Example 8.23: Expanding latent class model results

In Example 8.21 we described how to fit a latent class model to data from the HELP dataset using SAS and R (using poLCA(), and then followed up in example 8.22 using randomLCA(). In both entries, we classified subjects based on their observed (manifest) status on the following variables (on street or in shelter in past 180 days [homeless], CESD scores above 20, received substance abuse treatment [satreat], or linked to primary care [linkstatus]). We arbitrarily specify a three class solution.

In this example, we write a function to augment the default output of randomLCA() to make it easier for the analyst to interpret the results.

R

We begin by reading in the data.

ds = read.csv("http://www.math.smith.edu/r/data/help.csv")
attach(ds)
library(randomLCA)

We will write a function wrapper for randomLCA that does some additional work in a generic fashion. This will allow easier estimation of other models. We annotate the function to explain what we're doing. The resulting objects are outcomep, which contains the outcome probabilities, and classp, with the class probabilities.

runlca = function(df, nclass=2, names=c("item"), verbose=FALSE) {
   nvars = dim(df)[2]

   # create a list of names for the items
   if (length(names)==1) { names = rep(names, nvars) }

   # include only complete cases
   bigtable = table(na.omit(df))
   allpatterns = as.data.frame(ftable(bigtable))
   # keep only the patterns that occur
   nonzeropatterns = allpatterns[allpatterns$Freq > 0,]

   # fit the model
   results = randomLCA(nonzeropatterns[,1:nvars],
      nonzeropatterns$Freq, nclass=nclass, calcSE=FALSE)

   # display available sample size
   cat("nobs=", results$nobs, "\n")
   oldopt = options(digits=2)
   if (verbose==TRUE) {    # display patterns
        whichclass = apply(results$classprob, 1, which.max) 
        nonzeropatterns$class = whichclass
        print(nonzeropatterns[order(whichclass),])
   }
   print(summary(results))
   resvals = cbind(results$outcomep, results$classp)

   # label the margins with our desired variable names 
   # (plus class probability)
   colnames(resvals) = c(names, "classprob")
   # annotate standard output with rounded values
   print(round(resvals, 2))
   options(oldopt)
   return(results)
}

Now let's apply the function. We start by creating a dichotomous variable with high scores on the CESD, and put this together as part of a dataframe to be given as input to the function. Then we call the runlca() function. By specifying the verbose option the code displays each of the patterns, sorted by which class it is in (based on the highest predicted probability).

cesdcut = ifelse(cesd>20, 1, 0)

smallds = data.frame(homeless, cesdcut, satreat, linkstatus)
results = runlca(smallds, nclass=3, 
   names=c("homeless", "cesd", "satreat", "linkstatus"), 
   verbose=TRUE)

This generates the following output:

nobs= 431 
   homeless cesdcut satreat linkstatus Freq class
5         0       0       1          0   16     1
7         0       1       1          0   33     1

6         1       0       1          0    4     2
8         1       1       1          0   37     2
13        0       0       1          1    1     2
14        1       0       1          1    4     2
15        0       1       1          1    9     2
16        1       1       1          1   23     2

1         0       0       0          0   17     3
2         1       0       0          0   15     3
3         0       1       0          0   82     3
4         1       1       0          0   64     3
9         0       0       0          1   10     3
10        1       0       0          1    9     3
11        0       1       0          1   62     3
12        1       1       0          1   45     3
  Classes  AIC  BIC logLik
        3 2093 2150  -1032
Class probabilities 
Class  1 Class  2 Class  3 
 0.07846  0.21621  0.70534 
Outcome probabilities 
     homeless cesd satreat linkstatus classprob
[1,]     0.00 0.58       1       0.00      0.08
[2,]     0.73 0.88       1       0.40      0.22
[3,]     0.44 0.83       0       0.41      0.71

The results are equivalent to the results from the prior example, but the predicted classes are listed, and the class probabilities (and proportion endorsing the item) are more clearly discernible. It might be useful in a later iteration of the function to add some blank lines and the proportion of the seeds that resulted in the maximum likelihood.