Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:59 PM
INPUT INSTRUCTIONS
Title:
GMM
ordered polyt variables for conviction at each age11-21
dep. variable 0, 1 , 2 (0, 1, or more convictions)
Data:
file is naginORDERED.dat;
Variable:
names are u11 u12 u13 u14 u15
u16 u17 u18 u19 u20
u21 c1 c2 c3 c4 c;
usevar = u11-u21;
categorical = u11-u21;
Analysis:
algo = int;
Model:
i s q | u11@-.6 u12@-.5 u13@-.4 u14@-.3
u15@-.2 u16@-.1 u17@0 u18@.1 u19@.2
u20@.3 u21@.4;
q@0;
Output:
tech1 tech8;
Plot:
series = u11-u21(s);
type = plot3;
*** WARNING in MODEL command
All continuous latent variable covariances involving Q have been fixed to 0
because the variance of Q is fixed at 0.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
GMM
ordered polyt variables for conviction at each age11-21
dep. variable 0, 1 , 2 (0, 1, or more convictions)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 403
Number of dependent variables 11
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Binary and ordered categorical (ordinal)
U11 U12 U13 U14 U15 U16
U17 U18 U19 U20 U21
Continuous latent variables
I S Q
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 2
Adaptive quadrature ON
Link LOGIT
Cholesky ON
Input data file(s)
naginORDERED.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U11
Category 1 0.983 396.000
Category 2 0.012 5.000
Category 3 0.005 2.000
U12
Category 1 0.970 391.000
Category 2 0.025 10.000
Category 3 0.005 2.000
U13
Category 1 0.948 382.000
Category 2 0.045 18.000
Category 3 0.007 3.000
U14
Category 1 0.923 372.000
Category 2 0.062 25.000
Category 3 0.015 6.000
U15
Category 1 0.923 372.000
Category 2 0.055 22.000
Category 3 0.022 9.000
U16
Category 1 0.928 374.000
Category 2 0.045 18.000
Category 3 0.027 11.000
U17
Category 1 0.896 361.000
Category 2 0.069 28.000
Category 3 0.035 14.000
U18
Category 1 0.891 359.000
Category 2 0.084 34.000
Category 3 0.025 10.000
U19
Category 1 0.906 365.000
Category 2 0.072 29.000
Category 3 0.022 9.000
U20
Category 1 0.921 371.000
Category 2 0.057 23.000
Category 3 0.022 9.000
U21
Category 1 0.948 382.000
Category 2 0.042 17.000
Category 3 0.010 4.000
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -1072.396
H0 Scaling Correction Factor 0.990
for MLR
Information Criteria
Number of Free Parameters 7
Akaike (AIC) 2158.793
Bayesian (BIC) 2186.785
Sample-Size Adjusted BIC 2164.574
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes**
Pearson Chi-Square
Value 834.707
Degrees of Freedom 177112
P-Value 1.0000
Likelihood Ratio Chi-Square
Value 228.963
Degrees of Freedom 177112
P-Value 1.0000
** Of the 177147 cells in the latent class indicator table, 27
were deleted in the calculation of chi-square due to extreme values.
