Source Article: An Application of Cluster Analysis in the Financial Services Industry A Paper by Satish Nargundkar and Timothy J. Olzer
Analytical models are critical in the Financial Services Industry in every phase of the credit cycle – Marketing, Acquisitions, Customer Management, Collections, and Recovery. While such models are now commonplace, the search for competitive advantage requires continuous improvement in the models. Customization of the models for each segment of the population is a crucial step towards achieving that end. Segments in the population may be defined judgmentally using one or two variables, but Cluster Analysis is an excellent statistical tool for multivariate segmentation. The clusters may be used to drive the model development process, to assign appropriate strategies, or both.
The paper discusses the FASTCLUS procedure as a tool for segmentation of a population. The first phase involves preparing the data for clustering, which includes handling missing values and outliers, standardizing, and reducing the number of variables using tools such as the FACTOR procedure. The FASTCLUS discussion emphasizes the assumptions, the options available, and the interpretation of the SASâ output.
Finally, the business interpretation of the cluster analysis is provided within the context of this specific industry. This enables the analyst to identify the appropriate number of clusters to use in model development or strategic planning.
Introduction
Statistical Models are used for several purposes in the Financial Services industry, such as predicting the likelihood of response to a credit offer, predicting risk for making approval decisions, predicting likelihood of rolling to a higher level of delinquency, etc. Whatever the predicted variable, a single model may not perform effectively across the population because different segments in the population with very different characteristics usually exist.
Consider, for instance, a typical New Applicant Risk model, which is used to approve new customers. Application and Credit Bureau data are used to predict the likelihood of an applicant reaching a certain level of delinquency in a given time period, if accepted. If a single model is built for the entire population, younger applicants may tend to be systematically penalized by the model since they typically will lack depth of credit history compared to the population average. Hence it may make more sense to build two models for the two segments of the population, Young and Mature. Similarly, other variables, such as geographical region, product type, etc., may be candidates for segmenting the population depending on the purpose.
Segmentation may be done judgmentally based on experience, with some statistical testing after the fact, but such segmentation is limited to a handful of variables at best. For a true multivariate determination of homogeneous segments in a population, Cluster Analysis is an effective tool.
This paper discusses the process of segmenting a population for the purpose of making better modeling decisions using the FASTCLUS procedure. This is preceded by a brief discussion of the preliminary steps one must take to get the data ready for cluster analysis.
Preliminary Analysis
There are certain data cleaning and preparation procedures that should be performed prior to beginning an in-depth look at the data. The steps to take prior to running a cluster analysis are:
¨Select the variables to use in the analysis
¨Decide which observations to use
¨Decide if and how to weight the observations
¨Verify that all data values are valid and replacing any missing values
¨Standardize the data
¨Remove any data outliers
¨Decide what type of cluster analysis to perform
¨Ensure that the proper cautions have been taken before using a cluster analysis
Each of these steps is discussed in detail below.
1. Variable Selection When used as a segmentation technique, cluster analysis should only be performed on a small number of variables (or factors). The variable selection can be accomplished either by judgmental selection, or by a factor analysis. The preferred method is a factor analysis since it is a statistical procedure. However, the selection process is still judgmental; thus it is a good idea to select more variables than will be used in the final solution, then use the cluster analysis to determine which ones work the best.
If a factor analysis is used, there can be two ways of selecting the dimensions used in the cluster analysis. The first is to use the factors themselves as input to the cluster analysis. This amounts to using a linear combination of all the variables included in the factor analysis. This is a more difficult approach that in practice provides little lift in the clustering. Thus, a second approach, to select the variable that has the lowest correlation with the variables from the other factors and has a very high loading in it’s primary factor, is usually used. Not only does this approach create an almost identical solution to the first approach, it is much easier to implement. This latter approach was used to select the variables for the cluster analysis discussed in this paper. For details on how to use PROC FACTOR for factor analysis, refer to Goldberg [1997].
2. Invalid and Missing Values If a factor analysis has already been performed, then this issue has already been taken care of. If not, then it is critical that the following take place.
Any observations with invalid data values should be removed from the sample if they cannot be verified and fixed. Missing values need to be replaced with a value that makes sense. Usually for cluster analysis this will be the mean of the data without the missing values. There are certain variables where it will make more sense to set the value to 0. Examples of these include ordinal credit bureau variables. Also, most demographic variables will fall into this group. It is up to the analyst to determine which value is more appropriate. It will depend on why the value is missing as to what value to set it to. Any variable with a very high percentage of missing values should probably not be used in the Cluster Analysis.
There is another option for missing value replacement if there is a dependent variable in the data and model building will take place. By running a cross-tabulation of the variable with the missing value(s) by performance, we can tell how each value of the variable, including missing, performs. In this case, it makes sense to set the missing value to a value in the remainder of the distribution that performs similarly to missing.
