|
|
|
||||
|
|
|||||
We will illustrate a simple Latent Class Analysis (LCA) and show how the interpretation can be enhanced via Mplus graphics. We will see if we can identify 3 classes based on the variables read write math science and then see how well we can predict this class membership from female ses and socst. This is a very artificial example, so please extrapolate to your research interests.
Step 1. Run the LCA
Title:
Latent Class Analysis with Graphs
Data:
File is hsb2.dat ;
Variable:
Names are
id female race ses schtyp prog read write math science socst;
Usevariables are
read write math science female ses socst;
classes = grp(3);
Analysis:
type=mixture;
Model:
%overall%
grp#1 on female ses socst;
grp#2 on female ses socst;
Plot:
type is plot3;
series is read (1) write (2) math (3) science (4);
And here is the output from the LCA.
Mplus VERSION 3.0
MUTHEN & MUTHEN
04/29/2004 9:37 AM
INPUT INSTRUCTIONS
Title:
Latent Class Analysis with Graphs
Data:
File is hsb2.dat ;
Variable:
Names are
id female race ses schtyp prog read write math science socst;
Usevariables are
read write math science female ses socst;
classes = grp(3);
Analysis:
type=mixture;
Model:
%overall%
grp#1 on female ses socst;
grp#2 on female ses socst;
Plot:
type is plot3;
series is read (1) write (2) math (3) science (4);
*** WARNING in Model command
Variable is uncorrelated with all other variables: READ
*** WARNING in Model command
Variable is uncorrelated with all other variables: WRITE
*** WARNING in Model command
Variable is uncorrelated with all other variables: MATH
*** WARNING in Model command
Variable is uncorrelated with all other variables: SCIENCE
*** WARNING in Model command
All least one variable is uncorrelated with all other variables in the model.
Check that this is what is intended.
5 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
Latent Class Analysis with Graphs
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
READ WRITE MATH SCIENCE
Observed independent variables
FEMALE SES SOCST
Categorical latent variables
GRP
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
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
Random Starts Specifications
Number of initial stage starts 10
Number of final stage starts 1
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
Input data file(s)
hsb2.dat
Input data format FREE
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Initial stage loglikelihood values, seeds, and initial stage start numbers:
-2705.691 unperturbed 0
-2760.828 462953 7
-2861.398 939021 8
-2954.460 93468 3
-2954.460 415931 10
-2954.460 608496 4
-2954.460 195873 6
-2954.460 127215 9
-2954.460 903420 5
-2954.460 253358 2
-2954.460 285380 1
Loglikelihood values at local maxima, seeds, and initial stage start numbers:
-2703.289 unperturbed 0
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2703.289
Information Criteria
Number of Free Parameters 24
Akaike (AIC) 5454.579
Bayesian (BIC) 5533.738
Sample-Size Adjusted BIC 5457.704
(n* = (n + 2) / 24)
Entropy 0.842
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 68.35048 0.34175
2 88.44594 0.44223
3 43.20358 0.21602
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 68.35048 0.34175
2 88.44594 0.44223
3 43.20358 0.21602
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 68 0.34000
2 89 0.44500
3 43 0.21500
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2 3
1 0.947 0.053 0.000
2 0.045 0.914 0.042
3 0.000 0.082 0.918
MODEL RESULTS
Estimates S.E. Est./S.E.
Latent Class 1
Means
READ 42.658 0.784 54.386
WRITE 43.977 1.673 26.291
MATH 44.216 1.032 42.859
SCIENCE 42.081 1.536 27.402
Variances
READ 35.507 7.936 4.474
WRITE 42.315 6.466 6.544
MATH 34.903 5.016 6.959
SCIENCE 41.706 5.629 7.409
Latent Class 2
Means
READ 53.203 1.721 30.913
WRITE 55.080 1.443 38.162
MATH 53.626 1.481 36.216
SCIENCE 54.763 1.340 40.877
Variances
READ 35.507 7.936 4.474
WRITE 42.315 6.466 6.544
MATH 34.903 5.016 6.959
SCIENCE 41.706 5.629 7.409
Latent Class 3
Means
READ 65.381 2.231 29.305
WRITE 61.973 0.627 98.782
MATH 63.972 1.625 39.369
SCIENCE 61.341 1.197 51.234
Variances
READ 35.507 7.936 4.474
WRITE 42.315 6.466 6.544
MATH 34.903 5.016 6.959
SCIENCE 41.706 5.629 7.409
Categorical Latent Variables
GRP#1 ON
FEMALE -0.213 0.841 -0.254
SES -1.079 0.675 -1.597
SOCST -0.372 0.084 -4.427
GRP#2 ON
FEMALE -0.213 0.647 -0.330
SES -0.707 0.611 -1.157
SOCST -0.254 0.073 -3.500
Intercepts
GRP#1 23.775 5.283 4.500
GRP#2 17.583 4.760 3.694
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.225E-06
(ratio of smallest to largest eigenvalue)
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated values)
Scatterplots (sample values, estimated values)
Sample means
Estimated means
Sample and estimated means
Adjusted estimated means
Observed individual values
Estimated individual values
Estimated means and observed individual values
Estimated means and estimated individual values
Adjusted estimated means and observed individual values
Adjusted estimated means and estimated individual values
Mixture distributions
Estimated probabilities for a categorical latent variable as a
function of its covariates
Step 2. View the Graphs
Graph Example 1.
From Graph pulldown choose View Graphs then choose Estimated Means. This shows the graph below, showing the means broken down by the latent class membership. We can see that Class 1 is a poorly performing class, class 2 is a middle performing class, and class 3 is a well performing class.
Graph Example 2.
From Graph pulldown choose View Graphs then choose Estimated probabilities for a categorical.... Then make ses the X axis variable. This graph is shown below. The variable ses was not significantly related to class membership, but we see a small tendency for students to be in the better performing class (class 3) as ses increases, and less likely to be in the poor performing class (class 1).
Graph Example 3.
From Graph pulldown choose View Graphs then choose Estimated probabilities for a categorical.... Then make socst the X axis variable. As illustrated in the graph below, socst was significantly related to class membership. As socst increases, the probabilitiy of being in class 1 (the poor performing class) decreases and the probability of being in class 3 (the well performing class) increases. The probability of being in class 2 goes up and then tapers down as socst increases.
UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services
