Multistage Cross-Sell Model of Employers in the Financial Industry

Transcription

1 Paer 4-8 Multistage Cross-Sell Model of Emloyers in the Financial Industry Kwan Park and Steve Donohue The Princial Financial Grou ABSTRACT This aer details the stes to develo a multistage cross-sell model of emloyers in the Financial Services industry. This model can be used to score the likelihood of an emloyer to urchase multile roducts. Toics covered include data rearation for data mining, several advanced modeling techniques, and multistage cross-sell model score comarison. Strong non-linear curvatures among the inut variables were found during the modeling rocess and examined. The modeling techniques used were Decision Tree, Neural Network, Regression and Memory Based Reasoning in SAS Enterrise Miner (version 4.) of Windows 000 system. INTRODUCTION In the Financial Services industry, the cross-selling and retaining of customers have become very imortant issues. These issues have been addressed via the develoment of many redictive models. These models have been designed to identify customers having a high likelihood of urchasing multile roducts. However, the vast majority of these models have been done at the business-to-consumer level. The indeendent variables for these models have generally included transactional data: transaction frequency, amount of transaction and urchase sequence, and demograhic data (age, gender, income, geograhic location, etc.) Alternatively, this aer exlains an aroach for multistage cross-sell modeling at the business-to-business (or emloyer) level. For examle, it examines selling Grou Medical Insurance to emloyers Grou Long-Term Disability lans. The indeendent variables used were emloyer level transactional data (years of relationshi, number of roducts owned, total remium values, and firmagrahic data (total number of emloyees, residential oulation, sales volume, standard SIC code, legal status, region, etc.) The object of the modeling being to score the emloyers on likelihood to become multile roducts owners and redict the sequence of roduct urchase. SEMMA methodology was alied. Strong non-linear relationshis among the inut variables were found and these non-linear curvatures contributed to the models in different ways. OBJECTIVE The objectives for this modeling are the following:. Identify emloyers with a high likelihood of becoming multile roduct owners.. Determine the roduct urchase sequence. 3. Assign a score according to likelihood to urchase identified roduct. DATA This study deals with two tyes of data for each of the three emloyer grous: Transactional data roduct coverage, length of relationshi, total contract amount, remium amount, number of active emloyees under contract, etc. Firmagrahic data geograhic region, metroolitan area, total number of emloyees, sales volume, years in business, number of customers, legal status, gender of CEO, rivate/ublic comany, SIC industry code, etc. (The firmagrahic data was extracted from Dun and Bradstreet and matched with tax-id.) MODELING The first object function of the modeling efforts was to redict the multile roduct emloyers.. Data was samled to insure the same size of the rior target, and artitioned as training and validation data set of 60% and 40%, resectively, with strata information of rior target robability.. Data Mining Database Node was used to roduce only one data mining database, which otimized the erformance of analytic nodes. Three sets of roducts were analyzed: Grou Insurance, Pension, and Executive Benefits. Included in Grou Insurance were Medical/Health, Dental, Vision, Long-Term Disability, Short- Term Disability, and Life. Within the Pension set were 40(K) lans and Defined benefit cases. As for Executive Benefits, 9 roduct lines were utilized. Dun and Bradstreet emloyer data was emloyed for the firmagrahic data. SAS Enterrise Miner was used for modeling and the modeling techniques were decision trees, neural network, logistic regression and memory based reasoning. For the develoment rocedure, SAS s 3. Missing values were relaced by tree imutation with surrogates method. This method is identical to tree imutation, with the addition of surrogate slitting rules. A surrogate rule is a back u to the main slitting rule. When the main slitting rule relies on an inut whose value is missing, the first surrogate rule is invoked. If the first surrogate also relies on an inut whose value is missing, the next surrogate is invoked. If missing values revent the main rule and all the surrogates from alying to an observation, the main rule assigns the observation to the branch assigned to receive missing values.

