Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a loglinear model
for a three-way table with conditional
independence between the first two variables
montecarlo:
names are u1-u3;
genclasses = c1(2) c2(2) c3(2);
classes = c1(2) c2(2) c3(2);
generate = u1-u3(1);
categorical = u1-u3;
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex7.15.dat;
analysis:
type = mixture;
parameterization = loglinear;
model population:
%overall%
c1#1 with c3#1*.5;
c2#1 with c3#1*.75;
model population-c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model population-c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model population-c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
model:
%overall%
c1#1 with c3#1*.5;
c2#1 with c3#1*.75;
model c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a loglinear model
for a three-way table with conditional
independence between the first two variables
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 3
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 3
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3
Categorical latent variables
C1 C2 C3
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-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
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-05
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-05
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
Parameterization LOGLINEAR
Link LOGIT
MODEL FIT INFORMATION
Number of Free Parameters 5
Loglikelihood
H0 Value
Mean -969.990
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -969.990 -969.990
0.980 0.000 -969.990 -969.990
0.950 0.000 -969.990 -969.990
0.900 0.000 -969.990 -969.990
0.800 0.000 -969.990 -969.990
0.700 0.000 -969.990 -969.990
0.500 0.000 -969.990 -969.990
0.300 0.000 -969.990 -969.990
0.200 0.000 -969.990 -969.990
0.100 0.000 -969.990 -969.990
0.050 0.000 -969.990 -969.990
0.020 0.000 -969.990 -969.990
0.010 0.000 -969.990 -969.990
Information Criteria
Akaike (AIC)
Mean 1949.981
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1949.981 1949.981
0.980 0.000 1949.981 1949.981
0.950 0.000 1949.981 1949.981
0.900 0.000 1949.981 1949.981
0.800 0.000 1949.981 1949.981
0.700 0.000 1949.981 1949.981
0.500 0.000 1949.981 1949.981
0.300 0.000 1949.981 1949.981
0.200 0.000 1949.981 1949.981
0.100 0.000 1949.981 1949.981
0.050 0.000 1949.981 1949.981
0.020 0.000 1949.981 1949.981
0.010 0.000 1949.981 1949.981
Bayesian (BIC)
Mean 1971.054
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1971.054 1971.054
0.980 0.000 1971.054 1971.054
0.950 0.000 1971.054 1971.054
0.900 0.000 1971.054 1971.054
0.800 0.000 1971.054 1971.054
0.700 0.000 1971.054 1971.054
0.500 0.000 1971.054 1971.054
0.300 0.000 1971.054 1971.054
0.200 0.000 1971.054 1971.054
0.100 0.000 1971.054 1971.054
0.050 0.000 1971.054 1971.054
0.020 0.000 1971.054 1971.054
0.010 0.000 1971.054 1971.054
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1955.183
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1955.183 1955.183
0.980 0.000 1955.183 1955.183
0.950 0.000 1955.183 1955.183
0.900 0.000 1955.183 1955.183
0.800 0.000 1955.183 1955.183
0.700 0.000 1955.183 1955.183
0.500 0.000 1955.183 1955.183
0.300 0.000 1955.183 1955.183
0.200 0.000 1955.183 1955.183
0.100 0.000 1955.183 1955.183
0.050 0.000 1955.183 1955.183
0.020 0.000 1955.183 1955.183
0.010 0.000 1955.183 1955.183
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 1.066
Std Dev 0.000
Degrees of freedom 2
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.020 1.066
0.980 1.000 0.040 1.066
0.950 1.000 0.103 1.066
0.900 1.000 0.211 1.066
0.800 1.000 0.446 1.066
0.700 1.000 0.713 1.066
0.500 0.000 1.386 1.066
0.300 0.000 2.408 1.066
0.200 0.000 3.219 1.066
0.100 0.000 4.605 1.066
0.050 0.000 5.991 1.066
0.020 0.000 7.824 1.066
0.010 0.000 9.210 1.066
Likelihood Ratio Chi-Square
Mean 1.068
Std Dev 0.000
Degrees of freedom 2
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.020 1.068
0.980 1.000 0.040 1.068
0.950 1.000 0.103 1.068