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
U11 1.000 0.000 999.000 999.000
U12 1.000 0.000 999.000 999.000
U13 1.000 0.000 999.000 999.000
U14 1.000 0.000 999.000 999.000
U15 1.000 0.000 999.000 999.000
U16 1.000 0.000 999.000 999.000
U17 1.000 0.000 999.000 999.000
U18 1.000 0.000 999.000 999.000
U19 1.000 0.000 999.000 999.000
U20 1.000 0.000 999.000 999.000
U21 1.000 0.000 999.000 999.000
S |
U11 -0.600 0.000 999.000 999.000
U12 -0.500 0.000 999.000 999.000
U13 -0.400 0.000 999.000 999.000
U14 -0.300 0.000 999.000 999.000
U15 -0.200 0.000 999.000 999.000
U16 -0.100 0.000 999.000 999.000
U17 0.000 0.000 999.000 999.000
U18 0.100 0.000 999.000 999.000
U19 0.200 0.000 999.000 999.000
U20 0.300 0.000 999.000 999.000
U21 0.400 0.000 999.000 999.000
Q |
U11 0.360 0.000 999.000 999.000
U12 0.250 0.000 999.000 999.000
U13 0.160 0.000 999.000 999.000
U14 0.090 0.000 999.000 999.000
U15 0.040 0.000 999.000 999.000
U16 0.010 0.000 999.000 999.000
U17 0.000 0.000 999.000 999.000
U18 0.010 0.000 999.000 999.000
U19 0.040 0.000 999.000 999.000
U20 0.090 0.000 999.000 999.000
U21 0.160 0.000 999.000 999.000
S WITH
I -0.076 1.128 -0.067 0.946
Means
I 0.000 0.000 999.000 999.000
S 0.403 0.655 0.616 0.538
Q -7.032 1.069 -6.576 0.000
Thresholds
U11$1 3.624 0.228 15.897 0.000
U11$2 5.454 0.268 20.320 0.000
U12$1 3.624 0.228 15.897 0.000
U12$2 5.454 0.268 20.320 0.000
U13$1 3.624 0.228 15.897 0.000
U13$2 5.454 0.268 20.320 0.000
U14$1 3.624 0.228 15.897 0.000
U14$2 5.454 0.268 20.320 0.000
U15$1 3.624 0.228 15.897 0.000
U15$2 5.454 0.268 20.320 0.000
U16$1 3.624 0.228 15.897 0.000
U16$2 5.454 0.268 20.320 0.000
U17$1 3.624 0.228 15.897 0.000
U17$2 5.454 0.268 20.320 0.000
U18$1 3.624 0.228 15.897 0.000
U18$2 5.454 0.268 20.320 0.000
U19$1 3.624 0.228 15.897 0.000
U19$2 5.454 0.268 20.320 0.000
U20$1 3.624 0.228 15.897 0.000
U20$2 5.454 0.268 20.320 0.000
U21$1 3.624 0.228 15.897 0.000
U21$2 5.454 0.268 20.320 0.000
Variances
I 4.998 0.724 6.899 0.000
S 2.789 1.609 1.733 0.083
Q 0.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.413E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U11$1 U11$2 U12$1 U12$2 U13$1
________ ________ ________ ________ ________
1 6 7 6 7 6
TAU
U13$2 U14$1 U14$2 U15$1 U15$2
________ ________ ________ ________ ________
1 7 6 7 6 7
TAU
U16$1 U16$2 U17$1 U17$2 U18$1
________ ________ ________ ________ ________
1 6 7 6 7 6
TAU
U18$2 U19$1 U19$2 U20$1 U20$2
________ ________ ________ ________ ________
1 7 6 7 6 7
TAU
U21$1 U21$2
________ ________
1 6 7
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
1 0 0 0 0 0
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
1 0 0 0 0 0
NU
U21
________
1 0
LAMBDA
I S Q
________ ________ ________
U11 0 0 0
U12 0 0 0
U13 0 0 0
U14 0 0 0
U15 0 0 0
U16 0 0 0
U17 0 0 0
U18 0 0 0
U19 0 0 0
U20 0 0 0
U21 0 0 0
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 0
U12 0 0
U13 0 0 0
U14 0 0 0 0
U15 0 0 0 0 0
U16 0 0 0 0 0
U17 0 0 0 0 0
U18 0 0 0 0 0
U19 0 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 0
U17 0 0
U18 0 0 0
U19 0 0 0 0
U20 0 0 0 0 0
U21 0 0 0 0 0
THETA
U21
________
U21 0