2 4. Decision Tree, Neural Network, Logistic Regression and Memory Based Reasoning technologies were alied to redict the otential multile roducts owners. Among the Least Squares, Gini reduction and Entroy reduction, Gini with Model assessment measure of Total leaf imurity showed the best model. The Gini index is interreted as the robability that any two elements of a multiset chosen at random with relacement are different. A ure node has a Gini Index of 0, as the number of evenly distributed classes increases, the Gini index aroaches. The Gini Index formula is as follows: r j= j = Entroy is another measure of variability of categorical data. Consider r mutually exclusive events with robabilities,,, r, then Entroy is defines as: Chi-Squared test statistic is as follows: The artificial neural network was originally develoed by researchers who were trying to mimic the neural system of the human brain. By combining many simle comuting elements into a highly interconnected system, these researchers hoed to roduce comlex henomena such as intelligence. While there is considerable controversy over whether artificial neural networks are really intelligent, there is no doubt that they have develoed into very useful statistical models. More secifically, feedforward neural networks are a class of flexible nonlinear regression, discriminant, and data reduction models. By detecting comlex nonlinear relationshis in data, neural networks can hel to make redictions about real-world roblems. Neural Network architecture was set as one layer of five hidden nodes, and ordinal, nominal and interval variables and hidden nodes were used an inuts to target variable. Hyerbolic Tangent function was used as activation function and general linear combination function was used. The tangent hyerbolic function is defined as e g( a) = e The network architecture was: a a e + e j< k r,,, r ) = i log ( i ) i= H ( ( O = E E ) χ ν a a j k This network model is somewhat more comlex than usual neural network model architecture. The choice of model comlexity is always an issue to modelers. The above architecture was chosen by trial and error among many ossible architectures This multilayer ercetron (MLP) is a feed-forward neural network that uses sigmoid activation functions. This MLP is one of the most common tyes of neural network used for suervised rediction. Emirically, it is often found that the tangent hyerbolic function give rise to faster convergence of training algorithms than the logistic functions. Another alternative of the function is ordinary radial basis function (ORBF). ORBF networks are universal aroximators in theory, but in ractice they are often ineffective multivariate function estimators. In this modeling, ORBF networks were excluded. The most common incorrect concet of a neural network is that it cannot be exlained or cannot be reresented as an equation. However, a neural network is an alication of non-linear regression that can be reresented as a single equation even though that equation is very comlicated. The beauty of a neural network is that it can find very comlicated non-linear relationshi among variables under the condition that the errors are quite small. As the target variable is a dichotomous variable, a logistic regression model was used, and for the memory based reasoning model, a default setu was used. Usually, many modelers favor the backward selection method because it evaluates all the inut variables in relation to the target variable. In this modeling rocess, stewise selection, backward selection and forward selection methods were alied to develo regression model, and stewise method showed the best erformance. The logistic regression equation is as follows: log = β + x β + x β + 0 The last modeling technique alied in this modeling is memorybased reasoning (or case based reasoning). It is a rocess that identifies similar cases from history data or a database and alies the information that is obtained from these cases to a new x n β n

3 record. The memory based reasoning node in SAS Enterrise Miner is a modeling tool that uses a k-nearest neighbor algorithm to categorize or redict observations. The k-nearest neighbor algorithm takes a data set and a robe, where each observation in the data set is comosed of a set of variables and the robe has one value for each variable. The distance between an observation and the robe is calculated. The k observations that have the smallest distances to the robe are the k-nearest neighbor to that robe. A default set u of memory based reasoning node was used in this modeling. 5. The decision tree showed the highest lift values within the to 30 ercentiles. It roduced nine segmentations and the following roc sql (statement is to comute the lift values of each nodes.) roc sql; create table scored as select a._node_, a.single, b.multile from (select _node_, count(dunsno) as single from &_score where multile='single' grou by _node_ ) a left join (select _node_, count(dunsno) as multile from &_score where multile='multile' grou by _node_ ) b on a._node_ = b._node_ ; quit; data scored; set scored; if multile=. then multile=0; total=single+multile; score=int(multile/total*0000)/00; run; Enterrise Miner Diagram 3

