U.S. patent application number 13/463492 was filed with the patent office on 2012-11-08 for method and system for determining the importance of individual variables in a statistical model.
This patent application is currently assigned to Deloitte Development LLC. Invention is credited to Hrisanthi Adamopoulos, John R. Lucker, Raymond E. Stukel, Cheng-Sheng Peter Wu, Frank M. Zizzamia.
Application Number | 20120284059 13/463492 |
Document ID | / |
Family ID | 25542469 |
Filed Date | 2012-11-08 |
United States Patent
Application |
20120284059 |
Kind Code |
A1 |
Zizzamia; Frank M. ; et
al. |
November 8, 2012 |
METHOD AND SYSTEM FOR DETERMINING THE IMPORTANCE OF INDIVIDUAL
VARIABLES IN A STATISTICAL MODEL
Abstract
A method and system for determining the importance of each of
the variables that contribute to the overall score of a model for
predicting the profitability of an insurance policy. For each
variable in the model, an importance is calculated based on the
calculated slope and deviance of the predictive variable. Since the
score is developed using complex mathematical calculations
combining large numbers of parameters with predictive variables, it
is often difficult to interpret from the mathematical formula for
example, why some policyholders receive low scores while other
receive high scores. Such clear communication and interpretation of
insurance profitability scores is critical if they are used by the
various interested insurance parties including policyholders,
agents, underwriters, and regulators.
Inventors: |
Zizzamia; Frank M.; (Canton,
CT) ; Wu; Cheng-Sheng Peter; (Arcadia, CA) ;
Stukel; Raymond E.; (Elmhurst, IL) ; Adamopoulos;
Hrisanthi; (Wethersfield, CT) ; Lucker; John R.;
(Simsbury, CT) |
Assignee: |
Deloitte Development LLC
Hermitage
TN
|
Family ID: |
25542469 |
Appl. No.: |
13/463492 |
Filed: |
May 3, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
09996065 |
Nov 28, 2001 |
8200511 |
|
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13463492 |
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Current U.S.
Class: |
705/4 |
Current CPC
Class: |
G06F 17/18 20130101;
G06Q 40/08 20130101 |
Class at
Publication: |
705/4 |
International
Class: |
G06Q 40/08 20120101
G06Q040/08 |
Claims
1. A system for calculating the contribution of each of a plurality
of variables in a statistical model including a scoring formula for
generating a score comprising a database for storing values
associated with at least some of the plurality of variables, means
for calculating a slope for any of the plurality of variables,
means for calculating a deviance value for any of the plurality of
variables and means for calculating the contribution of any of the
plurality of variables based on the calculated slope and deviance
values.
2. The system of claim 1 wherein the means for calculating the
slope comprises a software module that takes the first derivative
of the scoring formula with respect to the variable being
analyzed.
3. The system of claim 1 wherein the plurality of variables
describe characteristics of at least one of an existing
policyholder and potential policyholder and the scoring formula is
used to generate a score reflective of the expected loss/premium
ratio for an insurance policy.
4. The system of claim 3 wherein the premium for the insurance
policy is based on the score.
5. The system of claim 1 further comprising means for ranking the
individual variables based on the calculated contribution.
6. The system of claim 1 wherein the means for calculating a
deviance value includes a software module that receives inputs for
a mean value and a standard deviation value and the deviance value
is calculated using the formula: Deviance of x i = ( x i - .mu. i )
.sigma. i ##EQU00006## where .mu..sub.i is the mean for x.sub.i and
.sigma..sub.i is the standard deviation for predicitve variable
x.
7. The system of claim 1 wherein the contribution is calculated for
any of the plurality of variables by multiplying the slope and
deviance values.
8. In a system that employs a statistical model comprised of a
scoring formula having a plurality of predictive variables for
generating a score that is representative of a risk associated with
an insurance policyholder, a method of evaluating the contribution
of each of the plurality of predictive variables to the score
generated by the model comprising the steps of populating a
database associated with the system with a mean value and standard
deviation value for each of the plurality of predictive variables,
calculating a slope value for each of the plurality of predictive
variables, calculating a deviance value based on the mean value and
the standard deviation value for each of the plurality of
predictive variables, and multiplying the deviance value and slope
value for each of the plurality of predictive variables to
determine the contribution of each of the plurality of predictive
variables to the score.
9. The method of claim 8 further comprising the step of defining at
least one assumption for the mean value associated with at least
one of the plurality of predictive variables.
