Supervised Learning Methods Used to Classify or Predict Physical Abuse

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Supervised Learning Methods Used to Classify or
Predict Physical Abuse

• Marit Gilkey
• Statistics Senior Seminar
• Spring 2004

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Methods

• CART Classification and Regression Trees
• CHAID Chi-Square Automatic Interaction
  Detector
• Logistic Regression

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CART Algorithm

• Step 1
• The best possible predictor is found to split
  the root node into two child nodes.
• Best the predictor that maximizes the
  reduction in impurity
• Gini Index ?k?k smk smk
• where smk (1/Nm) ?xi ? Rm I(yi k)

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CART Algorithm

• Step 2
• Each node is assigned a predicted outcome
  class. (yes, no)
• Step 3
• The process is repeated until the terminal
  nodes are too small or too few to split.

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CHAID Algorithm

• Step 1
• The best predictor is chosen from all of the
  predictors, by using a chi-squared test of
  independence.
• Best predictor with most significant pvalue.

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CHAID Algorithm

• Step 2
• With this predictor, the dataset is
  partitioned into 2 or more subsets based on the
  number of categories of this predictor.
• All insignificantly different subsets are
  combined.

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CHAID Algorithm

• Step 3
• Each subset is then partitioned further based
  on the same criterion in Step 1.
• This is repeated for each subset until it can no
  longer be split into statistically significant
  subsets.

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Logistic Regression

• The logistic regression model of a response, y,
  and one predictor variable, x, is
• P (y 1) exp(ß0 ß1X)
• 1 exp(ß0 ß1X)
• Uses maximum-likelihood estimation
• Estimates the probability of a given event
  occurring.

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Variables

• CART and CHAID Response is continuous or
  categorical. Predictors are continuous or
  categorical.
• Logistic Response is binary. Predictors are
  continuous or categorical.

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Data Description

• There are 2 sets of data.
• training set 999 observations validation set
  336 observations
• The data was obtained by those completing a
  womens health survey.

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Description of Variables Used
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Decision Trees

• Advantages
• Understandable rules
• All variable types can be used
• Identifies variables that are important
• Disadvantages
• Large and complex trees-CHAID

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Logistic Regression

• Advantages
• Model is clear
• All variable types can be used
• Disadvantages
• Determine if there are variable interactions

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CART Initial Tree

• Predicted
• 954 No
• 45 Yes
• Actual
• 936 No
• 63 Yes

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Deviance

• ? smk log(smk)
• Where smk (1/Nm) ?xi ? Rm I(yi k)
• smk Proportion of observations in node m which
  belong to class k.

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CART - Pruning

• Visually, after the 8th terminal node, adding
  another split does not look like it will benefit
  the classification much.

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CART -Misclassifications

• Training data

• Validation data

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CART - Final Pick

• 11 terminal nodes

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CART - Classification
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CHAID
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CHAID - Classifications

• 50/999 .05005
• 29/336 .0863

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Donut Chart
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Logistic Regression

• If P(Y1) gt .46, we will classify it as being an
  event, or a woman having been physically abused.
• The misclassification rate is 52/999 .05205

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Lift Chart

• Lift measures how well the predicted model is,
  calculated as a ratio.
• Cumulative Response and Lift Charts are visual
  ways to measure how well the model is.

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Cumulative Response
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Lift Chart
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ROC Curve

• c 0.917

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Comparisons
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Set up Breslow Day

• There are 3 2x2 tables.
• We want to test whether or not there are
  significant differences in association with the 3
  methods.

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Breslow Day Test

• Ho OR1 OR2OR3
• Ha ORs are not all equal
• Test Stat 0.3839
• Pvalue 0.8253
• Conclusion There is no evidence the ORs differ
  over the different methods.

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References

• 1. Berry, Michael J.A. and Linoff, Gordon Data
  Mining Techniques For Marketing, Sales, and
  Customer Support. John Wiley Sons, Inc. New
  York, 1997.
• 2. Breiman, L., Friedman, J.H., Olshen, R.A.,
  and Stone, C.J. Classification and Regression
  Trees. Wadsworth Inc. California, 1984.
• 3. Fernandez, George. Data Mining Using SAS
  Applications. Chapman Hall/CRC Boca Raton,
  FL, 2003.
• 4. Johnson, Dallas E. Applied Multivariate
  Methods for Data Analysts. Duxbury Press
  Pacific Grove, CA, 1998.
• 5. Kass, G.V. An Exploratory Technique for
  Investigating Large Quantities of Categorical
  Data. Applied Statistics. Vol.29, No.2
  (1980), 119-127.
• 6. http//marketing.byu.edu/download/measurementan
  alysis/DataSets/chd/
• 7. Logistic Regression Examples Using the SAS
  System. SAS Institute Inc. North Carolina,
  1995.
• 8. Hastie, T., Tibshirani, R., and Friedman, J.
  The Elements of Statistical Learning. Springer
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