
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                            10
Minimum value for logit thresholds                           -10
Minimum expected cell size for chi-square              0.100D-01
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Number of bootstrap draws
Requested                                                 1000
Completed                                                 1000
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                  15
Dimensions of numerical integration                            0
Cholesky                                                        ON

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

SUMMARY OF DATA

Number of missing data patterns             2
Number of y missing data patterns           2
Number of u missing data patterns           1

COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT FOR Y

Covariance Coverage
AFFECT        Y             ESTRESS
________      ________      ________
AFFECT         1.000
Y              0.702         0.702
ESTRESS        1.000         0.702         1.000

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

U
Category 1    0.298           78.000
Category 2    0.702          184.000

SAMPLE STATISTICS

ESTIMATED SAMPLE STATISTICS

Means
AFFECT        Y             ESTRESS
________      ________      ________
1              1.598         0.403         4.620

Covariances
AFFECT        Y             ESTRESS
________      ________      ________
AFFECT         0.522
Y              0.112         0.458
ESTRESS        0.349        -0.037         2.019

Correlations
AFFECT        Y             ESTRESS
________      ________      ________
AFFECT         1.000
Y              0.229         1.000
ESTRESS        0.340        -0.038         1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -917.123

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

AFFECT                1.598       1.985       1.000   24.81%       1.000      1.160      1.330
262.000       0.522       4.631       5.000    0.76%       1.500      2.000
Y                     0.435      -0.673      -1.109    7.61%       0.000      0.285      0.507
184.000       0.463      -0.174       1.792    0.54%       0.693      1.099
ESTRESS               4.620      -0.271       1.000    1.91%       3.500      4.000      4.500
262.000       2.019      -0.466       7.000    6.87%       5.000      6.000

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       10

Loglikelihood

H0 Value                        -594.173

Information Criteria

Akaike (AIC)                    1208.346
Bayesian (BIC)                  1244.029
(n* = (n + 2) / 24)

MODEL RESULTS

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

Y          ON
AFFECT             0.257      0.078      3.306      0.001
ESTRESS           -0.063      0.037     -1.708      0.088

AFFECT     ON
ESTRESS            0.173      0.040      4.290      0.000

U          ON
AFFECT             1.091      0.249      4.380      0.000
ESTRESS           -0.040      0.071     -0.563      0.574

Intercepts
AFFECT             0.799      0.184      4.333      0.000
Y                  0.283      0.168      1.682      0.093

Thresholds
U\$1                0.868      0.362      2.397      0.017

Residual Variances
AFFECT             0.461      0.086      5.371      0.000
Y                  0.427      0.041     10.518      0.000

X1                 6.040      0.000  *********      0.000
X0                 4.620      0.000  *********      0.000
EY1                1.125      0.196      5.743      0.000
EY0                1.229      0.176      6.981      0.000
MUM1               1.844      0.077     23.933      0.000
MUM0               1.598      0.043     36.795      0.000
AY1                0.118      0.036      3.306      0.001
AY0                0.118      0.036      3.306      0.001
BYM11              1.064      0.020     53.619      0.000
BYM10              1.074      0.022     48.989      0.000
BYM01              1.064      0.020     53.619      0.000
BYM00              1.074      0.022     48.989      0.000
EYM11              1.630      0.247      6.598      0.000
EYM10              1.530      0.203      7.541      0.000
EYM01              1.630      0.247      6.598      0.000
EYM00              1.530      0.203      7.541      0.000
TNIE               0.203      0.053      3.823      0.000
PNDE              -0.145      0.080     -1.814      0.070
TOTAL              0.058      0.092      0.630      0.529
PNIE               0.219      0.058      3.749      0.000
BETA3              0.000      0.000      0.000      1.000
SD                 1.245      0.113     10.983      0.000
PI11               0.796      0.037     21.496      0.000
PI10               0.730      0.039     18.938      0.000
PI01               0.809      0.029     27.522      0.000
PI00               0.745      0.027     27.769      0.000

TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS FOR LATENT RESPONSE VARIABLES

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

Effects from ESTRESS to U

Indirect             0.268      0.090      2.966      0.003
Direct effect       -0.057      0.101     -0.563      0.574

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

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

Effects from ESTRESS to U

Tot natural IE       0.071      0.019      3.694      0.000
Pure natural DE     -0.016      0.027     -0.576      0.564
Total effect         0.055      0.028      1.970      0.049