10. The method of claim 8 wherein the step of calculating the slope
further comprises the step of calculating the first derivative of
the scoring formula with respect to the predictive variable of the
plurality of predictive variables that is being analyzed.
11. The method of claim 8 wherein the deviance value is calculated
as follows: Deviance of x i = ( x i - .mu. i ) .sigma. i
##EQU00007## where .mu..sub.i is the mean for x.sub.i and
.sigma..sub.i is the standard deviation for predicitve variable
x.sub.i.
12. The method of claim 8 further comprising the step of ranking
each of the plurality of predictive variables based on the
contribution of a predictive variable to the score wherein a
predictive variable having a higher calculated contribution value
is assumed to have had a greater effect on the score.
13. A method of evaluating the contribution of each of the
plurality of variables in a statistical model comprised of a
scoring formula having at least one value associated with each of
the plurality of variables comprising the steps of obtaining a mean
value and a standard deviation value for each of the plurality of
variables, calculating a slope value for each of the plurality of
variables, calculating a deviance value based on the mean value and
the standard deviation value for each of the plurality of
variables, and multiplying the deviance value and slope value for
each of the plurality of variables to quantify the contribution of
each of the plurality of variables to the score.
14. The method of claim 13 further comprising the step of
populating a storage means with the mean value and standard
deviation values for each of the plurality of variables.
15. The method of claim 13 wherein the statistical model is used to
assess the profitability of an insurance policy and each of the
plurality of variables is associated with at least one of the
policyholder and item to be insured.
16. The method of claim 15 wherein a score generated by the model
determines the price for the insurance policy and the contribution
is used to identify which variables had the greatest effect on the
price.
17. In a system that employs a statistical model comprised of a
scoring formula having a plurality of predictive variables for
generating a score that is representative of a risk associated with
an insurance policyholder and for pricing a particular coverage
based on the score, a method of quantifying the contribution of
each of the plurality of predictive variables to the score
generated by the model comprising the steps of populating a
database associated with the system with a mean value and a
standard deviation value for each of the plurality of predictive
variables, calculating a slope value for each of the plurality of
predictive variables, calculating a deviance value based on the
mean value and the standard deviation value for each of the
plurality of predictive variables, and multiplying the deviance
value and slope value for each of the plurality of predictive
variables to quantify the contribution of each of the plurality of
predictive variables to the score.
18. The method of claim 17 further comprising the step of ranking
each of the plurality of variables based on the quantified
contribution as calculated for each of the plurality of predictive
variables.
19. The method of claim 17 wherein the step of calculating the
slope further comprises the step of calculating the first
derivative of the scoring formula with respect to a predictive
variable of the plurality of predictive variables that is being
analyzed.
20. The method of claim 17 wherein the deviance value is calculated
as follows: Deviance of x i = ( x i - .mu. i ) .sigma. i
##EQU00008## where .mu..sub.i is the mean for x.sub.i and
.sigma..sub.i is the standard deviation for predicitve variable
x.sub.i.
Description
RELATED APPLICATION DATA
[0001] This application is a continuation of U.S. Ser. No.
09/996,065, filed Nov. 28, 2001, the contents of each of which are
hereby incorporated by reference in their entirety.
BACKGROUND OF THE INVENTION
[0002] The present invention is directed to a method and system for
evaluating the results of a predictive statistical scoring model
and more particularly to a system and method that determines the
contribution of each of the variables that comprise the predictive
scoring model to the overall score generated by the model.
[0003] Insurance companies provide coverage for many different
types of exposures. These include several major lines of coverage,
e.g., property, general liability, automobile, and workers
compensation, which include many more types of sub-coverage. There
are also many other types of specialty coverages. Each of these
types of coverage must be priced, i.e., a premium selected that
accurately reflects the risk associated with issuing the coverage
or policy. Ideally, an insurance company would price the coverage
based on a policyholder's actual future losses. Since a
policyholder's future losses can only be estimated, an element of
uncertainty or imprecision is introduced in the pricing of a
particular type of coverage such that certain policies are priced
correctly, while others are under-priced or over-priced.
[0004] In the insurance industry, a common approach to pricing a
policy is to develop or create complex scoring models or algorithms
that generate a value or score that is indicative of the expected
future losses associated with a policy. The predictive scoring
models are used to price coverage for a new policyholder or an
existing policyholder. As is known, multivariate analysis
techniques such as linear regression, nonlinear regression, and
neural networks are commonly used to model insurance policy
profitability. A typical insurance profitability application will
contain many predictive variables. A profitability application may
be comprised of thirty to sixty different variables contributing to
the analysis.
