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3 9) Calibration 10) Once a model moves to a production environment, the results require regular monitoring and recalibration. Models in Production When the model has proven itself and provides sufficient lift, a scoring system will provide guidance. For example, a scoring system might provide a score designed by the model development team to suggest whether to order an APS. Based on the factors used in the model, a score of 0-60 might yield a pass result with no further action. A score of might generate a refer to underwriter with a recommendation for an APS. The next class of might generate an automatic APS. Finally, a score of might raise a red flag to the underwriter that, based on this sample model, there may be significant anti-selection or perhaps a suspicion of attempted fraud. Aside from the score, the system should feedback to the data warehouse providing additional data elements and outcome results that can assist in further improvement of the model. 1) Data and Algorithm Preparation a) Collect data for predictive variables b) Clean the data c) Assign data distribution to three portions: training, test, validation Data should be drawn from the same source, at the same time, properly randomized and divided, to be used through the stages of model development Establish the logic and algorithm 2) Develop decision trees 3) Use training data to identify factors and predictors Model builds require some trial and error to get the most lift 4) Build the model a) Build multiple models attempting to optimize lift b) Test the models using a portion of the identified data c) Watch for discordancy d) Calibrate 5) Validation Implementation and maintaining a good model 6) Implementation and use 7) Scoring system established 8) Establish audit procedures and feedback to data warehouse 38 Types of Predictive Models The following list provides a glimpse into the number of model possibilities. Unfortunately, fuller descriptions exceed this article s intent. The reader should consult the references for additional description and examples. 1) Classification and Regression Trees (CART) Sort groups and population into smaller discrete branches and nodes. 2) Cox Proportional Hazard A form of survival modeling and a hazard function. Hazard functions are an estimate of the relative risk of a terminal event, such as a death. This survival model is a multivariate technique for analyzing the effect of two or more metric and/or non-metric variables on survival. 3) Decision Tree Analysis Sorts decisions into smaller branches and nodes, weighting the decisions based on factors identified. 4) Generalized Linear Model (GLM) Linear or logistic regression models. The most commonly described in life insurance literature, relatively speaking, this is a simple way to model using multiple variables that interact in ways that are not obvious using univariate analysis. See expanded discussion below. 5) k-nearest Neighbor (knn) Uses data that aggregates based on classification. Predictions are based on population density of the factors in the training sample. A simple system often applied to machine learning. ON THE RISK vol.27 n.2 (2011)

4 6) Logistic Regression Logistic regression is a category of statistical models referred to as generalized linear models (q.v.). The goal of logistic regression is to predict the category of outcome for individual cases using the most efficient model. 7) Naïve Bayes Classifier Assumes that the presence (or absence) of a particular feature of a class is unrelated to the presence (or absence) of any other feature. 8) Neural Networks (NN) As the name suggests, models that have the structural appearance of animal neurons. The concept suggests that many inputs can result in a single (or at least smaller number) output. NNs can produce multiple outcomes however. (Figure 2) 9) Regression Splines Implies regression analysis that requires data points that must be interpolated, or somehow smoothed. In this equation b 0 is the regression coefficient for the intercept and the b i values are the regression coefficients (for variables 1 through k) computed from the data. Linear models as described make a set of somewhat restrictive assumptions: Dependent variable y is in normal distribution and conditioned on the value of predictors A constant variance, regardless of the predicted response The advantages of linear models with the above restrictions are: An easy-to-interpret model form Relatively simple computations Readily analyzed to determine the quality of the fit Generalized linear models relax these restrictions. They adjust responses that violate the linear model assumptions in two ways: 1) Link functions model responses when a dependent variable is assumed to be related to the predictors in a non-linear fashion. These functions, and there are many, transform a target range so the simple form of linear models can be maintained. 2) Variance functions used, which express the variance as a function of the predicted response. This allows responses with variances that are not constant. While this article has not to this point dwelt on the statistical details of predictive modeling, an example chosen from above will expand the description of one of the model types encountered in the actuarial literature. Advantages of Predictive Models 1) Ability to detect complex non-linear relationships between dependent and independent variables. 2) Ability to detect all possible interactions between predictor variables. 3) Availability of multiple training algorithms. 4) Some forms of predictive modeling, neural nets for example, require less formal statistical training. 5) Bayesian methods can arguably be used to discriminate between conflicting hypotheses: hypotheses with very high support should be accepted as true, and those with very low support should be rejected as false. Disadvantages of Predictive Models 1) A perceived black box nature, making it difficult to describe and explain results; the proprietary nature and structure of each model reinforces the Generalized Linear Modeling (GLM) Extends perception. linear regression models to both non-normal distributions and linear transformation (transformation methodology might be biased by perceptions held 2) Subject to bias, some may argue that inference of linearity). First we can describe a conventional before any evidence is collected. linear model that specifies the relationship between a 3) Computational intensity requiring adequate dependent variable Y, and a set of predictor variables, technology infrastructure and statistical analysis the X s, so that acumen. Y = b 0 + b 1 X 1 + b 2 X b k X k 4) Prone to overfitting and therefore inaccuracies caused by fluctuations in irrelevant or erroneous predictors. ON THE RISK vol.27 n.2 (2011) 39

