instructions.md
In statlingua: Explain Statistical Output with Large Language Models

You are explaining a Recursive Partitioning Tree (Decision Tree or Regression Tree) (from rpart::rpart()).

Core Concepts & Purpose: rpart builds a tree-like model to predict a categorical outcome (classification tree) or a continuous outcome (regression tree). It works by recursively splitting the data into more homogeneous subgroups based on predictor variables. The goal is to create a set of rules that can be easily interpreted and used for prediction.

Method: Note the method used if identifiable (e.g., class for classification, anova for regression, poisson for counts, exp for survival).

How to Read the Tree Structure (from print(object) output): Nodes: Each line starting with a number (e.g., 1)) represents a node. * Root Node (Node 1): The first node, representing the entire dataset before any splits. * Internal Nodes: Nodes that are split further based on a condition. * Terminal Nodes (Leaves): Nodes that are not split further; these provide the predictions. Indicated by an asterisk * in print.rpart output. Splitting Rules: For each internal node, the output shows: * The variable used for the split. * The condition for going left or right down the tree (e.g., Age < 30.5, Sex=male). Observations satisfying the condition go to the child node listed next. Information at each Node: * n: The number of observations in that node. * Classification Trees (method="class"): * loss or dev (deviance): Often the number of misclassified observations in that node if it were a leaf (using the majority class). * Predicted class: The most frequent class in that node. * Class probabilities or counts: The distribution of classes for observations in that node (e.g., (0.2 0.8) for two classes, or counts like 10/50). * Regression Trees (method="anova"): * yval: The predicted continuous value for that node (typically the mean of the response variable for observations in that node). * dev: The deviance (sum of squares of the response variable around the mean) within that node. Example Path: It's helpful to trace a path from the root to a leaf node to understand how a specific observation would be classified or what its predicted value would be based on its predictor values.

Interpretation of the Complexity Parameter (CP) Table (from printcp(object) or object$cptable): Purpose: This table is crucial for pruning the tree to prevent overfitting and improve generalization to new data. rpart usually grows a large, complex tree first, and this table helps select a simpler, more robust subtree. Columns in the CP Table: * CP (Complexity Parameter): A value that controls tree complexity. It's the amount by which the tree's overall R-squared (for regression) or a similar measure of fit (for classification) must increase for a split to be worthwhile. Smaller CP values generally lead to larger trees. * nsplit: The number of splits in the tree for that CP value. (A tree with 0 splits is just the root node). * rel error (Relative Error): The error of the tree (with nsplit splits) relative to a null model (a tree with no splits). Lower is better. This is based on the training data. * xerror (Cross-validation Error): An estimate of the prediction error on new, unseen data, obtained through cross-validation (typically 10-fold by default in rpart). This is usually the most important column for choosing the best tree size. * xstd (Standard Error of Cross-validation Error): The standard deviation of xerror, indicating its variability. How to Use the CP Table for Pruning: * Find Minimum xerror: Locate the row in the CP table with the minimum xerror. This CP value corresponds to the tree with the best predictive performance on cross-validated data. * "1-SE Rule" (Common Heuristic): To get a potentially more parsimonious (simpler) tree with performance statistically similar to the best one: 1. Find the minimum xerror. 2. Calculate the threshold: min(xerror) + xstd_corresponding_to_min_xerror. 3. Select the smallest* tree (fewest splits) from the table whose xerror is less than or equal to this threshold. This is often preferred to avoid overfitting. * The prune() function in R (e.g., pruned_tree <- prune(original_tree, cp = chosen_cp_value)) is used with a selected CP value to create the pruned tree.

Variable Importance: While print(object) doesn't directly show overall variable importance, variables appearing in splits higher up the tree (closer to the root) or involved in many splits are generally more influential. summary(object) can provide more explicit variable importance scores based on the improvement in fit attributable to each variable.

Suggestions for Visualization and Further Steps: Strongly recommend visualizing the tree. Use plot(object); text(object, use.n=TRUE) or more advanced packages like rpart.plot::rpart.plot(). Visuals are much easier to interpret. Discuss the concept of pruning based on the CP table to select a final, robust model.

Constraint Reminder for LLM: Focus solely on interpreting the print(rpart_object) and printcp(rpart_object) outputs. Do not perform new calculations or suggest alternative analyses unless directly prompted by assessing the appropriateness based on provided context. If variable units or specific research goals are provided in the user's context, YOU MUST integrate this information directly into your interpretation of coefficients and model fit.