Odds ratios for binary Y

Tot natural IE       1.435      0.154      9.296      0.000
Pure natural DE      0.927      0.124      7.455      0.000
Total effect         1.331      0.221      6.031      0.000

Other effects

Pure natural IE      0.069      0.018      3.901      0.000
Tot natural DE      -0.014      0.024     -0.573      0.567
Total effect         0.055      0.028      1.970      0.049

Odds ratios for other effects for binary Y

Pure natural IE      1.439      0.157      9.157      0.000
Tot natural DE       0.925      0.129      7.182      0.000
Total effect         1.331      0.221      6.031      0.000

CONFIDENCE INTERVALS OF MODEL RESULTS

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

Y        ON
AFFECT           0.063       0.106       0.132       0.257       0.384       0.419       0.469
ESTRESS         -0.160      -0.136      -0.125      -0.063      -0.003       0.008       0.030

AFFECT   ON
ESTRESS          0.054       0.094       0.105       0.173       0.237       0.251       0.273

U        ON
AFFECT           0.584       0.691       0.765       1.091       1.573       1.676       1.937
ESTRESS         -0.233      -0.192      -0.161      -0.040       0.071       0.093       0.135

Intercepts
AFFECT           0.320       0.449       0.504       0.799       1.103       1.180       1.325
Y               -0.162      -0.058       0.005       0.283       0.557       0.615       0.748

Thresholds
U\$1              0.868       0.868       0.868       0.868       0.868       0.868       0.868

Residual Variances
AFFECT           0.267       0.302       0.324       0.461       0.614       0.648       0.700
Y                0.316       0.340       0.353       0.427       0.485       0.497       0.517

X1               6.040       6.040       6.040       6.040       6.040       6.040       6.040
X0               4.620       4.620       4.620       4.620       4.620       4.620       4.620
EY1              0.698       0.780       0.838       1.125       1.490       1.587       1.724
EY0              0.853       0.906       0.960       1.229       1.544       1.619       1.725
MUM1             1.637       1.689       1.718       1.844       1.973       1.994       2.029
MUM0             1.483       1.513       1.529       1.598       1.667       1.688       1.723
AY1              0.025       0.050       0.060       0.118       0.178       0.187       0.208
AY0              0.025       0.050       0.060       0.118       0.178       0.187       0.208
BYM11            1.014       1.025       1.032       1.064       1.096       1.104       1.117
BYM10            1.016       1.031       1.037       1.074       1.109       1.116       1.126
BYM01            1.014       1.025       1.032       1.064       1.096       1.104       1.117
BYM00            1.016       1.031       1.037       1.074       1.109       1.116       1.126
EYM11            1.123       1.225       1.281       1.630       2.079       2.231       2.404
EYM10            1.105       1.195       1.239       1.530       1.899       2.027       2.156
EYM01            1.123       1.225       1.281       1.630       2.079       2.231       2.404
EYM00            1.105       1.195       1.239       1.530       1.899       2.027       2.156
TNIE             0.065       0.104       0.121       0.203       0.293       0.311       0.348
PNDE            -0.349      -0.304      -0.276      -0.145      -0.011       0.019       0.074
TOTAL           -0.190      -0.124      -0.089       0.058       0.207       0.246       0.287
PNIE             0.068       0.116       0.131       0.219       0.318       0.343       0.385
BETA3            0.000       0.000       0.000       0.000       0.000       0.000       0.000
SD               1.059       1.098       1.116       1.245       1.473       1.531       1.699
PI11             0.690       0.720       0.732       0.796       0.854       0.863       0.887
PI10             0.620       0.656       0.665       0.730       0.792       0.804       0.824
PI01             0.734       0.750       0.761       0.809       0.856       0.864       0.881
PI00             0.669       0.692       0.700       0.745       0.789       0.794       0.809

CONFIDENCE INTERVALS OF TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS FOR LATENT RESPONSE VARIABLES

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

Effects from ESTRESS to U

Indirect           0.082       0.130       0.145       0.268       0.436       0.466       0.569
Direct effect     -0.331      -0.273      -0.229      -0.057       0.101       0.132       0.192

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 ESTRESS to U

Tot natural IE     0.023       0.036       0.041       0.071       0.103       0.108       0.122
Pure natural DE   -0.085      -0.074      -0.062      -0.016       0.028       0.035       0.055
Total effect      -0.028      -0.006       0.005       0.055       0.098       0.105       0.116