ALPHA
I S Q
________ ________ ________
1 0 1 2
BETA
I S Q
________ ________ ________
I 0 0 0
S 0 0 0
Q 0 0 0
PSI
I S Q
________ ________ ________
I 3
S 4 5
Q 0 0 0
STARTING VALUES
TAU
U11$1 U11$2 U12$1 U12$2 U13$1
________ ________ ________ ________ ________
1 2.710 4.200 2.710 4.200 2.710
TAU
U13$2 U14$1 U14$2 U15$1 U15$2
________ ________ ________ ________ ________
1 4.200 2.710 4.200 2.710 4.200
TAU
U16$1 U16$2 U17$1 U17$2 U18$1
________ ________ ________ ________ ________
1 2.710 4.200 2.710 4.200 2.710
TAU
U18$2 U19$1 U19$2 U20$1 U20$2
________ ________ ________ ________ ________
1 4.200 2.710 4.200 2.710 4.200
TAU
U21$1 U21$2
________ ________
1 2.710 4.200
NU
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
NU
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
NU
U21
________
1 0.000
LAMBDA
I S Q
________ ________ ________
U11 1.000 -0.600 0.360
U12 1.000 -0.500 0.250
U13 1.000 -0.400 0.160
U14 1.000 -0.300 0.090
U15 1.000 -0.200 0.040
U16 1.000 -0.100 0.010
U17 1.000 0.000 0.000
U18 1.000 0.100 0.010
U19 1.000 0.200 0.040
U20 1.000 0.300 0.090
U21 1.000 0.400 0.160
THETA
U11 U12 U13 U14 U15
________ ________ ________ ________ ________
U11 1.000
U12 0.000 1.000
U13 0.000 0.000 1.000
U14 0.000 0.000 0.000 1.000
U15 0.000 0.000 0.000 0.000 1.000
U16 0.000 0.000 0.000 0.000 0.000
U17 0.000 0.000 0.000 0.000 0.000
U18 0.000 0.000 0.000 0.000 0.000
U19 0.000 0.000 0.000 0.000 0.000
U20 0.000 0.000 0.000 0.000 0.000
U21 0.000 0.000 0.000 0.000 0.000
THETA
U16 U17 U18 U19 U20
________ ________ ________ ________ ________
U16 1.000
U17 0.000 1.000
U18 0.000 0.000 1.000
U19 0.000 0.000 0.000 1.000
U20 0.000 0.000 0.000 0.000 1.000
U21 0.000 0.000 0.000 0.000 0.000
THETA
U21
________
U21 1.000
ALPHA
I S Q
________ ________ ________
1 0.000 0.000 0.000
BETA
I S Q
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.000
Q 0.000 0.000 0.000
PSI
I S Q
________ ________ ________
I 0.050
S 0.000 0.050
Q 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.12796711D+04 0.0000000 0.0000000 EM
2 -0.11734403D+04 106.2307827 0.0830141 FS
3 -0.11352973D+04 38.1430380 0.0325053 FS
4 -0.11136860D+04 21.6112876 0.0190358 FS
5 -0.10970697D+04 16.6162348 0.0149200 FS
6 -0.10845784D+04 12.4912976 0.0113861 FS
7 -0.10767999D+04 7.7785793 0.0071720 FS
8 -0.10733905D+04 3.4093139 0.0031662 FS
9 -0.10725259D+04 0.8646632 0.0008055 FS
10 -0.10724085D+04 0.1174037 0.0001095 FS
11 -0.10723973D+04 0.0111777 0.0000104 FS
12 -0.10723964D+04 0.0008879 0.0000008 FS
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
I S Q
________ ________ ________
1 -0.001 0.403 -7.032
Covariances
I S Q
________ ________ ________
I 2.622
S -0.059 0.220
Q 0.000 0.000 0.000
Correlations
I S Q
________ ________ ________
I 1.000
S -0.077 1.000
Q 999.000 999.000 1.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated factor scores)
Scatterplots (sample values, estimated factor scores)
Sample proportions
Estimated probabilities
Item characteristic curves
Information curves
Beginning Time: 22:59:01
Ending Time: 22:59:02
Elapsed Time: 00:00:01
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