3. Standardizing the Data - All variables included in the analysis must be standardized to a mean of 0 and a standard deviation of 1. The reason for this is to put the variables on an equivalent scale. For instance, a balance variable might range from $0 to $100,000. However, an ordinal variable might range from 0 to 30. Also, a value of 5 means something entirely different for balance then it does for number of trades.
Standardization can be accomplished in SASâ using the PROC STANDARD statement as shown below.
proc standard data= input data set out= output data set
mean=0 std=1 replace;
var varlist;;
run;
The above statements will replace variable values with their standardized ones, and the replace option replaces missing values with the mean for the variable.
4. Removing Outliers - If a factor analysis was completed, outliers were probably accounted for. However, the process should be completed again for the Cluster Analysis if observations were removed. The reason for this is that observations were removed based on all the variables included in the factor analysis. Since there are fewer variables in the cluster analysis (unless the actual factor loadings are used), an outlier should only be defined using these variables. This will yield more observations to include in the cluster analysis.
If capping the variables was used, or the actual factors will be used in the cluster analysis, nothing else needs to be done with the outliers.
If no factor analysis was performed, the next step is to account for any outliers (extreme values) in the data. There are two methods for doing this: 1) Remove any observations outside of a given value, or 2) Cap each variable at a given value.
If you choose to remove outliers, standardizing the data set makes this very easy. After the data is standardized, it is only a matter of choosing how many standard deviations from the mean is too far and should be considered an outlier. The advantage to using this method is that it is easy to apply since standardization is done anyway. The disadvantages are selecting the number of standard deviations is judgmental and that observations are lost.
5. Types of Cluster Analysis : There are two basic types of cluster analysis, 1) Agglomerative Hierarchical (PROC CLUSTER in SASâ)and 2) Disjoint or Euclidean Distance (PROC FASTCLUS). Agglomerative Hierarchical Clustering takes each observation and places it in it’s own cluster. Next the two closest clusters are combined. This continues until there is only one cluster left. Then an analysis is made to determine the appropriate number of clusters. Since Hierarchical Cluster Analysis is extremely time consuming, it is rarely used in practice. It is recommended in instances where there were a small number of observations.
Disjoint or Euclidean Distance Clustering starts with seeds for each cluster (the number of clusters is specified by the user). Each observation is assigned to the nearest seed (by Euclidean distance) to form a cluster. The seeds are then replaced by the means of the temporary clusters. The process continues until there are no further changes in the cluster means. This type of clustering is much more efficient, and thus can be used on very large data sets (SASâ says 100 to 100,000 observations). It should not be used on small data sets, as it is not guaranteed to converge.
6. Cautions on Clustering: It is important to keep these cautions in mind prior to running a cluster analysis:
¨Cluster analysis is extremely sensitive to correlation. All efforts should be taken to eliminate variables that are correlated with one another, and if this is not possible, then make sure a validation of the clustering is done. One way to use correlated variables is to use them as a factor, or a linear combination of the variables that are correlated.
¨Cluster analysis is more of a heuristic than a statistical technique. As such, it does not have the foundation of statistical tests and reasoning (unlike regression analysis, for instance),
¨Cluster analysis evolved from many different disciplines and has inherent biases from these disciplines. Thus, the analysis can be biased by the questions asked of it, and
¨Different methods and different numbers of clusters generate different solutions from the same data, so it is important to validate your findings.
Detailed Cluster Analysis
The list below shows the components of a cluster analysis solution that are discussed in the sections that follow:
1. The SASâ program
2. Interpretation of Output
3. Cluster Analysis Iterations
4. Selection of Final Cluster Solution
5. Validation of Results
6. Implementation of Clusters
The paper describes a detailed step by step procedure about how to go about applying a Cluster Analysis and how to implement the same in Business Intelligence using SAS Program.
The total analysis however can be referred to in the article; “An Application of Cluster Analysis in the Financial Services Industry” A Paper by Satish Nargundkar and Timothy J. Olzer; May & Speh, Strategic Decision Services; Atlanta, GA
Implementation
Implementing a cluster solution for modeling purposes is certainly more complex than a single model solution. In the case of a New Applicant modeling situation in the credit industry, for instance, each applicant has to first be assigned to a cluster, based on minimum distance to each cluster. In other words, if clusters were based on 15 variables, and there are 10 clusters, the distance of each variable for the applicant to each of the cluster means have to be computed. This can add processing time and cost to the implementation. This further underscores the importance of using a relatively small number of variables instead of factors that comprise of many more variables. Once the cluster is assigned, the appropriate model can be used to score the applicant.
Further, if strategies are implemented to change the behavior of people in certain clusters, then the clusters themselves have to be monitored and perhaps refined periodically.
Conclusion
Despite the added complexity, clustering can provide a much needed lift for financial institutions looking for better ways to manage their portfolios in a highly competitive environment. It provides a way to treat different segments of the population differently, increasing the probability of a more accurate decision.
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