Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:26 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level growth model
for a continuous outcome (three-level analysis) with
variation of a random slope on both the within and
between levels
montecarlo:
names are y1-y4 x a1-a4 w;
nobservations = 500;
ncsizes = 3;
csizes = 10 (5) 50 (3) 30 (10);
seed = 58459;
nreps = 1;
within = x a1-a4;
between = w;
save = ex9.14.dat;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
algorithm = integration;
integration = 10;
MODEL POPULATION:
%WITHIN%
x@1; a1-a4@1;
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4*.5 (1);
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;
s* | y1 ON a1;
s* | y2 ON a2;
s* | y3 ON a3;
s* | y4 ON a4;
s*.5;
%BETWEEN%
w@1;
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib ON w*.5;
sb ON w*.2;
s ON w*.6;
s with ib-sb@0;
[ib*1 sb*.5 s*1];
ib*.5; sb*.2; s*.3;
MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4*.5 (1);
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;
s* | y1 ON a1;
s* | y2 ON a2;
s* | y3 ON a3;
s* | y4 ON a4;
s*.5;
%BETWEEN%
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib ON w*.5;
sb ON w*.2;
s ON w*.6;
s with ib-sb@0;
[ib*1 sb*.5 s*1];
ib*.5; sb*.2; s*.3;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level growth model
for a continuous outcome (three-level analysis) with
variation of a random slope on both the within and
between levels
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 58459
Number of dependent variables 4
Number of independent variables 6
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X A1 A2 A3 A4 W
Continuous latent variables
IW SW S IB SB
Variables with special functions
Within variables
X A1 A2 A3 A4
Between variables
W
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 10
Dimensions of numerical integration 4
Adaptive quadrature ON
Cholesky OFF
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
3 50
5 10
10 30
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1.019 1.653 2.015 2.701 0.033
Means
A1 A2 A3 A4 W
________ ________ ________ ________ ________
-0.078 -0.061 -0.002 0.039 -0.091
Covariances
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 5.276
Y2 3.073 8.072
Y3 3.628 6.355 10.410
Y4 3.609 7.548 10.017 16.330
X 0.900 1.184 1.513 1.623 0.922
A1 1.066 0.066 0.145 0.199 0.030
A2 0.043 1.265 0.277 0.153 -0.013
A3 -0.021 -0.028 0.821 -0.250 -0.066
A4 -0.105 -0.127 -0.078 0.871 -0.079
W 0.489 0.996 1.083 1.403 -0.027
Covariances
A1 A2 A3 A4 W
________ ________ ________ ________ ________
A1 0.985
A2 -0.009 1.073
A3 -0.012 0.019 1.022
A4 0.041 -0.035 -0.008 1.080
W 0.040 0.126 -0.041 0.004 0.956
Correlations
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1.000
Y2 0.471 1.000
Y3 0.489 0.693 1.000
Y4 0.389 0.657 0.768 1.000
X 0.408 0.434 0.488 0.418 1.000
A1 0.468 0.024 0.045 0.050 0.031
A2 0.018 0.430 0.083 0.037 -0.013
A3 -0.009 -0.010 0.252 -0.061 -0.068
A4 -0.044 -0.043 -0.023 0.207 -0.079
W 0.218 0.359 0.343 0.355 -0.029
Correlations
A1 A2 A3 A4 W
________ ________ ________ ________ ________
A1 1.000
A2 -0.009 1.000
A3 -0.012 0.018 1.000
A4 0.039 -0.032 -0.008 1.000
W 0.041 0.125 -0.041 0.004 1.000
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -3616.302
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3616.302 -3616.302
0.980 0.000 -3616.302 -3616.302
0.950 0.000 -3616.302 -3616.302
0.900 0.000 -3616.302 -3616.302
0.800 0.000 -3616.302 -3616.302
0.700 0.000 -3616.302 -3616.302
0.500 0.000 -3616.302 -3616.302
0.300 0.000 -3616.302 -3616.302
0.200 0.000 -3616.302 -3616.302
0.100 0.000 -3616.302 -3616.302
0.050 0.000 -3616.302 -3616.302
0.020 0.000 -3616.302 -3616.302
0.010 0.000 -3616.302 -3616.302
Information Criteria
Akaike (AIC)
Mean 7266.605
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7266.605 7266.605
0.980 0.000 7266.605 7266.605
0.950 0.000 7266.605 7266.605
0.900 0.000 7266.605 7266.605
0.800 0.000 7266.605 7266.605
0.700 0.000 7266.605 7266.605
0.500 0.000 7266.605 7266.605
0.300 0.000 7266.605 7266.605
0.200 0.000 7266.605 7266.605
0.100 0.000 7266.605 7266.605
0.050 0.000 7266.605 7266.605
0.020 0.000 7266.605 7266.605
0.010 0.000 7266.605 7266.605
Bayesian (BIC)
Mean 7338.253
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7338.253 7338.253
0.980 0.000 7338.253 7338.253
0.950 0.000 7338.253 7338.253
0.900 0.000 7338.253 7338.253
0.800 0.000 7338.253 7338.253
0.700 0.000 7338.253 7338.253
0.500 0.000 7338.253 7338.253
0.300 0.000 7338.253 7338.253
0.200 0.000 7338.253 7338.253
0.100 0.000 7338.253 7338.253
0.050 0.000 7338.253 7338.253
