Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016 5:16 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;
link = probit;
bootstrap = 1000;
model:
y on affect (beta1)
estress (beta2);
[y] (beta0);
y (v);
affect on estress (gamma1);
[affect] (gamma0);
affect (sig);
u on affect
estress;
model indirect:
u IND affect estress;
model constraint:
new(x1 x0
ey1 ey0 mum1 mum0 ay1 ay0 bym11 bym10 bym01 bym00
eym11 eym10 eym01 eym00 tnie pnde total pnie beta3);
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);
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=ey1*eym11-ey1*eym10;
pnde=ey1*eym10-ey0*eym00;
total=ey1*eym11-ey0*eym00;
pnie=ey0*eym01-ey0*eym00;
plot:
type = plot3;
output:
sampstat tech1 tech8 cinterval(bootstrap);
INPUT READING TERMINATED NORMALLY
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
Adaptive quadrature ON
Link PROBIT
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
Sample-Size Adjusted BIC 1212.325
(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
New/Additional Parameters
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 0.112 0.039 2.844 0.004
PNDE -0.160 0.089 -1.793 0.073
TOTAL -0.048 0.089 -0.543 0.587
PNIE 0.122 0.045 2.704 0.007
BETA3 0.000 0.000 0.000 1.000
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 0.189 0.064 2.966 0.003
Direct effect -0.040 0.071 -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 0.060 0.017 3.585 0.000
Pure natural DE -0.013 0.021 -0.620 0.535
Total effect 0.048 0.025 1.924 0.054
Odds ratios for binary Y
Tot natural IE 1.274 0.089 14.286 0.000
Pure natural DE 0.950 0.087 10.931 0.000
Total effect 1.210 0.131 9.240 0.000
Other effects
Pure natural IE 0.060 0.017 3.521 0.000
Tot natural DE -0.013 0.020 -0.626 0.532
Total effect 0.048 0.025 1.924 0.054
Odds ratios for other effects for binary Y
Pure natural IE 1.274 0.089 14.322 0.000
Tot natural DE 0.950 0.087 10.896 0.000
Total effect 1.210 0.131 9.240 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
New/Additional Parameters
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 0.028 0.043 0.053 0.112 0.177 0.194 0.232
PNDE -0.391 -0.322 -0.299 -0.160 -0.008 0.023 0.080
TOTAL -0.287 -0.219 -0.184 -0.048 0.105 0.131 0.200
PNIE 0.027 0.046 0.057 0.122 0.202 0.225 0.264
BETA3 0.000 0.000 0.000 0.000 0.000 0.000 0.000
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 0.058 0.091 0.102 0.189 0.307 0.328 0.401
Direct effect -0.233 -0.192 -0.161 -0.040 0.071 0.093 0.135
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 0.016 0.028 0.032 0.060 0.086 0.092 0.099
Pure natural DE -0.061 -0.050 -0.045 -0.013 0.023 0.029 0.043
Total effect -0.016 -0.004 0.004 0.048 0.085 0.089 0.100
Odds ratios for binary Y
Tot natural IE 1.086 1.134 1.153 1.274 1.435 1.464 1.584
Pure natural DE 0.764 0.792 0.818 0.950 1.102 1.138 1.214
Total effect 0.902 0.980 1.018 1.210 1.442 1.502 1.603
Other effects
Pure natural IE 0.015 0.026 0.032 0.060 0.086 0.091 0.101
Tot natural DE -0.057 -0.047 -0.043 -0.013 0.023 0.031 0.047
Total effect -0.016 -0.004 0.004 0.048 0.085 0.089 0.100
Odds ratios for other effects for binary Y
Pure natural IE 1.086 1.136 1.154 1.274 1.436 1.463 1.580
Tot natural DE 0.759 0.788 0.815 0.950 1.100 1.136 1.211
Total effect 0.902 0.980 1.018 1.210 1.442 1.502 1.603
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
NEW/ADDITIONAL PARAMETERS
X1 X0 EY1 EY0 MUM1
________ ________ ________ ________ ________
1 11 12 13 14 15
NEW/ADDITIONAL PARAMETERS
MUM0 AY1 AY0 BYM11 BYM10
________ ________ ________ ________ ________
1 16 17 18 19 20
NEW/ADDITIONAL PARAMETERS
BYM01 BYM00 EYM11 EYM10 EYM01
________ ________ ________ ________ ________
1 21 22 23 24 25
NEW/ADDITIONAL PARAMETERS
EYM00 TNIE PNDE TOTAL PNIE
________ ________ ________ ________ ________
1 26 27 28 29 30
NEW/ADDITIONAL PARAMETERS
BETA3
________
1 31
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
NEW/ADDITIONAL PARAMETERS
X1 X0 EY1 EY0 MUM1
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
MUM0 AY1 AY0 BYM11 BYM10
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
BYM01 BYM00 EYM11 EYM10 EYM01
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
EYM00 TNIE PNDE TOTAL PNIE
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
BETA3
________
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\ex8.18.dgm
Beginning Time: 17:16:34
Ending Time: 17:16:41
Elapsed Time: 00:00:07
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