## Appendix  
CART analysis uses independent variables provided by the researcher to produce sub-groupings of individuals who are homogeneous with respect to a dependent variable. CART analysis is a form of binary recursive partitioning. The term \"binary\" implies that each collection of cases can only be split into two sub-groups, called child nodes. Because the process is \"recursive\", the partitioning process is applied over and over again. Each parent node can produce two child nodes and, in turn, each of these child nodes may themselves be split. The term \"partitioning\" refers to the fact that the dataset is split into homogenous sub-groups. Strictly speaking, a classification tree involves the prediction of a dichotomous variable, while a regression tree involves the prediction of an ordinal variable. The first step in CART analysis consists of partitioning the entire dataset into binary subsets on the basis of a selected variable split. Initially, all cases are clustered into one \"parent node\". This initial node has a certain level of heterogeneity, or impurity with respect to the dependent variable. This impurity can be considered a statistic that measures the degree to which cases differ on values of the dependent variable. The calculation for impurity in any given population is:  
\[D=\sum_{i=1}^{S}p_{i}^{2}\,.\]  
In this equation, \(\mathrm{p_{i}}\) is the proportion of cases in the population which have a certain value. Each proportion is squared, and then all squared proportions are summed. The rationale behind splitting is to reduce the impurity of a parent node by selecting the one variable that is most effective in dividing the original population into less heterogeneous sub-groups. The most common statistical technique used for determining a reduction of impurity, and the one used in this research, is the Gini improvement measure. To calculate improvement, first the impurity of the original node is calculated. A variable is selected and used to split this original parent node into child nodes. For example, if the variable is race, all respondents who identified themselves as \"Asians\" would be lumped together, and all non-Asians are lumped together. Next, the impurities for these new child nodes are calculated in the same manner. Then, a weighted average of the Gini diversity index is computed according to the proportion of the parent node included in each of the child nodes:  
\[\text{Weighted Gini diversity index}=[(\rho_{1})(\text{impurity}_{1})]+[(\rho_{2})( \text{impurity}_{2})]\]  
Finally, a Gini improvement measure is calculated:  
\[\text{Improvement measure}=\text{impurity of parent node - weighted Gini diversity index}\]  
The independent variable which produces the largest improvement measure is retained as the splitting variable. This process then repeats itself for each of the two child nodes (which now have become parent nodes). In this way, impurity is steadily reduced, leading to more homogeneous sub-groupings. Trees can grow to large sizes. Large trees present more splits and more homogenous sub-groups, however a large tree has terminal nodes that are too numerous to be theoretically interesting or the N of these nodes are so small that these nodes are not capturing reproducible phenomena. In other words, a tree that has grown to its maximal size predicts the data perfectly, but is likely capturing idiosyncrasies in the data instead of generalizable patterns. Thus, the second step in CART analysis is stopping the splitting process and producing a tree that balances accuracy with parsimony. One way of controlling size is by assigning stopping rules. These rules define the minimum number of respondents per parent node, child node, and the maximum levels of the tree. The default option in SPSS is 100 for parent nodes, 50 for child nodes, and a maximum depth of 5 levels. Further, the minimum amount of improvement in impurity needed for a predictor variable to split a population can be modified. Higher minimum levels of improvement mean that fewer splits will occur.