[0005] The potential target variables in such models can include
frequency (number of claims per premium or exposure), severity
(average loss amount per claim), or loss ratio (loss divided by
premium). The algorithm or formula will directly predict the target
variable in the model. The scoring formula contains a series of
parameters that are mathematically combined with the predictive
variables for a given policyholder to determine the predicted
profitability or final score. Various mathematical functions and
operations can be used to produce the final score. For example,
linear regression uses addition and subtraction operations, while
neural networks involve the use of functions or options that are
more complex such as sigmoid or hyperbolic functions and
exponential operations.
[0006] In creating the predictive model, often the predictive
variables that comprise the scoring formula or algorithm are
selected from a larger pool of variables for their statistical
significance to the likelihood that a particular policyholder will
have future losses. Once selected from the larger pool of
variables, each of the variables in this subset of variables is
assigned a weight in the scoring formula or algorithm based on
complex statistical and actuarial transformations. The result is a
scoring model that may be used by insurers to determine in a more
precise manner the risk associated with a particular policyholder.
This risk is represented as a score that is the result of the
algorithm or model. Based on this score, an insurer can price the
particular coverage or decline coverage, as appropriate.
[0007] As noted, the problem of how to adequately price insurance
coverage is challenging, often requiring the application of complex
and highly technical actuarial transformations. These technical
difficulties with pricing coverages are compounded by real world
marketplace pressures such as the need to maintain an
"ease-of-business-use" process with policyholders and insurers, and
the underpricing of coverages by competitors attempting to buy
market share. Notwithstanding the recognized value of these pricing
models and their simplicity of use, known models provide insurers
with little information as to why a particular policyholder
received his or her score. Consequently, insurers are unable to
advise policyholders with any precision as to the reason a
policyholder has been quoted a high premium, a low premium, or why,
in some instances, coverage has been denied. This leaves both
insurers and policyholders alike with a feeling of frustration and
almost helpless reliance on the model that is used to determine
pricing.
[0008] While predictive scoring models are available in the
insurance industry to assist insurers in pricing insurance
coverage, there is still a need for a method and system to that
overcomes the foregoing shortcomings in the prior art. Accordingly,
there exists a need for a system and method to interpret the
results of any scoring model used in the insurance industry to
price coverage. Indeed, the system and method may be used to
interpret the results of any complex formula. There is especially a
need for a system and a method that allow an insurer to determine
and rank the contribution of each of the individual predictive
variables to the overall score generated by the scoring model. In
this manner, insurers and policyholders alike may know with
certainty the factors or variables that most influenced the premium
paid or price of an insurance policy.
SUMMARY OF THE INVENTION
[0009] It is an object of the present invention to address and
overcome the deficiencies of the prior art by providing a system
and a method for interpreting the results of a scoring model used
to price insurance coverage.
[0010] It is another object of the invention to provide a system
and a method that determine the significance or contribution of
each predictive variable to the score generated by such a scoring
model.
[0011] It is another object of the invention to provide a system
and a method that permit insurers to rank the variables according
to their significance or contribution to such overall score.
[0012] It is still another object of the present invention to
provide a system and method that allow insurers to utilize the rank
information to inform potential or existing policyholders of those
variables that most influenced or affected the pricing.
[0013] Accordingly, in one aspect of the invention a method is
provided of evaluating the scoring formula or algorithm to
determine the contribution of each of the individual predictive
variables to the overall score generated by the scoring model. For
example, in the commercial auto industry, sophisticated scoring
models are created for predicting the profitability of issuing a
particular policy based on variables that have been determined to
be predictive of profitability. These predictive variables may
include the age of the vehicle owner, total number of drivers,
speeding violations and the like. In a scoring algorithm having
over a dozen variables, the analysis or their individual
contributions to the overall score would be very difficult without
the present invention.
[0014] In another aspect of the present invention, in a system that
employs a statistical model comprised of a scoring formula having a
plurality of predictive variables for generating a score that is
representative of a risk associated with an insurance policyholder
and for pricing a particular coverage based on the score, a method
is provided of quantifying the contribution of each of the
plurality of predictive variables to the score generated by the
model including the steps of populating a database associated with
the system with a mean value and standard deviation value for each
of the plurality of variables, calculating a slope value for each
of the plurality of variables, calculating a deviance value based
on the slope and standard deviation for each of the plurality of
variables, and multiplying the deviance value and slope value for
each of the plurality of variables to quantify the contribution of
each of the plurality of variables to the score. This quantified
contribution may then be used to rank the variables by importance
to the overall score.
