Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 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
DATA: FILE IS ex7.15.dat;
VARIABLE: NAMES ARE u1 u2 u3 w;
FREQWEIGHT = w;
CATEGORICAL = u1-u3;
CLASSES = c1 (2) c2 (2) c3 (2);
ANALYSIS: TYPE = MIXTURE;
STARTS = 0;
PARAMETERIZATION = LOGLINEAR;
MODEL:
%OVERALL%
c1 WITH c3;
c2 WITH c3;
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: TECH1 TECH8;
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 713
Number of patterns 500
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
Variables with special functions
Weight variable 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-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
Input data file(s)
ex7.15.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.403 287.000
Category 2 0.597 426.000
U2
Category 1 0.619 441.000
Category 2 0.381 272.000
U3
Category 1 0.686 489.000
Category 2 0.314 224.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 5
Loglikelihood
H0 Value -1380.635
H0 Scaling Correction Factor 1.0000
for MLR
Information Criteria
Akaike (AIC) 2771.269
Bayesian (BIC) 2794.117
Sample-Size Adjusted BIC 2778.241
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.472
Degrees of Freedom 2
P-Value 0.4791
Likelihood Ratio Chi-Square
Value 1.470
Degrees of Freedom 2
P-Value 0.4794
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON THE ESTIMATED MODEL
Latent Class
Variable Class
C1 1 286.99994 0.40252
2 426.00003 0.59748
C2 1 441.00006 0.61851
2 271.99994 0.38149
C3 1 489.00009 0.68583
2 223.99992 0.31417
CLASSIFICATION QUALITY
Entropy 1.000
LATENT CLASS INDICATOR MEANS AND PROBABILITIES FOR EACH LATENT CLASS
MEAN/PROBABILITY PROFILES FOR C1
Latent class
1 2
U1
Category 1 1.000 0.000
Category 2 0.000 1.000
MEAN/PROBABILITY PROFILES FOR C2
Latent class
1 2
U2
Category 1 1.000 0.000
Category 2 0.000 1.000
MEAN/PROBABILITY PROFILES FOR C3
Latent class
1 2
U3
Category 1 1.000 0.000
Category 2 0.000 1.000
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 Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.000 0.000
2 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 13.816 0.000
2 -13.816 0.000
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 Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.000 0.000
2 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 13.816 0.000
2 -13.816 0.000
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
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.000 0.000
2 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 13.816 0.000
2 -13.816 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Parameters for Class-specific Model Parts of C1
Latent Class C1#1
Thresholds
U1$1 15.000 0.000 999.000 999.000
Latent Class C1#2
Thresholds
U1$1 -15.000 0.000 999.000 999.000
Parameters for Class-specific Model Parts of C2
Latent Class C2#1
Thresholds
U2$1 15.000 0.000 999.000 999.000
Latent Class C2#2
Thresholds
U2$1 -15.000 0.000 999.000 999.000
Parameters for Class-specific Model Parts of C3
Latent Class C3#1
Thresholds
U3$1 15.000 0.000 999.000 999.000
Latent Class C3#2
Thresholds
U3$1 -15.000 0.000 999.000 999.000
Categorical Latent Variables
C1#1 WITH
C3#1 0.168 0.166 1.014 0.311
C2#1 WITH
C3#1 0.967 0.166 5.824 0.000
Means
C1#1 -0.511 0.138 -3.701 0.000
C2#1 -0.161 0.134 -1.201 0.230
C3#1 0.155 0.140 1.110 0.267
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.475E-01
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Results for Class-specific Model Parts of C1
Latent Class C1#1
U1
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
Latent Class C1#2
U1
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
Results for Class-specific Model Parts of C2
Latent Class C2#1
U2
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
Latent Class C2#2
U2
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
Results for Class-specific Model Parts of C3
Latent Class C3#1
U3
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
Latent Class C3#2
U3
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 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 0.000 0.000
C3#2 0.000 0.000
PSI(C)
C2#1 C2#2
________ ________
C3#1 0.000 0.000
C3#2 0.000 0.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.14826418D+04 0.0000000 0.0000000 EM
2 -0.13865224D+04 96.1194308 0.0648298 EM
3 -0.13806407D+04 5.8817201 0.0042421 EM
4 -0.13806347D+04 0.0059747 0.0000043 EM
5 -0.13806347D+04 0.0000000 0.0000000 EM
Beginning Time: 23:12:57
Ending Time: 23:12:58
Elapsed Time: 00:00:01
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