cchaid: Chi-squared Automated Interaction Detection for continuous...

In tpgjs66/cchaidR: Chi-squared Automated Interaction Detection for continuous response variable

Description

Fits a classification tree by the CHAID algorithm for continuous response variable

Usage

cchaid(formula, data, weights = NULL, minbucket = 100, minsplit = 200,
  alpha_split = 0.05, alpha_merge = 0.05, max_depth = 10)

Arguments

formula	an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. Response variable should be continuous and all predictors should be categorical (either ordered or not).
weights	an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector.
minbucket	Minimum number of observations in terminal nodes.
minsplit	Number of observations in split response at which no further split is desired.
alpha_split	Level of significance used for splitting of a node in the most significant predictor
alpha_merge	Level of significance used for merging of predictor categories
max_depth	Maximum depths for the tree

Details

The CHAID algorithm is originally proposed by Kass (1980) which allow multiple splits of a node. The current implementation only accepts continuous response variable and categorical predictors (nominal or ordinal). If response variable is categorical, refer to chaid. CHAID consist of three steps: merging, splitting and stopping. A tree is grown by repeatedly using the three steps below on each node starting from the root node.

• Merging: For each predictor variable X, merge non-significant categories. Each final category of X will result in one child node if X is used to split the node. The merging step also calculates the adjusted p-value that is to be used in the splitting step.

  • 1. If X has 1 category only, stop and set the adjusted p-value to be 1.

  • 2. If X has 2 categories, go to step 8.

  • 3. Else, find the allowable pair of categories of X (an allowable pair of categories for ordinal predictor is two adjacent categories, and for nominal predictor is any two categories) that is least significantly different (i.e., most similar). The most similar pair is pair whose test statistic gives the largest p-value with respect to the dependent variable Y.

  • 4. For the pair having the largest p-value, check if its p-value is larger than a user-specified alpha-level α merge (alpha_merge). If it does, this pair is merged into a single compound category. Then a new set of categories of X is formed. If it does not, then go to step 7.

  • 5. (Optional) If the newly formed compound category consists of three or more original categories, then find the best binary split within the compound category which p-value is the smallest. Perform this binary split if its p-value is not larger than an alpha-level split-merge α (alpha_spli-merge).

  • 6. Go to step 2.

  • 7. (Optional) Any category having too few observations (as compared with a user-specified minimum segment size) is merged with the most similar other category as measured by the largest of the p-values.

  • 8. The adjusted p-value is "mandatorily" computed for the merged categories by applying Bonferroni adjustments.

• Splitting: The “best” split for each predictor is found in the merging step. The splitting step selects which predictor to be used to best split the node. Selection is accomplished by comparing the adjusted p-value associated with each predictor. The adjusted p-value is obtained in the merging step.

  • 1. Select the predictor that has the smallest adjusted p-value (i.e., most significant).

  • 2. If this adjusted p-value is less than or equal to a user-specified alpha-level split α (alpha_split), split the node using this predictor. Else, do not split and the node is considered as a terminal node.

• Stopping: The stopping step checks if the tree growing process should be stopped according to the following stopping rules.

  • 1. If a node becomes pure; that is, all cases in a node have identical values of the dependent variable, the node will not be split.

  • 2. If all cases in a node have identical values for each predictor, the node will not be split.

  • 3. If the current tree depth reaches the user specified maximum tree depth limit value, the tree growing process will stop.

  • 4. If the size of a node is less than the user-specified minimum node size value, the node will not be split.

  • 5. If the split of a node results in a child node whose node size is less than the userspecified minimum child node size value, child nodes that have too few cases (as compared with this minimum) will merge with the most similar child node as measured by the largest of the p-values. However, if the resulting number of child nodes is 1, the node will not be split.

Value

An object of class constparty, see package party.

References

Kass, G. V. (1980). An exploratory technique for investigating large quantities of categorical data. Applied statistics, 119-127.
Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. Journal of Machine Learning Research, 16, 3905–3909.

See Also

chaid ctree glmtree

Examples

library("cchaid")
require("partykit")

set.seed(100)
WorkDurationS <- WorkDuration[sample(1:nrow(WorkDuration), 1000),]
formula <- (Dur ~ Urb + Comp + Child + Day + pAge + SEC + Ncar + Gend +
            Driver + wstat + Pwstat + Xdag + Xn.dag + Xarb + Xpop + Ddag +
            Dn.dag + Darb + Dpop)
mytree <- cchaid(formula,data = WorkDurationS, weights = NULL, minbucket = 57,
                 minsplit = 114, alpha_split=0.05, alpha_merge=0.05,
                 max_depth = 8)
mytree
plot(mytree)

tpgjs66/cchaidR documentation built on Oct. 28, 2021, 7:31 p.m.