5 5) Sensitive to changes in conditions and therefore require close monitoring of the environment to which the model is being applied. 6) Models as mathematical constructs can at times yield results that fly in the face of common sense 7) Regulatory concerns if models are not adequately understood or explained. Modeling Concepts and Terms The following terms and concepts provide readers new to the area of predictive modeling a basic lexicon, useful for discussions within their respective organizations. Algorithms Expression of a problem as a sequence of logical steps. Bayesian Methods Based on Bayes theorem. Bayesian inference presumes collection of evidence that is either consistent with or inconsistent with a given hypothesis (H1). As we gather evidence, our confidence in the hypothesis ought to change. Given sufficient evidence, the degree of confidence should become either much higher or much lower. Underwriters should already be familiar with other Bayesian models, specifically the specificity and sensitivity of a test, and the test s corresponding positive or negative predictive values. Calibration During development and thereafter, as the environment changes, or to maintain lift, predictive models must be calibrated, reworking predictors and factors. Some circumstances will change frequently, for example, a new life insurance marketing plan, a new product with different pricing and expense assumptions, or outside influences such as competition with similar products. Data Mining Data mining is the process of finding patterns and correlations among dozens of data elements in relational databases, especially large databases. This process allows a user the ability to analyze data from different perspectives and summarize the data into useful information. The software to mine the data is often a different tool than one used to build a predictive model. Decision Trees A decision tree as discussed here depicts rules for dividing data into groups. The first rule splits the entire data set into a number of pieces, and then another rule may be applied to a piece, different rules to different pieces, forming a second generation of pieces. In general, a piece may be either split or left alone to form a final group. (Figure 3) Derived Predictors Mathematically transformed predictor variables, sometimes known as synthetic predictors. These predictors are derived from mined data and through application of algorithms developed during the model-building process. They were not identified as useful until discovered during the development phase. 42 Lifestyle Based Analytics Most readers are familiar with the links between lifestyle characteristics and various medical conditions. Various data aggregators and vendors now offer over 2,000 pieces of information (data fields) on various applicants. While a powerful tool for marketing segmentation, which can arguably raise flags concerning higher incidence of disease based on the population predictors, LBA cannot provide the same predictive value to which we are currently accustomed from routine fully underwritten business on an individual case-by-case basis. LBA may be considered in building predictive models for life insurance risk selection, but it should not be confused with the term predictive modeling. Robust life insurance predictive models can be prepared without LBA. Linear Regression Regression uses the value of one variable in a pair of variables, to predict the value of the second variable. Linear regression attempts to pass a line through the observed variable pairs in a given sample data set. Models built using linear regression are fine when the value of one variable changes, is conditional, upon the value of the other variable. If we wish to study the probability distribution of both variables (or more variables) as they both change, we move to the realm of multivariate analysis (q.v.). ON THE RISK vol.27 n.2 (2011)

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