[0015] Additional objects, features and advantages of the invention
appear from the following detailed disclosure.
[0016] The present invention accordingly comprises the various
steps and the relation of one or more of such steps with respect to
each of the others, and the product which embodies features of
construction, combinations of elements, and arrangement of parts
which are adapted to effect such steps, all as exemplified in the
following detailed disclosure, and the scope of the invention will
be indicated in the claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] For a fuller understanding of the invention, reference is
made to the following description, taken in connection with the
accompanying drawings, in which:
[0018] FIG. 1 illustrates a system that may be used to interpret
and rank the predictive variables according to an exemplary
embodiment of the present invention;
[0019] FIG. 2 is a flow diagram depicting the steps carried out in
interpreting the contribution of each of the predictive external
variables in a scoring model according to an exemplary embodiment
of the present invention;
[0020] FIG. 3 specifies the description of the variables in an
example illustrating the application of the method of the present
invention to an exemplary scoring formula;
[0021] FIG. 4 specifies assumptions made regarding the variables in
the exemplary scoring formula; and
[0022] FIG. 5 specifies the values for the variables used in the
exemplary scoring formula, the application of the method of the
present invention and the results thereof.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0023] The invention described herein creates an explanatory system
and method to quantitatively interpret the contribution or
significance of any particular variable to a policyholder's
profitability score (hereinafter the "Importance"). The methodology
of the present invention considers both a) the overall impact of a
variable to the scoring model as well as b) the particular value of
each variable in determining its Importance to the final score.
[0024] As is known, scoring models are developed and used by the
insurance industry (as well as other industries) to set an ideal
price for a coverage. Many off-the-shelf statistical programs and
applications are known to assist developers in creating the scoring
models. Once created relatively standard or common computer
hardware may be used to store and run the scoring model. FIG. 1
illustrates an exemplary system 10 that may be employed to
implement a scoring model and calculate the Importance of
individual predictive variables according to an exemplary
embodiment of the present invention. Referring to FIG. 1, the
system includes a database 20 for storing the values for each of
the variables in the scoring formula, a processor 30 for
calculating the target variable in the scoring algorithm as well as
the values associated with the present invention, monitor 40 and
input/output means 50 (i.e., keyboard and mouse). Alternatively,
the system 10 may housed on a stand alone personal computer having
a processor, storage means, monitor and input/output means.
[0025] Referring to FIG. 2, the steps of a method according to an
exemplary embodiment of the present invention are shown generally
as 100. The method assumes a model has been generated utilizing one
of many statistical and actuarial techniques briefly discussed
herein and known in the art. The model is typically a scoring
formula or algorithm comprised of a plurality of weighted
variables. The database 20 is populated with values for the
variables that define the scoring model. These values in the
database are used by the scoring model to generate the
profitability score. It should be noted that some of the values
might be supplied as a separate input from an external source or
database.
[0026] Similarly, in step 101, the database 20 or a different
database is populated with values for the population mean and
standard deviation for each of the predictive variables. These
values will be used in calculating the Importance as will be
described. Next, in step 102, the slope for each predictive
variable in the scoring model is determined As discussed below,
this may be simply done in a scoring mode or require a separate
calculation. In step 103, a deviance is calculated. After the
deviance is calculated, in step 104, the Importance is calculated
for each variable by multiplying the slope by the deviance. The
variables are then ranked by Importance in step 105. The higher the
value the more important the variable was toward the overall
profitability score.
[0027] Steps 102 through 104 are now explained in more detail:
Step 102
[0028] The first criterion in determining the most important
variables for a particular score is the impact that each variable
contributes to the overall scoring formula. Mathematically, such
impact is given by the slope of the scoring function with respect
to the variable being analyzed. To calculate the slope, the first
derivative of the formula with respect to the variable is
generated. For a nonlinear profitability formula such as a neural
network formula or a nonlinear regression formula, the slope may be
different from one data point (i.e. policyholder) to the next.
Therefore, the average of the slope across all of the data points
is used as the first criteria to measure Importance.
[0029] Since the first derivative can be either positive or
negative for each data point and since the impact should be treated
equally regardless of the sign of the slope, it is necessary to
calculate the average of the first derivative and then take the
absolute value of the average. In summary, the first criteria in
determining the most important variables can be represented as
follows:
Slope of Predictive Variable x i = avg ( .differential. F ( X )
.differential. x i ) ##EQU00001##
(where F(X) is the scoring function which depends on a number of
predictive variables, x.sub.i, i=1, 2, 3 . . . n.b).