0.900 1.000 0.211 1.068
0.800 1.000 0.446 1.068
0.700 1.000 0.713 1.068
0.500 0.000 1.386 1.068
0.300 0.000 2.408 1.068
0.200 0.000 3.219 1.068
0.100 0.000 4.605 1.068
0.050 0.000 5.991 1.068
0.020 0.000 7.824 1.068
0.010 0.000 9.210 1.068
MODEL RESULTS USE THE LATENT CLASS VARIABLE ORDER
C1 C2 C3
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON THE ESTIMATED MODEL
Latent Class
Pattern
1 1 1 140.22261 0.28045
1 1 2 39.81815 0.07964
1 2 1 62.77744 0.12555
1 2 2 44.18181 0.08836
2 1 1 98.77748 0.19755
2 1 2 33.18179 0.06636
2 2 1 44.22252 0.08845
2 2 2 36.81818 0.07364
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON THE ESTIMATED MODEL
Latent Class
Variable Class
C1 1 287.00003 0.57400
2 212.99997 0.42600
C2 1 312.00003 0.62400
2 187.99995 0.37600
C3 1 346.00006 0.69200
2 153.99994 0.30800
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent Class
Pattern
1 1 1 140.00007 0.28000
1 1 2 42.99996 0.08600
1 2 1 62.99999 0.12600
1 2 2 41.00000 0.08200
2 1 1 99.00002 0.19800
2 1 2 29.99998 0.06000
2 2 1 43.99998 0.08800
2 2 2 39.99999 0.08000
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent Class
Variable Class
C1 1 287.00003 0.57400
2 212.99997 0.42600
C2 1 312.00003 0.62400
2 187.99995 0.37600
C3 1 346.00006 0.69200
2 153.99994 0.30800
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON THEIR MOST LIKELY LATENT CLASS PATTERN
Class Counts and Proportions
Latent Class
Pattern
1 1 1 140 0.28000
1 1 2 43 0.08600
1 2 1 63 0.12600
1 2 2 41 0.08200
2 1 1 99 0.19800
2 1 2 30 0.06000
2 2 1 44 0.08800
2 2 2 40 0.08000
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON THEIR MOST LIKELY LATENT CLASS PATTERN
Latent Class
Variable Class
C1 1 287 0.57400
2 213 0.42600
C2 1 312 0.62400
2 188 0.37600
C3 1 346 0.69200
2 154 0.30800
CLASSIFICATION QUALITY
Entropy 1.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Parameters for Class-specific Model Parts of C1
Latent Class C1#1
Thresholds
U1$1 15.000 15.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class C1#2
Thresholds
U1$1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Parameters for Class-specific Model Parts of C2
Latent Class C2#1
Thresholds
U2$1 15.000 15.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class C2#2
Thresholds
U2$1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Parameters for Class-specific Model Parts of C3
Latent Class C3#1
Thresholds
U3$1 15.000 15.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class C3#2
Thresholds
U3$1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Categorical Latent Variables
C1#1 WITH
C3#1 0.500 0.1680 0.0000 0.1952 0.1102 1.000 0.000
C2#1 WITH
C3#1 0.750 0.9076 0.0000 0.1989 0.0248 1.000 1.000
Means
C1#1 0.000 0.1823 0.0000 0.1618 0.0332 1.000 0.000
C2#1 0.000 -0.1040 0.0000 0.1614 0.0108 1.000 0.000
C3#1 0.000 0.1832 0.0000 0.1862 0.0336 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.412E-01
(ratio of smallest to largest eigenvalue)
C-SPECIFIC CLASSIFICATION RESULTS
Classification Quality for C1
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
Classification Quality for C2
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
Classification Quality for C3
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 1 1
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 1 2
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 2 1
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 2 2
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 1 1
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 1 2
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 2 1
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 2 2
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1 1
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 1 1 2
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 1 2 1
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 1 2 2
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 2 1 1
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 2 1 2
