Chi-Squared Automatic Inference Detection

This package provides a python implementation of the Chi-Squared Automatic Inference Detection (CHAID) decision tree as well as exhaustive CHAID

Installation

CHAID is distributed via pypi and can be installed like:

pip3 install CHAID

Alternatively, you can clone the repository and install via

pip install -e path/to/your/checkout

N.B. although we've made some attempt at supporting python 2.7 see here, we don't encourage the use of it as it's reached it's End Of Life (EOL).

Creating a CHAID Tree

from CHAID import Tree, NominalColumn
import pandas as pd
import numpy as np


## create the data
ndarr = np.array(([1, 2, 3] * 5) + ([2, 2, 3] * 5)).reshape(10, 3)
df = pd.DataFrame(ndarr)
df.columns = ['a', 'b', 'c']
arr = np.array(([1] * 5) + ([2] * 5))
df['d'] = arr

>>> df
   a  b  c  d
0  1  2  3  1
1  1  2  3  1
2  1  2  3  1
3  1  2  3  1
4  1  2  3  1
5  2  2  3  2
6  2  2  3  2
7  2  2  3  2
8  2  2  3  2
9  2  2  3  2

## set the CHAID input parameters
independent_variable_columns = ['a', 'b', 'c']
dep_variable = 'd'

## create the Tree via pandas
tree = Tree.from_pandas_df(df, dict(zip(independent_variable_columns, ['nominal'] * 3)), dep_variable)
## create the same tree, but without pandas helper
tree = Tree.from_numpy(ndarr, arr, split_titles=['a', 'b', 'c'], min_child_node_size=5)
## create the same tree using the tree constructor
cols = [
  NominalColumn(ndarr[:,0], name='a'),
  NominalColumn(ndarr[:,1], name='b'),
  NominalColumn(ndarr[:,2], name='c')
]
tree = Tree(cols, NominalColumn(arr, name='d'), {'min_child_node_size': 5})

>>> tree.print_tree()
([], {1: 5, 2: 5}, ('a', p=0.001565402258, score=10.0, groups=[[1], [2]]), dof=1))
├── ([1], {1: 5, 2: 0}, <Invalid Chaid Split>)
└── ([2], {1: 0, 2: 5}, <Invalid Chaid Split>)

## to get a LibTree object,
>>> tree.to_tree()
<treelib.tree.Tree object at 0x114e2e350>

## the different nodes of the tree can be accessed like
first_node = tree.tree_store[0]

>>> first_node
([], {1: 5, 2: 5}, ('a', p=0.001565402258, score=10.0, groups=[[1], [2]]), dof=1))

## the properties of the node can be access like
>>> first_node.members
{1: 5, 2: 5}

## the properties of split can be accessed like
>>> first_node.split.p
0.001565402258002549
>>> first_node.split.score
10.0

Creating a Tree using Bartlett's or Levene's Significance Test for Continuous Variables

When the dependent variable is continuous, the chi-squared test does not work due to very low frequencies of values across subgroups. As a consequence, and because the F-test is very susceptible to deviations from normality, the normality of the dependent set is determined and Bartlett's test for significance is used when the data is normally distributed (although the subgroups may not necessarily be so) or Levene's test is used when the data is non-normal.

from CHAID import Tree

## create the data
ndarr = np.array(([1, 2, 3] * 5) + ([2, 2, 3] * 5)).reshape(10, 3)
df = pd.DataFrame(ndarr)
df.columns = ['a', 'b', 'c']
df['d'] = np.random.normal(300, 100, 10)
independent_variable_columns = ['a', 'b', 'c']
dep_variable = 'd'

>>> df
   a  b  c           d
0  1  2  3  262.816747
1  1  2  3  240.139085
2  1  2  3  204.224083
3  1  2  3  231.024752
4  1  2  3  263.176338
5  2  2  3  440.371621
6  2  2  3  221.762452
7  2  2  3  197.290268
8  2  2  3  275.925549
9  2  2  3  238.471850

