Fit a CHAID or Exhaustive CHAID decision tree

Grows a CHAID (Chi-squared Automatic Interaction Detection) or Exhaustive CHAID decision tree following the IBM SPSS Statistics algorithm specification. Nominal (factor), ordinal (ordered) and continuous (numeric) predictors are supported; continuous predictors are discretised into quantile bins first. The response may be nominal (Pearson or likelihood-ratio chi-squared test), ordinal (Goodman row effects test) or continuous (one-way ANOVA F test).

Usage

chaid(
  formula,
  data,
  weights = NULL,
  freq = NULL,
  method = c("chaid", "exhaustive"),
  control = chaid_control(),
  costs = NULL,
  y_scores = NULL
)

Arguments

formula: A model formula of the form response ~ predictors.
data: A data frame containing the variables in the formula.
weights: Optional numeric vector of case weights. They only affect the estimation of expected cell frequencies; cases with missing, zero or negative weights are excluded.
freq: Optional numeric vector of frequency weights. They determine observed counts, degrees of freedom and node sizes. Non-integer values are rounded to the nearest integer (IBM specification).
method: "chaid" (default) for the Kass (1980) algorithm or "exhaustive" for Exhaustive CHAID (Biggs, de Ville and Suen, 1991).
control: A "chaid_control" object created by chaid_control().
costs: Optional misclassification cost matrix C[truth, pred] for categorical responses (same convention as the loss matrix of 'rpart': zero diagonal, non-negative entries, dimnames matching the response levels). When supplied, node predictions minimise expected cost instead of taking the majority class. As in SPSS, costs do not affect tree growing or the significance tests.
y_scores: Optional numeric vector of class scores for an ordinal response, in the order of levels(y). Defaults to the class ranks 1..J. Fixed at the start of tree growing and not re-ranked in subtables (IBM specification).

Value

An object of class "chaid": a list with components call, method, control, response (name, type, levels, scores), predictors (internal coding of each predictor), nodes (list of node records with distribution, prediction and split information), costs, n (number of cases used) and n_dropped (number of excluded cases).

Details

Missing predictor values are handled as in SPSS: for ordinal predictors they form a floating category that may merge with any group, for nominal predictors they form an ordinary extra category. Cases with a missing response, missing/zero/negative weights, or all predictors missing are dropped before fitting.

References

Kass, G. V. (1980). An exploratory technique for investigating large quantities of categorical data. Applied Statistics, 29(2), 119-127.

Biggs, D., de Ville, B., & Suen, E. (1991). A method of choosing multiway partitions for classification and decision trees. Journal of Applied Statistics, 18(1), 49-62.

Examples

fit <- chaid(Species ~ ., data = iris,
             control = chaid_control(min_parent = 30, min_child = 10))
print(fit)
#> CHAID decision tree (method = "chaid")
#> Response: Species (categorical) 
#> Valid cases: 150 (data: 150 rows) 
#> 
#> [1] root: setosa (33.3%), n=150 | split: Petal.Length (adj.p=1.35e-44, chi2=243.8, B=126)
#>   [2] Petal.Length in {<= 1.6}: setosa (100.0%), n=44 *
#>   [3] Petal.Length in {(1.6, 3.8]}: versicolor (57.1%), n=14 *
#>   [4] Petal.Length in {(3.8, 4.6]}: versicolor (96.9%), n=32 *
#>   [5] Petal.Length in {(4.6, 4.9]}: versicolor (64.3%), n=14 *
#>   [6] Petal.Length in {(4.9, 5.3]}: virginica (87.5%), n=16 *
#>   [7] Petal.Length in {> 5.3}: virginica (100.0%), n=30 *
predict(fit, head(iris))
#> [1] setosa     setosa     setosa     setosa     setosa     versicolor
#> Levels: setosa versicolor virginica