0.020 0.000 7338.253 7338.253
0.010 0.000 7338.253 7338.253
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 7284.294
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7284.294 7284.294
0.980 0.000 7284.294 7284.294
0.950 0.000 7284.294 7284.294
0.900 0.000 7284.294 7284.294
0.800 0.000 7284.294 7284.294
0.700 0.000 7284.294 7284.294
0.500 0.000 7284.294 7284.294
0.300 0.000 7284.294 7284.294
0.200 0.000 7284.294 7284.294
0.100 0.000 7284.294 7284.294
0.050 0.000 7284.294 7284.294
0.020 0.000 7284.294 7284.294
0.010 0.000 7284.294 7284.294
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
IW |
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
SW |
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
IW ON
X 1.000 1.0055 0.0000 0.0635 0.0000 1.000 1.000
SW ON
X 0.200 0.2617 0.0000 0.0449 0.0038 1.000 1.000
SW WITH
IW 0.000 0.0454 0.0000 0.0515 0.0021 1.000 0.000
Variances
S 0.500 0.6126 0.0000 0.0476 0.0127 0.000 1.000
Residual Variances
Y1 0.500 0.5090 0.0000 0.0314 0.0001 1.000 1.000
Y2 0.500 0.5090 0.0000 0.0314 0.0001 1.000 1.000
Y3 0.500 0.5090 0.0000 0.0314 0.0001 1.000 1.000
Y4 0.500 0.5090 0.0000 0.0314 0.0001 1.000 1.000
IW 1.000 0.8350 0.0000 0.0825 0.0272 0.000 1.000
SW 0.500 0.5598 0.0000 0.0501 0.0036 1.000 1.000
Between Level
IB |
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
SB |
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
IB ON
W 0.500 0.5269 0.0000 0.0997 0.0007 1.000 1.000
SB ON
W 0.200 0.3193 0.0000 0.0589 0.0142 0.000 1.000
S ON
W 0.600 0.6169 0.0000 0.0684 0.0003 1.000 1.000
S WITH
IB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SB WITH
IB 0.000 -0.0663 0.0000 0.0618 0.0044 1.000 0.000
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
IB 1.000 1.0878 0.0000 0.0882 0.0077 1.000 1.000
SB 0.500 0.5669 0.0000 0.0630 0.0045 1.000 1.000
S 1.000 1.0583 0.0000 0.0723 0.0034 1.000 1.000
Residual Variances
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
IB 0.500 0.4139 0.0000 0.0939 0.0074 1.000 1.000
SB 0.200 0.1994 0.0000 0.0562 0.0000 1.000 1.000
S 0.300 0.2763 0.0000 0.0645 0.0006 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.217E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
NU
A1 A2 A3 A4
________ ________ ________ ________
0 0 0 0
LAMBDA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
LAMBDA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
LAMBDA
A3 A4
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
X 0 0
A1 0 0
A2 0 0
A3 0 0
A4 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
THETA
A1 A2 A3 A4
________ ________ ________ ________
A1 0
A2 0 0
A3 0 0 0
A4 0 0 0 0
ALPHA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
A3 A4
________ ________
0 0
BETA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0 0 0 0 0
SW 0 0 0 0 0
S%W 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
BETA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
IW 0 0 1 0 0
SW 0 0 2 0 0
S%W 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
BETA
A3 A4
________ ________
IW 0 0
SW 0 0
S%W 0 0
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
X 0 0
A1 0 0
A2 0 0
A3 0 0
A4 0 0
PSI
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 3
SW 4 5
S%W 0 0 6
Y1 0 0 0 7
Y2 0 0 0 0 7
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
PSI
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y3 7
Y4 0 7
X 0 0 0
A1 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
PSI
A3 A4
________ ________
A3 0
A4 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
LAMBDA
Y3 Y4 W
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
W 0 0 0 0 0
ALPHA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
8 9 10 0 0
ALPHA
Y3 Y4 W
________ ________ ________
0 0 0
BETA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0 0 0 0 0
SB 0 0 0 0 0
S%B 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
BETA
Y3 Y4 W
________ ________ ________
IB 0 0 11
SB 0 0 12
S%B 0 0 13
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
PSI
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 14
SB 15 16
S%B 0 0 17
Y1 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
PSI
Y3 Y4 W
________ ________ ________
Y3 0
Y4 0 0
W 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
A1 A2 A3 A4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
X 0.000 0.000 1.000 0.000 0.000
A1 0.000 0.000 0.000 1.000 0.000
A2 0.000 0.000 0.000 0.000 1.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
A3 A4
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 1.000 0.000
A4 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
THETA
A1 A2 A3 A4
________ ________ ________ ________
A1 0.000
