Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix2
An example of LCA with insufficient number of iterations
DATA: FILE IS bart.dat;
VARIABLE: NAMES ARE u1-u4;
USEV ARE u1-u4;
CATEGORICAL = u1 - u4;
CLASSES = c(2);
ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 2;
! this is a latent class analysis of 4 binary indicators of a
! categorical latent variable with 2 classes
! the default number of E step iterations is reduced from 100
! to 2 to illustrate nonconvergence
MODEL:
%OVERALL%
! c#1 BY u1*-2 u2*-2 u3*-2 u4*-2;
! c#2 BY u1*1 u2*1 u3*1 u4*1;
[u1$1*2 u2$1*2 u3$1*2 u4$1*2];
%C#2%
[u1$1*-1 u2$1*-1 u3$1*-1 u4$1*-1];
! the two lines above refer to the logits of the conditional
! probabilities of u = 1 given latent class 1 and 2, respectively.
! Starting values are required for these parameters.
! Starting values can for example be obtained
! by having lower u probabilities for the first class than for the second
! class. There is no need to provide starting values for the latent class
! probabilities - the default is equal probabilities. As an example of
! giving a starting value with a small probability for class 1 is as
! follows:
!
! [c#1*-2];
!
! The following shows how to set starting values in the logit scale.
! the relationship between logits and probabilities is
!
! probability = 1/(1+exp(-logit))
!
! logit = elog(probability/(1-probability))
!
! which means that
!
! Probability Logit
! 0 -100 (approximately)
! 0.5 0
! 1 +100 (approximately)
OUTPUT:
TECH8;
! tech8 is needed to monitor the convergence of mixture modeling
INPUT READING TERMINATED NORMALLY
mix2
An example of LCA with insufficient number of iterations
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 142
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Categorical latent variables
C
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 2
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
Random Starts Specifications
Number of initial stage random starts 10
Number of final stage optimizations 2
Number of initial stage iterations 10
Initial stage convergence criterion 0.100D+01
Random starts scale 0.500D+01
Random seed for generating random starts 0
Link LOGIT
Input data file(s)
bart.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.472 67.000
Category 2 0.528 75.000
U2
Category 1 0.514 73.000
Category 2 0.486 69.000
U3
Category 1 0.739 105.000
Category 2 0.261 37.000
U4
Category 1 0.563 80.000
Category 2 0.437 62.000
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
Unperturbed starting value run did not converge.
1 perturbed starting value run(s) did not converge.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN INSUFFICIENT
NUMBER OF E STEPS. INCREASE THE NUMBER OF MITERATIONS. ESTIMATES
CANNOT BE TRUSTED.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A CHANGE IN THE
LOGLIKELIHOOD DURING THE LAST E STEP.
AN INSUFFICENT NUMBER OF E STEP ITERATIONS MAY HAVE BEEN USED. INCREASE
THE NUMBER OF MITERATIONS OR INCREASE THE MCONVERGENCE VALUE. ESTIMATES
CANNOT BE TRUSTED.
SLOW CONVERGENCE DUE TO PARAMETER 9.
THE LOGLIKELIHOOD DERIVATIVE FOR THIS PARAMETER IS -0.89765970D-02.
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 67.57111 0.47585
2 74.42889 0.52415
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 66.29643 0.46688
2 75.70357 0.53312
CLASSIFICATION QUALITY
Entropy 0.715
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 65 0.45775
2 77 0.54225
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.933 0.067
2 0.073 0.927
MODEL RESULTS
Estimate
Latent Class 1
Thresholds
U1$1 1.249
U2$1 1.912
U3$1 3.060
U4$1 2.136
Latent Class 2
Thresholds
U1$1 -1.420
U2$1 -1.451
U3$1 0.175
U4$1 -1.031
Categorical Latent Variables
Means
C#1 -0.097
MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES
%OVERALL%
[ c#1*-0.097 ];
%C#1%
[ u1$1*1.249 ];
[ u2$1*1.912 ];
[ u3$1*3.060 ];
[ u4$1*2.136 ];
%C#2%
[ u1$1*-1.420 ];
[ u2$1*-1.451 ];
[ u3$1*0.175 ];
[ u4$1*-1.031 ];
TECHNICAL 8 OUTPUT
INITIAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.35341784D+03 0.0000000 0.0000000 67.571 74.429 EM
2 -0.33273204D+03 20.6858009 0.0585307 66.296 75.704 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48417716D+03 0.0000000 0.0000000 90.980 51.020 EM
2 -0.34687327D+03 137.3038923 0.2835819 88.175 53.825 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.77768249D+03 0.0000000 0.0000000 46.971 95.029 EM
2 -0.36949672D+03 408.1857690 0.5248746 48.542 93.458 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.61820111D+03 0.0000000 0.0000000 47.935 94.065 EM
2 -0.37843203D+03 239.7690785 0.3878496 46.882 95.118 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48659193D+03 0.0000000 0.0000000 44.898 97.102 EM
2 -0.37742247D+03 109.1694573 0.2243553 44.122 97.878 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.41231589D+03 0.0000000 0.0000000 45.822 96.178 EM
2 -0.33561386D+03 76.7020372 0.1860274 49.722 92.278 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.79307525D+03 0.0000000 0.0000000 68.408 73.592 EM
2 -0.33398857D+03 459.0866854 0.5788690 67.718 74.282 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.52760607D+03 0.0000000 0.0000000 109.495 32.505 EM
2 -0.36030670D+03 167.2993712 0.3170914 107.529 34.471 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.51298960D+03 0.0000000 0.0000000 95.411 46.589 EM
2 -0.34268810D+03 170.3014993 0.3319785 93.883 48.117 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.65538774D+03 0.0000000 0.0000000 100.101 41.899 EM
2 -0.35243394D+03 302.9537974 0.4622512 95.169 46.831 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.61777512D+03 0.0000000 0.0000000 126.981 15.019 EM
2 -0.36283884D+03 254.9362853 0.4126684 123.421 18.579 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
2 -0.33273204D+03 20.6858009 0.0585307 66.296 75.704 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
2 -0.33398857D+03 459.0866854 0.5788690 67.718 74.282 EM
Beginning Time: 22:58:12
Ending Time: 22:58:12
Elapsed Time: 00:00:00
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