4 6. Node Descrition The following table exlains the node definitions and lift values Segment Lift Years of Business >00 years AND.99 Headquarter Location AND.6 Sales Volume IS : [M,00M] Single Location AND.49 Sales Volume IS : [M,00M] Years of Business IS : (5,00] AND.5 Years of Business IS : (0,5] AND 0.95 Sales Volume IS: [300K,400K] [500K,M] [500M+] 0.56 Sales Volume IS : [,300K] [400K,500K] 0.36 Location Status IS MISSING AND 0.00 Sales Volume IS : [M,00M] Public/Private IS MISSING AND 0.00 The lift values of the to four nodes are greater than, and the emloyers in these four nodes were selected to find the sequence of the next roducts. For this analysis SAS Enterrise Miner s Association node was alied. This is the second objective function of this modeling. The roduct urchase date is needed to run the association node. The next table is the to 5 roduct sequences. Product A Product B showed the highest frequency of roduct urchasing sequence followed by Product B Product A. Product Sequence Frequency Percent Product A ==> Product B, Product B ==> Product A Product A ==> Product C Product C ==> Product A 4.84 Product A ==> Product D Product A ==> Product E 33.6 Product B & Product C ==> Product A Product A ==> Product F Product A ==> Product B & Product C Product F ==> Product A 44. Product A ==> Product B & Product E 43.5 Product A ==> Product B & Product D 43.5 Product E ==> Product A Product D ==> Product A Product B ==> Product C The second stage models are to redict the emloyers who will be Product B among current Product A customers and to redict the emloyers who will be Product B customers among current Product A customers, etc. Since so many models are required, only the to six nodes were chosen. Each was then scored for each individual emloyer. Next, the cross-sell scores were comuted. The following table is an examle of the scores.. 4

5 Emloyer ID Product A Product B Product A Product C Product A Product A Cross sell score Product B Product A Product C Product A Product D Product E Etc. APPLICATION The alication of this aroach is to aid the cross-sell marketing efforts at the emloyer level. Emloyers can be selected and aroriately targeted based on their roensity to urchase selected roducts. Marketing camaigns can be designed to focus on those emloyers that are most likely to urchase. Thus, this methodology can greatly imact the efficiency of marketing camaigns. CONCLUSION This aer describes emloyer level cross sell modeling to identify the likelihood of urchasing multile roducts and the roduct urchase sequence. It should also be noted that camaign results of emloyer level cross sell can take more effort and time comared to emloyee level camaign. Tracking must be established to identify the imact of any marketing efforts. Steve Donohue The Princial Financial Grou 7 High Street Des Moines IA, 5039 Work Phone: (55) Fax: (55) Donohue.Steve@rincial.com Web: SAS and all other SAS Institute Inc. roduct or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and roduct names are trademarks of their resective comanies. REFERENCES Bisho, C.M. (995), Neural Networks for Pattern Recognition, New York: Oxford University Press. Breiman, L., Friedman, J. H., Olshen, R.A., and Stone, C. J. (984), Classification and Regression Trees, Chaman and Hall. Enterrise Miner Software, Online Tutorial (SAS V8). Riley, B.D. (996), Pattern Recognition and Neural Networks, Cambridge University Press. Rud, Olivia Parr (00), Data Mining Cookbook, New York: John Wiley & Sons. Zahavi, J. and Levin, N. (997), Alying Neural Comuting to Target Marketing, Journal of Direct Marketing,, 5-. CONTACT INFORMATION Your comments and questions are valued and encouraged. Contact the author at: Kwan Park The Princial Financial Grou 7 High Street Des Moines IA, 5039 Work Phone: (55) Fax: (55) Park.Kwan.Soo@rincial.com Web: 5