Transcript Handout 1
Review of Fraud Classification Using Principal Components Analysis of RIDITS By Louise A. Francis Francis Analytics and Actuarial Data Mining, Inc. Objectives Address question: Why use new method, PRIDIT? Introduce other methods used in similar circumstances Explain how PRIDIT adds to methods available Explain limitations of PRIDIT/RIDIT A Key Problem in Fraud Modeling Most data mining methods need a target (dependent) variable Y = a + b1x1 + b2x2 + … bnxn Fraud (Yes/No or Fraud Score) = f(predictor variables) Need sample of data where claims have been determined to be fraudulent or legitimate Dependent variable hard to get In a large sample of automobile insurance claims perhaps 1/3 may have an element of abuse or fraud Scarce resources are not expensed on such large volumes of claims to determine their legitimacy Only a small percentage referred to SIU investigators or other investigations There are time lags in determining the outcome of investigations Unsupervised learning Another approach that does not require a dependent variable Two Key Kinds Cluster Analysis Principal Components/Factor Analysis Pridit uses this approach It is applied to ordered categorical variables Cluster Analysis Records are grouped in categories that have similar values on the variables Examples Marketing: People with similar values on demographic variables (i.e., age, gender, income) may be grouped together for marketing Text analysis: Use words that tend to occur together to classify documents Note: no dependent variable used in analysis Clustering Common Method: k-means, hierarchical No dependent variable – records are grouped into classes with similar values on the variable Start with a measure of similarity or dissimilarity Maximize dissimilarity between members of different clusters Dissimilarity (Distance) Measure – Continuous Variables Euclidian Distance dij 1/ 2 m 2 ( xik x jk ) i, j = records k=variable k 1 Manhattan Distance dij m xik x jk k 1 Column Variable Binary Variables Row Variable 1 0 1 a b a+b 0 c d c+d a+c b+d Binary Variables Sample Matching bc d abcd Rogers and Tanimoto 2(b c) d (a d ) 2(b c) Example: Fraud Data Data from 1993 closed claim study conducted by Automobile Insurers Bureau of Massachusetts Claim files often have variables which may be useful in assessing suspicion of fraud, but a dependent variable is often not available Variables used for clustering: Legal representation Prior Claim SIU Investigation At fault Police report Number of providers Statistics for Clusters Based on descriptive statistics, Cluster 2 appears to have higher likelihood of fraudulent claims – more about this later Police Medical At Legal SIU Number Cluster Report Audit Fault Rep Investigation Providers Percentage Yes 1 46.7% 0.1% 42.2% 6.1% 0.0% 2 2 49.8% 5.9% 2.4% 96.0% 6.5% 4 Principal Components Analysis A form of dimension (variable) reduction Suppose we want to combine all the information related to the “financial” dimension of fraud Medical provider bill (indicative of padding claim) Hospital bill Number of providers Economic Losses Claimed wages Incurred Losses Principal Components These variables are correlated but not perfectly correlated We replace many variables with a weighted sum of the variables Correlation Matrix for Variables Correlations Number Medical Provider Economic Hospital Providers Bill Paid Losses Incurred Pymt Number Providers 1.000 0.387 0.571 0.382 0.382 0.168 Medical Bill Provider Paid Economic Losses 0.387 1.000 0.539 0.952 0.952 0.922 0.571 0.539 1.000 0.531 0.531 0.327 0.382 0.952 0.531 1.000 1.000 0.888 Inourred Hospital Pymt 0.382 0.952 0.531 1.000 1.000 0.888 0.168 0.922 0.327 0.888 0.888 1.000 Finding Factor or Component The correlation matrix is used to find the factor that explains the most variance (captures most of the correlation) for the set of variables That component or factor extracted will be a weighted average of the variables More than one Component or Factor may result from applying the method Evaluating Importance of Variables Use factor loadings Component Matrix Variable Loading Number Providers 0.497 Medical Bill 0.974 Provider Paid 0.646 Economic Losses 0.976 Incurred 0.976 Hospital Pymt 0.886 Problem: Categorical Variables It is not clear how to best perform Principal Components/Factor Analysis on categorical variables The categories may be coded as a series of binary dummy variables If the categories are ordered categories, you may loose important information This is the problem that PRIDIT addresses RIDIT Variables are ordered so that lowest value is associated with highest probability of fraud Use Cumulative distribution of claims at each value, i, to create RIDIT statistic for claim t, value i Rti pˆ tj j i ˆ tj p j i Example: RIDIT for Legal Representation Legal Representation Proportion Proportion Value Code Number Proportion Yes No 1 2 706 694 0.504 0.496 Below 0.000 0.504 Above RIDIT 0.496 -0.496 0.000 0.504 PRIDIT Use RIDIT statistics in Principal Components Analysis Component Matrixa Component 1 S IU .2 48 Poli ce Report .2 20 At Fault .7 09 Leg al Rep .7 52 Medical Audit .3 41 Prior Cl ai m .4 06 Extracti on Method: Princi pal Component Analysi s. a. 1 co mpo nent s ext racted. Scoring Assign a score to each claim The score can be used to sort claims More effort expended on claims more likely to be fraudulent or abusive In the case of AIB data, we can use additional information to test how well PRIDIT did, using the PRIDIT score A suspicion score was assigned to each claim by an expert PRIDIT vs. Suspicion Score Suspicion Score vs PRIDIT Score 0.50 (1.00) (1.50) Suspicion Score 10 .0 0 9. 00 8. 00 7. 00 6. 00 5. 00 4. 00 3. 00 2. 00 (0.50) 1. 00 0.00 0. 00 PRIDIT Score 1.00 Clustering and Suspicion Score Report Mean TwoStep Cluster Number 1 Sus picion Level .6445 2 3.3737 Total 1.9643 Result There appears to be a strong relationship between PRIDIT score and suspicion that claim is fraudulent or abusive The clusters resulting from the cluster procedure also appeared to be effective in separating legitimate from fraudulent or abusive claims Comparison: PRIDIT and Clustering PRIDIT gives a score, which may be very useful for claims sorting. Clustering assigns claims to classes. They are either in or out of the assigned class. Clustering ignores information about the order of values for categorical variables Clustering can accommodate both categorical and continuous variables Comparison Unordered categorical variables with many values (i.e., injury type): Clustering has a procedure for measuring dissimilarity for these variables and can use them in clustering If the values for the variables contain no meaningful order, PRIDIT will not help in creating variables to use in Principal Components Analysis. Review of Fraud Classification Using Principal Components Analysis of RIDITS By Louise A. Francis Francis Analytics and Actuarial Data Mining, Inc.