[0030] This technique is also directly applicable to the linear
regression model results. However, in a linear regression model,
the slope of a variable is constant (same sign and same value)
across all of the data points and therefore the average is simply
equal to the value of the slope at any particular point.
Step 103
[0031] Although the slope impact of a predictive variable as
determined in Step 102 is applied to every data point, it is
expected that the Importance of any particular variable will be
different from one data point to another. Therefore, the overall
Importance of a variable should include a measure of its value for
each specific policyholder as well as the overall average value
determined in Step 102. For example, if the value of a variable
deviates "significantly" from the general population mean for a
given policyholder, the conclusion might be that the variable
played a significant role in determining why that policy received
its particular score. On the other hand, if the value of a
particular variable for a chosen policy is close to the overall
population mean, it should not be judged to have an influential
impact on the score, even if the average value of the variable
impact (from Step 102) is large, because its value for that policy
is similar to the majority of the population.
[0032] Therefore, the second criterion in measuring Importance,
Deviance, is a measure of how similar or dissimilar a variable is
relative to the population mean. Deviance may be calculated using
the following formula:
Deviance of x i = ( x i - .mu. i ) .sigma. i ##EQU00002##
[0033] where .mu..sub.i is the mean for x.sub.i and .sigma..sub.i
is the standard deviation for predicitve variable x.sub.i.
Step 104
[0034] The final step, 105, defines the importance of a predictive
variable as the product of the slope (Step 1) and the deviance
(Step 2) of the variable:
Importance=Slope*Deviance
[0035] For each policy that is scored, the Importance of each
variable is calculated according to the above methodology. The
predictive variables are then sorted for every policy according to
their Importance measurement to determine which variables
contributed the most to the predicted profitability.
[0036] Referring to FIGS. 3 through 5, the Importance calculation
is applied to an exemplary situation illustrating the usage of the
proposed Importance calculation in a typical multivariate auto
insurance scoring formula. In the example, the following should be
assumed: (i) a personal automobile book of business is being
analyzed, and (ii) the book has a large quantity of data, e.g.,
40,000 data points, available for the analysis. In this example, a
linear regression formula is used for its simplicity. As described
in more detail below, the scoring formula is given as follows:
Y = 0.376 + 0.0061 X 1 - 0.0106 X 2 + 0.00593 X 3 - 0.00334 X 4 +
0.011 X 5 + 0.075 X 6 + 0.049 X 7 + 0.027 X 8 + 0.0106 X 9 + 0.061
X 10 - 0.00242 X 11 - 0.062 X 12 + 0.0109 X 13 + 0.000403 X 14 -
0.00194 X 15 - 0.0017 X 16 + 0.000704 X 17 ##EQU00003##
[0037] In the above scoring formula, the target variable, Y, will
predict the loss ratio (loss/premium) for a personal automobile
policy. A multivariate technique, which can be a traditional linear
regression or a more advanced nonlinear technique such as nonlinear
regression or neural networks, was used to develop the scoring
formula. The formula uses seventeen (17) driver and vehicle
characteristics to predict the loss ratio, which are described in
FIG. 3.
[0038] Any assumptions made for the variables are specified in FIG.
4. For each variable, the information gives a further description
of the possible values for each variable based on the total
population of the data points used in the model development and
stored in database 20. Additionally, FIG. 4 specifies the Mean of
the modeling data population and Standard Deviation for each
variable.
[0039] This example illustrates a "bad" (predicted to be
unprofitable) policy having the values for the particular variables
specified in FIG. 5. The scoring formula contains a constant term,
0.376, and a parameter for each predictive variable. When the
parameter is positive, it indicates that the higher the variable,
the higher the Y and hence the worse the predicted profitability.
When the parameter is negative, it indicates the opposite. For
example, the parameter for vehicle age, X.sub.2, is -0.0106. This
suggests that the older the vehicle, the lower the Y and the better
the profitability. It also suggests that as the vehicle age
increases by 1 year, the Y will decrease by 0.0106. On the other
hand, the parameter for the number of minor traffic violation,
X.sub.5, is 0.011. This suggests that the more the violations, the
higher the Y and the worse the profitability. It also suggests that
as the number of the violation increases by one, the Y will
increase by 0.011.