## create the Tree via pandas
tree = Tree.from_pandas_df(df, dict(zip(independent_variable_columns, ['nominal'] * 3)), dep_variable, dep_variable_type='continuous')

## print the tree (though not enough power to split)
>>> tree.print_tree()
([], {'s.t.d': 86.562258585515579, 'mean': 297.52027436303212}, <Invalid Chaid Split>)

Parameters

• df: Pandas DataFrame
• i_variables: Dict<string, string>: Independent variable column names as keys and the type as the values (nominal or ordinal)
• d_variable: String: Dependent variable column name
• opts: {}:
  • alpha_merge: Float (default = 0.05): If the respective test for a given pair of predictor categories is not statistically significant as defined by an alpha_merge value, the least significant predictor categories are merged and the splitting of the node is attempted with the newly formed categories
  • max_depth: Integer (default = 2): The maximum depth of the tree
  • min_parent_node_size: Float (default = 30): The minimum number of respondents required for a split to occur on a particular node
  • min_child_node_size: Float (default = 0): If the split of a node results in a child node whose node size is less than min_child_node_size, child nodes that have too few cases (as 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.
  • split_threshold: Float (default = 0): The split threshold when bucketing root node surrogate splits
  • weight: String (default = None): The name of the weight column
  • dep_variable_type (default = categorical, other_options = continuous): Whether the dependent variable is 'categorical' or 'continuous' Running from the Command Line

You can play around with the repo by cloning and running this from the command line:

python -m CHAID tests/data/titanic.csv survived sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05

It calls the print_tree() method, which prints the tree to terminal:

([], {0: 809, 1: 500}, (sex, p=1.47145310169e-81, chi=365.886947811, groups=[['female'], ['male']]))
├── (['female'], {0: 127, 1: 339}, (embarked, p=9.17624191599e-07, chi=24.0936494474, groups=[['C', '<missing>'], ['Q', 'S']]))
│   ├── (['C', '<missing>'], {0: 11, 1: 104}, <Invalid Chaid Split>)
│   └── (['Q', 'S'], {0: 116, 1: 235}, <Invalid Chaid Split>)
└── (['male'], {0: 682, 1: 161}, (embarked, p=5.017855245e-05, chi=16.4413525404, groups=[['C'], ['Q', 'S']]))
    ├── (['C'], {0: 109, 1: 48}, <Invalid Chaid Split>)
    └── (['Q', 'S'], {0: 573, 1: 113}, <Invalid Chaid Split>)

or to test the continuous dependent variable case:

python -m CHAID tests/data/titanic.csv fare sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05 --dependent-variable-type continuous

([], {'s.t.d': 51.727293077231302, 'mean': 33.270043468296414}, (embarked, p=8.46027456424e-24, score=55.3476155546, groups=[['C'], ['Q', '<missing>'], ['S']]), dof=1308))
├── (['C'], {'s.t.d': 84.029951444532529, 'mean': 62.336267407407405}, (sex, p=0.0293299541476, score=4.7994643184, groups=[['female'], ['male']]), dof=269))
│   ├── (['female'], {'s.t.d': 90.687664523113241, 'mean': 81.12853982300885}, <Invalid Chaid Split>)
│   └── (['male'], {'s.t.d': 76.07029674707077, 'mean': 48.810619108280257}, <Invalid Chaid Split>)
├── (['Q', '<missing>'], {'s.t.d': 15.902095006812658, 'mean': 13.490467999999998}, <Invalid Chaid Split>)
└── (['S'], {'s.t.d': 37.066877311088625, 'mean': 27.388825164113786}, (sex, p=3.43875930713e-07, score=26.3745361415, groups=[['female'], ['male']]), dof=913))
    ├── (['female'], {'s.t.d': 48.971933059814894, 'mean': 39.339305154639177}, <Invalid Chaid Split>)
    └── (['male'], {'s.t.d': 28.242580058030033, 'mean': 21.806819261637241}, <Invalid Chaid Split>)

Note that the frequency of the dependent variable is replaced with the standard deviation and mean of the continuous set at each node and that any NaNs in the dependent set are automatically converted to 0.0.

