A lasso regression analysis was conducted to identify a subset of variables from a pool of 6 quantitative predictor variables that best predicted a quantitative response variable measuring the number of people employed. Quantitative predictor variables include Gross National Product (GNP), GNP implicit price deflator (1954=100), number of unemployed, number of people in the armed forces, ‘noninstitutionalized’ population ≥ 14 years of age, and the year (time). Because of the small size of the data set (N=16), data were not split into training and test sets.

Random forest analysis was performed to evaluate the importance of a series of explanatory variables in predicting a binary, categorical response variable. The following explanatory variables were included as possible contributors to a random forest evaluating after surgery deformation (kyphosis) (my response variable), age in months (Age), number of vertebrae involved (Number), and the highest vertebrae operated on (Start). The accuracy of the random forest was 80%, with the subsequent growing of multiple trees rather than a single tree, adding little to the overall accuracy of the model, and suggesting that interpretation of a single decision tree may be appropriate.

Figure 1. Classification tree (N=81) to predict a type of deformation (kyphosis) after surgery (target variable) Decision tree analysis was performed to test nonlinear relationships among a series of explanatory variables and a binary, categorical response variable. All possible separations (categorical) or cut points (quantitative) are tested. For the present analyses, the entropy “goodness of split” criterion was used to grow the tree and a cost complexity algorithm was used for pruning the full tree into a final subtree.