1. Latent Class Analysis Computing examples
Karen Bandeen-Roche
October 28, 2016

2. Objectives For you to leave here knowing…
How to use the LCR SAS Macro for latent class analysis
Brief introduction to poLCA in R
How to interpret, report output
How to create residuals and conduct model checking with them

3. Basics on using the software
Part I:
Basics on using the software

4. SAS MACRO … Beginning of file— basic documentation
/* */
/* */
/* TITLE: LCR */
/* */
/* A SAS Macro for Latent Class Regression using PROC IML */
/* Requires SAS/IML */
/* Please send any suggestions or corrections to */
/* DESCRIPTION */
/* */
/* This program contains a macro for fitting LCA and LCR models and an example */
/* To fit a standard latent class model, only include an intercept in the model */
/* The macro uses the algorithm describe in */
/* Bandeen-Roche, K; Miglioretti, DL; Zeger, SL; Rathouz, P, */
/* "Latent variable regression for multiple discrete outcomes," */
/* JASA, In Press (1997) */
/* to fit latent class regression models. …
Beginning of file—
basic documentation

5. SAS MACRO … This text creates output data sets!
create &outlib..beta from beta [colname='value' rowname=betaname];
append from beta [rowname=betaname];
close &outlib..beta;
create &outlib..eta from eta [colname=etaname];
append from eta;
close &outlib..eta;
create &outlib..theta from h [colname=thetanam];
append from h;
close &outlib..theta;
expct = nrow(x)#bottom;
create &outlib..expect from expct [colname='expected'];
append from expct;
close &outlib..expect;
create &outlib..pi from pi [colname=pi2name rowname=varname];
append from pi [rowname=varname];
close &outlib..pi;
create &outlib..var from var [colname=parm rowname=parm];
append from var [rowname=parm];
close &outlib..var;
title;
%mend lcr;
This text creates
output data sets!
Posterior probabilities
Expected cell counts
Before anything else—
need to run through here

6. Toy example (in software: immediately follows the macro)
BINARY INDICATORS
data dataset; set a;
if y1=. | y2=. | y3=. | y4=. | y5=. then delete;
int=1;
run;
Create “intercept”
Designed for complete data

7. SAS Macro Command line format
Name of your dataset
Response variables
Covariates (just intercept for LCA)
Number of classes
Initial parameters (“0” triggers self-initialization)
Iterate to criterion precision

8. SAS Macro Output format
Top: initial estimates,
# iterations
Bottom:
final estimates,
fit criteria

9. SAS Macro Command line format
Example with initial estimates
filled in rather than self-initialization
“pi” = as we have defined it
(conditional probabilities)
“eta” = our “Pj”
(latent class probabilities)

10. R function: poLCA
> poLCA(formula = cbind(Y1, Y2, Y3, Y4, Y5) ~ 1, data = j2, nclass = 2)
Conditional item response (column) probabilities,
by outcome variable, for each class (row)
$V1
Pr(1) Pr(2)
class 1:
class 2:
$V2
class 1:
class 2:
$V3
class 1:
class 2:
$V4
Pr(1) Pr(2)
class 1:
class 2:
$V5
class 1:
class 2:
Estimated class population shares

11. R function: poLCA
=========================================================
Fit for 2 latent classes:
number of observations: 100
number of estimated parameters: 11
residual degrees of freedom: 20
maximum log-likelihood:
AIC(2):
BIC(2):
G^2(2): (Likelihood ratio/deviance statistic)
X^2(2): (Chi-square goodness of fit)

12. Post-traumatic stress disorder
Part II:
Application
Post-traumatic stress disorder

15. Data set up (immediately following Macro)
Pull in pre-existing data
A convenient way to code “patterns”
Dataset to pass on to LCA

16. Pattern frequency listing
pscor=b1+10*b4+100*b5+1000*c *c *c *d *d *d3;
No symptoms
b1 only
b4 only
b1 & b4

17. LCA Macro “Call” Name of dataset Response variables (9 of them)
Number of classes
Initial parameters
“Canned” initialization & other starts yield same
Am arranging for “low” symptom probability to
be the “last” class (relevant for LCR)

18. Output Class Latent class probabilities Class 3 prevalence1 2 3
Latent class probabilities
Class 3 prevalence
Class conditional probabilities
Pr(B1=1|Class 3)

19. Classes reordered
for reporting

20. Revisiting the Model for “Fit”
5 class model
“None,”
“PTSD”
classes
very stable
AIC,
BIC:
both lower
AIC,
BIC
LR test:
Better LR
test

21. Revisiting the Model for “Fit”
Five class model appears “better”
Trustworthy? Data quite sparse!
Seeing is believing—thus….

22. Checking Fit - Residuals
Standardized residuals
(multinomial)
In this case, residuals are actual cell counts vs. expected cell counts.

23. Expected counts: SAS Macro
Pull the expected values into a dataset.
They’re labeled “expected”—rename them
to avoid code-word problems
Sort and tabulate to show the pattern,
observed count, and expected count

24. Observed vs. Expected Comparison
Three class
Five class
Cut and paste
into Excel:
Stat transfer to
Stata

25. Data structure in Stata
Obs Class Class

26. QQPlot of residuals, 5 vs 3 class
. gen resid3=n-tclass
. gen resid5=n-fclass
. qqplot resid5 resid3

27. QQPlot of standardized residuals, 5 vs 3 class
. gen sresid3 = resid3/sqrt(tclass*(1-tclass/1827))
. gen sresid5 = resid5/sqrt(fclass*(1-fclass/1827))
. qqplot sresid5 sresid3
Favors
5-class
model

28. Listing–Largest |Standardized Residual| Differences
Negative difference
favor 3-class model.
Only a few large—
these have small n.
. gen sadiff = abs(sresid3)-abs(sresid5)
. sort sadiff
. list Pattern sadiff n tclass fclass sresid3 sresid5

29. Listing–Largest |Standardized Residual| Differences
. gen sadiff = abs(sresid3)-abs(sresid5)
. sort sadiff
. list Pattern sadiff n tclass fclass sresid3 sresid5
Both models underestimate the number having all symptoms
Positive values
favor 5-class model.
A few large values
have considerably large n (ex/ 110 = cues create distress, reactivity
without re-experiencing).

30. Conclusion
The latent class model fit suggests a nosology with subpopulations exhibiting “few” (just over half), “many” (~14%) and “re-experiencing plus a few other” symptoms.
The conditional independence assumption may not be reasonable for these data

31. Objectives For you to leave here knowing…
How to use the LCR SAS Macro for latent class analysis
Brief introduction to poLCA in R
How to interpret, report output
How to create residuals and conduct model checking with them