Generating Splitting Rules

Append --rules to the cli or call tree.classification_rules(node) (either pass in the node or if node is None then it will return all splitting rules)

python -m CHAID tests/data/titanic.csv fare sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05 --dependent-variable-type continuous --rules

{'node': 2, 'rules': [{'variable': 'sex', 'data': ['female']}, {'variable': 'embarked', 'data': ['C']}]}
{'node': 3, 'rules': [{'variable': 'sex', 'data': ['male']}, {'variable': 'embarked', 'data': ['C']}]}
{'node': 4, 'rules': [{'variable': 'embarked', 'data': ['Q', '<missing>']}]}
{'node': 6, 'rules': [{'variable': 'sex', 'data': ['female']}, {'variable': 'embarked', 'data': ['S']}]}
{'node': 7, 'rules': [{'variable': 'sex', 'data': ['male']}, {'variable': 'embarked', 'data': ['S']}]}

Parameters

Run python -m CHAID -h to see description of command line arguments

How to Read the Tree

We'll start with a real world example using the titanic dataset.

First make sure to install all required packages:

python setup.py install && pip install ipdb

Run:

python -m CHAID tests/data/titanic.csv survived sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05

after placing an ipdb statement on like 55 on __main__.py as in the example below. The parameters mean max depth two 4 levels, a minimum parent node size threshold to 2 and merge the groups if the p-value is greater than 0.05 when comparing the groups.

82        tree = Tree.from_pandas_df(data, independent_variables,
83                                   nspace.dependent_variable[0],
84                                   variable_types=types, **config)
---> 85   import ipdb; ipdb.set_trace()
86    
87        if nspace.classify:
88            predictions = pd.Series(tree.node_predictions())
89            predictions.name = 'node_id'
90            data = pd.concat([data, predictions], axis=1)
91            print(data.to_csv())
92        elif nspace.predict:

Running tree.print_tree() gives:

([], {0: 809, 1: 500}, (sex, p=1.47145310169e-81, score=365.886947811, groups=[['female'], ['male']]), dof=1))
├── (['female'], {0: 127, 1: 339}, (embarked, p=9.17624191599e-07, score=24.0936494474, groups=[['C', '<missing>'], ['Q', 'S']]), dof=1))
│   ├── (['C', '<missing>'], {0: 11, 1: 104}, <Invalid Chaid Split>)
│   └── (['Q', 'S'], {0: 116, 1: 235}, <Invalid Chaid Split>)
└── (['male'], {0: 682, 1: 161}, (embarked, p=5.017855245e-05, score=16.4413525404, groups=[['C'], ['Q', 'S']]), dof=1))
    ├── (['C'], {0: 109, 1: 48}, <Invalid Chaid Split>)
    └── (['Q', 'S'], {0: 573, 1: 113}, <Invalid Chaid Split>)

as show above. The first line is the root node, all the data is present in this node. The the vertical bars originating from a node represents paths to that node's children.

Running tree.tree_store will give you a list of all the nodes in the tree:

[
  ([], {0: 809, 1: 500}, (sex, p=1.47145310169e-81, score=365.886947811, groups=[['female'], ['male']]), dof=1)),
  (['female'], {0: 127, 1: 339}, (embarked, p=9.17624191599e-07, score=24.0936494474, groups=[['C', '<missing>'], ['Q', 'S']]), dof=1)),
  (['C', '<missing>'], {0: 11, 1: 104}, <Invalid Chaid Split>), (['Q', 'S'], {0: 116, 1: 235}, <Invalid Chaid Split>),
  (['male'], {0: 682, 1: 161}, (embarked, p=5.017855245e-05, score=16.4413525404, groups=[['C'], ['Q', 'S']]), dof=1)),
  (['C'], {0: 109, 1: 48}, <Invalid Chaid Split>), (['Q', 'S'], {0: 573, 1: 113}, <Invalid Chaid Split>)
]