[0040] Referring to FIG. 5, the solution of the model indicates
that the policy has a predicted loss ratio score of 1.19, which is
more than twice the population average of 0.54. A close review of
the seventeen (17) predictive variables further indicates that it
has many bad characteristics. For example, it has a number of
accidents and violations (X.sub.5, X.sub.6, X.sub.9). It also has a
very high number of safety surcharge points (X.sub.4) as well as a
bad financial credit score (X.sub.14). Also, the vehicle is very
expensive (X.sub.1) and the driver is relatively young
(X.sub.11).
[0041] While the policy is obviously a bad policy, the unanswered
question is which of the seventeen (17) variables are the key
driving factors for the bad score? Are the ten (10) driver safety
points the number one reason, or the three (3) major violations the
number one reason for such a bad score? In addition, what are the
top 5 most important reasons? In order to address these questions,
the Importance of each variable is calculated using the method
described above and in FIG. 2. The first step (102) is to calculate
the slope of each predictive variable:
Slope of Predictive Variable x i = avg ( .differential. F ( X )
.differential. x i ) ##EQU00004##
[0042] Since the scoring formula used in the example is a linear
formula, the slope is the same as the parameter or coefficient
preceding each variable in the scoring formula, as illustrated in
column 3 of FIG. 5. The next step (103) is to calculate the
deviance for each predictive variable:
Deviance of x i = ( x i - .mu. i ) .sigma. i ##EQU00005##
[0043] where .mu..sub.i is the mean for x.sub.i and .sigma..sub.i
is the standard deviation for predicitve variable x.sub.i.
[0044] The value (X.sub.i) for each variable for the sample policy
is given in the second column, and the population mean and the
population standard deviation are given in columns 3 and 4 of FIG.
4. The calculated slope and deviance for each variable are shown in
columns 3 and 4, respectively, of FIG. 5. The next step (104) is to
calculate the Importance, which is the product of slope and
deviance. The calculated importance is given in column 5 of FIG. 5.
In a final step (105), from the calculated value of the Importance,
the variables can be ranked from highest to lowest value as shown
in column 6 of FIG. 5.
[0045] The ranking is directly translated into a reasons ranking.
From column 6, it can be see that the most important reason why the
sample policy is a "bad" policy is because the policy has three
major traffic (X.sub.10) violations, compared to the average 0.11
violations for the general population. The second most important
reason is that the policy has two no-fault incidences (X.sub.6),
while the general population on average only has 0.1
violations.
[0046] When these two variables are compared to the other fifteen
(15) variables, it becomes clear that this policy has values for
these two variables that are very different from the general
population, as indicated by the high value of deviance. In
addition, the parameters (the slopes) for these two variables are
also very high, indicating that both variables have a significant
impact on the predicted loss ratio and profitability of the policy.
In the case of these two variables, the high values of both the
slope and the deviance causes these two variables to emerge as the
top two most Important factors to explain the bad score for the
policy.
[0047] With the foregoing method and system an easy-to-understand
explanation of which variables are most significant to the score
(i.e., Importance) is made available to non-technical end users.
Such clear communication and interpretation of insurance
profitability scores is critical if they are used by the various
interested insurance parties including policyholders, agents,
underwriters, and regulators.
[0048] In so far as embodiments of the invention described herein
may be implemented, at least in part, using software controlled
programmable processing devices, such as a computer system, it will
be appreciated that one or more computer programs for configuring
such programmable devices or system of devices to implement the
foregoing described methods are to be considered an aspect of the
present invention. The computer programs may be embodied as source
code and undergo compilation for implementation on processing
devices or a system of devices, or may be embodied as object code,
for example. Those of ordinary skill will readily understand that
the term computer in its most general sense encompasses
programmable devices such as those referred to above, and data
processing apparatus, computer systems and the like.
[0049] Preferably, the computer programs are stored on carrier
media in machine or device readable form, for example in
solid-state memory or magnetic memory such as disk or tape, and
processing devices utilize the programs or parts thereof to
configure themselves for operation. The computer programs may be
supplied from remote sources embodied in communications media, such
as electronic signals, radio frequency carrier waves, optical
carrier waves and the like. Such carrier media are also
contemplated as aspects of the present invention.
[0050] It will thus be seen that the objects set forth above, among
those made apparent from the preceding description, are efficiently
attained and, since certain changes may be made in carrying out the
above method and in the system set forth without departing from the
spirit and scope of the invention, it is intended that all matter
contained in the above description and shown in the accompanying
drawings shall be interpreted as illustrative and not in a limiting
sense.
[0051] It is also to be understood that the following claims are
intended to cover all of the generic and specific features of the
invention herein described and all statements of the scope of the
invention which, as a matter of language, might be said to fall
therebetween.
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