Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:29 AM

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;

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

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

Latent Class Variable Patterns

C1        C2        C3
Class     Class     Class

1         1         1
1         1         2
1         2         1
1         2         2
2         1         1
2         1         2
2         2         1
2         2         2

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

Average Latent Class Probabilities for Most Likely Latent Class Pattern (Row)
by Latent Class Pattern (Column)

Latent Class Variable Patterns

Latent Class         C1        C2        C3
Pattern No.      Class     Class     Class

1             1         1         1
2             1         1         2
3             1         2         1
4             1         2         2
5             2         1         1
6             2         1         2
7             2         2         1
8             2         2         2

1        2        3        4        5        6        7        8

1   1.000    0.000    0.000    0.000    0.000    0.000    0.000    0.000
2   0.000    1.000    0.000    0.000    0.000    0.000    0.000    0.000
3   0.000    0.000    1.000    0.000    0.000    0.000    0.000    0.000
4   0.000    0.000    0.000    1.000    0.000    0.000    0.000    0.000
5   0.000    0.000    0.000    0.000    1.000    0.000    0.000    0.000
6   0.000    0.000    0.000    0.000    0.000    1.000    0.000    0.000
7   0.000    0.000    0.000    0.000    0.000    0.000    1.000    0.000
8   0.000    0.000    0.000    0.000    0.000    0.000    0.000    1.000

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
Latent Class Pattern 1 1 1

Thresholds
U1\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 1 1 2

Thresholds
U1\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 1 2 1

Thresholds
U1\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 1 2 2

Thresholds
U1\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 2 1 1

Thresholds
U1\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 2 1 2

Thresholds
U1\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 2 2 1

Thresholds
U1\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U3\$1               15.000    15.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class Pattern 2 2 2

Thresholds
U1\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
U2\$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
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)

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

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.97226043D+03    0.0000000    0.0000000    140.000    43.000    EM
63.000    41.000
99.000    30.000
44.000    40.000
2 -0.96999552D+03    2.2649052    0.0023295    140.000    43.000    EM
63.000    41.000
99.000    30.000
44.000    40.000
3 -0.96999030D+03    0.0052263    0.0000054    140.000    43.000    EM
63.000    41.000
99.000    30.000
44.000    40.000
4 -0.96999030D+03    0.0000000    0.0000000    140.000    43.000    EM
63.000    41.000
99.000    30.000
44.000    40.000

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:  03:29:20
Ending Time:  03:29:20
Elapsed Time:  00:00:00

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