So let's inspect the root node tree.tree_store[0]:

([], {0: 809, 1: 500}, (sex, p=1.47145310169e-81, score=365.886947811, groups=[['female'], ['male']]), dof=1))

Nodes have certain properties. Firstly, they show the column that was chosen to split to this node (for a root node the column is empty '([])'). The second property {0: 809, 1: 500} show the members of that node, and represent the current frequency of the dependent variable. In this case, it is all the answers in the 'survived' column, as that was the first column past to the program in the command line (python -m CHAID tests/data/titanic.csv survived). The next property represents the splitting of the node. What column was chosen to make that split (in this case, sex), the p-value of the split and the chi-score and most importantly, which variables in sex create the new nodes and the degrees of freedom associated with that split (1, in this case)

These properties that can be accessed:

ipdb> root_node = tree.tree_store[0]
ipdb> root_node.choices
[]
ipdb> root_node.members
{0: 809, 1: 500}
ipdb> root_node.split
(sex, p=1.47145310169e-81, score=365.886947811, groups=[['female'], ['male']]), dof=1)

The split variable can be further inspected:

ipdb> split = root_node.split
ipdb> split.column
'sex'
ipdb> split.p
1.4714531016922664e-81
ipdb> split.score
365.88694781112048
ipdb> split.dof
1
ipdb> split.groupings
"[['female'], ['male']]"

Therefore, in this example, the root node is split on the column 'sex' in the data, splitting up the females and males. These females and males each form a new node and further down, the all male and all female nodes are split on the column 'embarked' (although they needn't split on the same column). A <Invalid Chaid Split> is reached when either the node is pure (only one dependent variable remains) or when a terminating parameter is met (e.g. min node size, or max depth [see tree parameters above])

The conclusion drawn from this tree is that: "Gender was the most important factor driving the survival of people on the titanic. Whereby females had a much higher likelihood of surviving (survival = 1 in the survival column and 0 means they died). Of those females, those who embarked first class (class 'C', node 2) had a much higher likelihood of surviving."

Exporting the tree

If you want to export the tree to a dot file, then use:

tree.to_tree()

This creates a treelib which has a .to_graphviz() method here.

In order to use visually graph the CHAID tree, you'll need to install two more libraries that aren't distributed via pypi:

• graphviz - see here for platform specific installations
• orca - see the README.md for platform specific installations

You can export the tree to .gv and png using:

tree.render(path=None, view=False)

Which will save it to a file specified at path and can be instantly viewed when view=True.

This can also be triggered from the command line using --export or --export-path. The former causes it to be stored in a newly created trees folder and the latter specifies the location of the file. Both will trigger an auto-viewing of the tree. E.g:

python -m CHAID tests/data/titanic.csv survived sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05 --export

python -m CHAID tests/data/titanic.csv survived sex embarked --max-depth 4 --min-parent-node-size 2 --alpha-merge 0.05 --export-path YOUR_PATH.gv

The output will look like:

Testing

CHAID uses pytest for its unit testing. The tests can be run from the root of a checkout with:

py.test

If you so wish to run the unit tests across multiple python versions to make sure your changes are compatible, run: tox (detox to run in parallel). You may need to run pip install tox tox-pyenv detox & brew install pyenv beforehand.

Caveats

• Unlike SPSS, this library doesn't modify the data internally. This means that weight variables aren't rounded as they are in SPSS.
• Every row is valid, even if all values are NaN or undefined. This is different to SPSS where in the weighted case it will strip out all rows if all the independent variables are NaN

Upcoming Features

• Accuracy Estimation using Machine Learning techniques on the data
• Binning of continuous independent variables

Generating the CHANGELOG.md

gem install github_changelog_generator && github_changelog_generator --exclude-labels maintenance,refactor,testing