1. Read about the diabetes example in Updated Sage Article section 4.3 (pages 32-34, and Table 14).
Download the associated data files diabetes.dat and diabetes.lgf for these data.
After estimating a model, double click on that model and click the Residuals Tab. Here you will see the bivariate residuals associated with each pair of indicators, sorted from high to low. A checkmark preceding an indicator pair indicates that a direct effect parameter for that pair has been included in the model. In the Model tab, you will see which (if any) of the effects are specified as class independent. Which model do you think is best? What is your criteria? Add the true diagnosis – the variable TRUE — as an inactive covariate in each of these models. Examine the Profile and ProbMeans output to see which model most closely relates the latent classes to the desired true states.
2. Re-estimate model type 5, requesting the posterior membership probabilities (Classification – Posterior) be output to a file. Then open the newly created outfile and use the Step3 option to obtain the scoring formula that can be used to score new cases as a function of the 3 indicators. Hint: Since model type 5 does not assume the variances and covariances to be equal within each of the 3 latent classes, a quadratic function must be specified in order to obtain an R2=1 (i.e., to perfectly reproduce the posterior membership probabilities). Which quadratic terms entered into the model have non-zero coefficients? What is the formula for the posterior membership probabilities as a function of the 3 indicators? For assistance, see: ‘Step 3 Tutorial 3.
3. Using only the 2 variables GLUCOSE and INSULIN, how well are you able to distinguish persons with overt diabetes from the others using a 2-class model? How can you tell that only 3 cases are misclassified?
4. Optional: If you have access to SPSS, use the K-Means procedure (using the Analyze/Classify menu), specifying 2 clusters and requesting that cluster membership probabilities be used. Confirm that 7 cases are misclassified. Now repeat the analysis after standardizing the variable to Z scores (using the Analyze/Description Statistics/Descriptive menu), check “Save standardized values”. Are there more or
less misclassifications? Show that the latent class model is unchanged when Z scores are used.