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 2 2 1
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
TAU(U) FOR LATENT CLASS PATTERN 2 2 2
U1$1 U2$1 U3$1
________ ________ ________
0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C1#1 C1#2 C2#1 C2#2 C3#1
________ ________ ________ ________ ________
1 0 2 0 3
ALPHA(C)
C3#2
________
0
PSI(C)
C1#1 C1#2
________ ________
C3#1 4 0
C3#2 0 0
PSI(C)
C2#1 C2#2
________ ________
C3#1 5 0
C3#2 0 0
STARTING VALUES FOR LATENT CLASS PATTERN 1 1 1
STARTING VALUES FOR LATENT CLASS PATTERN 1 1 2
STARTING VALUES FOR LATENT CLASS PATTERN 1 2 1
STARTING VALUES FOR LATENT CLASS PATTERN 1 2 2
STARTING VALUES FOR LATENT CLASS PATTERN 2 1 1
STARTING VALUES FOR LATENT CLASS PATTERN 2 1 2
STARTING VALUES FOR LATENT CLASS PATTERN 2 2 1
STARTING VALUES FOR LATENT CLASS PATTERN 2 2 2
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1 1
U1$1 U2$1 U3$1
________ ________ ________
15.000 15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 1 1 2
U1$1 U2$1 U3$1
________ ________ ________
15.000 15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2 1
U1$1 U2$1 U3$1
________ ________ ________
15.000 -15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2 2
U1$1 U2$1 U3$1
________ ________ ________
15.000 -15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1 1
U1$1 U2$1 U3$1
________ ________ ________
-15.000 15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1 2
U1$1 U2$1 U3$1
________ ________ ________
-15.000 15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2 1
U1$1 U2$1 U3$1
________ ________ ________
-15.000 -15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2 2
U1$1 U2$1 U3$1
________ ________ ________
-15.000 -15.000 -15.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C1#1 C1#2 C2#1 C2#2 C3#1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA(C)
C3#2
________
0.000
PSI(C)
C1#1 C1#2
________ ________
C3#1 0.500 0.000
C3#2 0.000 0.000
PSI(C)
C2#1 C2#2
________ ________
C3#1 0.750 0.000
C3#2 0.000 0.000
POPULATION VALUES FOR LATENT CLASS PATTERN 1 1 1
POPULATION VALUES FOR LATENT CLASS PATTERN 1 1 2
POPULATION VALUES FOR LATENT CLASS PATTERN 1 2 1
POPULATION VALUES FOR LATENT CLASS PATTERN 1 2 2
POPULATION VALUES FOR LATENT CLASS PATTERN 2 1 1
POPULATION VALUES FOR LATENT CLASS PATTERN 2 1 2
POPULATION VALUES FOR LATENT CLASS PATTERN 2 2 1
POPULATION VALUES FOR LATENT CLASS PATTERN 2 2 2
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1 1
U1$1 U2$1 U3$1
________ ________ ________
15.000 15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 1 1 2
U1$1 U2$1 U3$1
________ ________ ________
15.000 15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2 1
U1$1 U2$1 U3$1
________ ________ ________
15.000 -15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2 2
U1$1 U2$1 U3$1
________ ________ ________
15.000 -15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1 1
U1$1 U2$1 U3$1
________ ________ ________
-15.000 15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1 2
U1$1 U2$1 U3$1
________ ________ ________
-15.000 15.000 -15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2 1
U1$1 U2$1 U3$1
________ ________ ________
-15.000 -15.000 15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2 2
U1$1 U2$1 U3$1
________ ________ ________
-15.000 -15.000 -15.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C1#1 C1#2 C2#1 C2#2 C3#1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA(C)
C3#2
________
0.000
PSI(C)
C1#1 C1#2
________ ________
C3#1 0.500 0.000
C3#2 0.000 0.000
PSI(C)
C2#1 C2#2
________ ________
C3#1 0.750 0.000
C3#2 0.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.97226043D+03 0.0000000 0.0000000 EM
2 -0.96999552D+03 2.2649052 0.0023295 EM
3 -0.96999030D+03 0.0052263 0.0000054 EM
4 -0.96999030D+03 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
C1
C2
C3
Save file
ex7.15.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:29
Ending Time: 22:24:29
Elapsed Time: 00:00:00
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