Odds ratios for binary Y

Tot natural IE     1.124       1.199       1.232       1.435       1.716       1.776       1.963
Pure natural DE    0.685       0.721       0.751       0.927       1.153       1.216       1.336
Total effect       0.870       0.972       1.026       1.331       1.738       1.833       2.035

Other effects

Pure natural IE    0.023       0.035       0.041       0.069       0.098       0.102       0.115
Tot natural DE    -0.075      -0.064      -0.056      -0.014       0.025       0.031       0.047
Total effect      -0.028      -0.006       0.005       0.055       0.098       0.105       0.116

Odds ratios for other effects for binary Y

Pure natural IE    1.126       1.202       1.231       1.439       1.724       1.793       2.000
Tot natural DE     0.674       0.714       0.743       0.925       1.157       1.224       1.344
Total effect       0.870       0.972       1.026       1.331       1.738       1.833       2.035

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

TAU
U\$1
________
1                 10

NU
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
1                  0             0             0             0

LAMBDA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U                  0             0             0             0
AFFECT             0             0             0             0
Y                  0             0             0             0
ESTRESS            0             0             0             0

THETA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U                  0
AFFECT             0             0
Y                  0             0             0
ESTRESS            0             0             0             0

ALPHA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
1                  0             1             2             0

BETA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U                  0             3             0             4
AFFECT             0             0             0             5
Y                  0             6             0             7
ESTRESS            0             0             0             0

PSI
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U                  0
AFFECT             0             8
Y                  0             0             9
ESTRESS            0             0             0             0

PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS

X1            X0            EY1           EY0           MUM1
________      ________      ________      ________      ________
1                 11            12            13            14            15

MUM0          AY1           AY0           BYM11         BYM10
________      ________      ________      ________      ________
1                 16            17            18            19            20

BYM01         BYM00         EYM11         EYM10         EYM01
________      ________      ________      ________      ________
1                 21            22            23            24            25

EYM00         TNIE          PNDE          TOTAL         PNIE
________      ________      ________      ________      ________
1                 26            27            28            29            30

BETA3         SD            PI11          PI10          PI01
________      ________      ________      ________      ________
1                 31            32            33            34            35

PI00
________
1                 36

STARTING VALUES

TAU
U\$1
________
1             -0.477

NU
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

LAMBDA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U              1.000         0.000         0.000         0.000
AFFECT         0.000         1.000         0.000         0.000
Y              0.000         0.000         1.000         0.000
ESTRESS        0.000         0.000         0.000         1.000

THETA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U              0.000
AFFECT         0.000         0.000
Y              0.000         0.000         0.000
ESTRESS        0.000         0.000         0.000         0.000

ALPHA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
1              0.000         1.598         0.435         0.000

BETA
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U              0.000         0.000         0.000         0.000
AFFECT         0.000         0.000         0.000         0.000
Y              0.000         0.000         0.000         0.000
ESTRESS        0.000         0.000         0.000         0.000

PSI
U             AFFECT        Y             ESTRESS
________      ________      ________      ________
U              1.000
AFFECT         0.000         0.261
Y              0.000         0.000         0.232
ESTRESS        0.000         0.000         0.000         1.009

STARTING VALUES FOR THE ADDITIONAL PARAMETERS

X1            X0            EY1           EY0           MUM1
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

MUM0          AY1           AY0           BYM11         BYM10
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

BYM01         BYM00         EYM11         EYM10         EYM01
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

EYM00         TNIE          PNDE          TOTAL         PNIE
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

BETA3         SD            PI11          PI10          PI01
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

PI00
________
1              0.500

TECHNICAL 8 OUTPUT

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.70498617D+03    0.0000000    0.0000000  EM
2 -0.66955755D+03   35.4286211    0.0502543  FS
3 -0.64453443D+03   25.0231257    0.0373726  FS
4 -0.62898558D+03   15.5488479    0.0241242  FS
5 -0.61930508D+03    9.6804970    0.0153907  FS
6 -0.61374087D+03    5.5642113    0.0089846  FS
7 -0.61049647D+03    3.2443994    0.0052863  FS
8 -0.61039746D+03    0.0990125    0.0001622  FS
9 -0.59417282D+03   16.2246413    0.0265805  EM
10 -0.59417281D+03    0.0000052    0.0000000  FS

PLOT INFORMATION

The following plots are available:

Histograms (sample values)
Scatterplots (sample values)
Sample proportions
Bootstrap distributions

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\ex8.15.dgm

Beginning Time:  17:15:32
Ending Time:  17:15:39
Elapsed Time:  00:00:07

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