Identifying the Intercept and Slope of Normal and Dis Sample Clauses

Identifying the Intercept and Slope of Normal and Dis crete Feature Variables The results of the first simulation study suggest that the proposed latent trajectory model can effectively detect the presence of the two underlying classes and correctly identify the mean structure based on a set of normally distributed feature variables. In the second set of simulations, we considered a slightly more general simulation design that incorporates non-zero slopes and non-normal feature variables. More specifically, the second simulation contains 6 feature variables. Of these 6 feature variables, 2 are normally distributed, 2 are binary, and 2 follow a Poisson distribution. In addition, the second simulation allows for non-zero slope with respect to time for a subset of the feature variables. Again, the simulation was performed under the assumption that there were two latent classes and two designs were considered with varying class membership proba- bilities. Again, in the first design, subjects were evenly divided between two classes. In the second, 80% of subjects belonged to one latent class and the remaining 20% belonged to the other. For each of five hundred individuals, ten distinct realizations of longitudinal data with six evenly spaced measurement occasions and no missing data were generated. Within each latent class, the features were assumed to be independent and data for each feature was generated separately based on an autore- gressive (AR1) correlation structure with a correlation coefficient of 0.3. Let β0jg and β1jg for j = 1, . . . , 6 and g = 1, 2 be class- and feature-specific intercepts and slopes, respectively. The Poisson feature variables were generated using the over- lapping sums (OS) approach of Xxxxxx and Xxxxxxxx(2007) [10] with a mean of eβ0jg +β1jg×time(j = 1, 2; g = 1, 2). The binary feature variables were generated using β0jg +β1jg×time the approach of Xxxxxx(2003)[67] with a mean of eβ0jg +β1jg×time (j = 3, 4; g = 1, 2). The normal feature variables were generated with a standard deviation of 5 and a mean of eβ0jg +β1jg×time(j = 5, 6; g = 1, 2). As in the first set of simulations, each sub- ject was also randomly assigned a value for a binary covariate, which may be involved in determining class membership probabilities. Table 3.5 provides a summary of the class-specific intercept and slope used to generate each of the feature variables.