A2 0.000 0.000
A3 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000
ALPHA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
A3 A4
________ ________
0.000 0.000
BETA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0.000 0.000 0.000 0.000 0.000
SW 0.000 0.000 0.000 0.000 0.000
S%W 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
IW 0.000 0.000 1.000 0.000 0.000
SW 0.000 0.000 0.200 0.000 0.000
S%W 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
A3 A4
________ ________
IW 0.000 0.000
SW 0.000 0.000
S%W 0.000 0.000
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 0.000 0.000
A4 0.000 0.000
PSI
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 1.000
SW 0.000 0.500
S%W 0.000 0.000 0.500
Y1 0.000 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.000 0.500
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y3 0.500
Y4 0.000 0.500
X 0.000 0.000 0.500
A1 0.000 0.000 0.000 0.500
A2 0.000 0.000 0.000 0.000 0.500
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
A3 A4
________ ________
A3 0.500
A4 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 W
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
1.000 0.500 1.000 0.000 0.000
ALPHA
Y3 Y4 W
________ ________ ________
0.000 0.000 0.000
BETA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.000 0.000 0.000 0.000 0.000
SB 0.000 0.000 0.000 0.000 0.000
S%B 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.200
S%B 0.000 0.000 0.600
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.500
SB 0.000 0.200
S%B 0.000 0.000 0.300
Y1 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 W
________ ________ ________
Y3 0.000
Y4 0.000 0.000
W 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
A1 A2 A3 A4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
X 0.000 0.000 1.000 0.000 0.000
A1 0.000 0.000 0.000 1.000 0.000
A2 0.000 0.000 0.000 0.000 1.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
A3 A4
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 1.000 0.000
A4 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
THETA
A1 A2 A3 A4
________ ________ ________ ________
A1 0.000
A2 0.000 0.000
A3 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000
ALPHA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
A3 A4
________ ________
0.000 0.000
BETA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0.000 0.000 0.000 0.000 0.000
SW 0.000 0.000 0.000 0.000 0.000
S%W 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
IW 0.000 0.000 1.000 0.000 0.000
SW 0.000 0.000 0.200 0.000 0.000
S%W 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
A3 A4
________ ________
IW 0.000 0.000
SW 0.000 0.000
S%W 0.000 0.000
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 0.000 0.000
A4 0.000 0.000
PSI
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 1.000
SW 0.000 0.500
S%W 0.000 0.000 0.500
Y1 0.000 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.000 0.500
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y3 0.500
Y4 0.000 0.500
X 0.000 0.000 1.000
A1 0.000 0.000 0.000 1.000
A2 0.000 0.000 0.000 0.000 1.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
A3 A4
________ ________
A3 1.000
A4 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 W
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
1.000 0.500 1.000 0.000 0.000
ALPHA
Y3 Y4 W
________ ________ ________
0.000 0.000 0.000
BETA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.000 0.000 0.000 0.000 0.000
SB 0.000 0.000 0.000 0.000 0.000
S%B 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.200
S%B 0.000 0.000 0.600
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.500
SB 0.000 0.200
S%B 0.000 0.000 0.300
Y1 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 W
________ ________ ________
Y3 0.000
Y4 0.000 0.000
W 0.000 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.36279127D+04 0.0000000 0.0000000 EM
2 -0.36181862D+04 9.7265087 0.0026810 EM
3 -0.36169697D+04 1.2164754 0.0003362 EM
4 -0.36165910D+04 0.3786802 0.0001047 EM
5 -0.36164351D+04 0.1559628 0.0000431 EM
6 -0.36163646D+04 0.0704903 0.0000195 EM
7 -0.36163316D+04 0.0330362 0.0000091 EM
8 -0.36163158D+04 0.0157127 0.0000043 EM
9 -0.36163083D+04 0.0075076 0.0000021 EM
10 -0.36163048D+04 0.0035783 0.0000010 EM
11 -0.36163031D+04 0.0016885 0.0000005 EM
12 -0.36163023D+04 0.0007804 0.0000002 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
X
A1
A2
A3
A4
W
CLUSTER
Save file
ex9.14.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:26:02
Ending Time: 22:26:38
Elapsed Time: 00:00:36
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