Segmentation and estimation of claim severity in motor third-party liability insurance through contrast analysis

Authors

DOI:

https://doi.org/10.24136/eq.2022.028

Keywords:

general linear model, claim severity, motor third party liability insurance, least squares means, contrast analysis

Abstract

Research background: Using the marginal means and contrast analysis of the target variable, e.g., claim severity (CS), the actuary can perform an in-depth analysis of the portfolio and fully use the general linear models potential. These analyses are mainly used in natural sciences, medicine, and psychology, but so far, it has not been given adequate attention in the actuarial field.

Purpose of the article: The article's primary purpose is to point out the possibilities of contrast analysis for the segmentation of policyholders and estimation of CS in motor third-party liability insurance. The article focuses on using contrast analysis to redefine individual relevant factors to ensure the segmentation of policyholders in terms of actuarial fairness and statistical correctness. The aim of the article is also to reveal the possibilities of using contrast analysis for adequate segmentation in case of interaction of factors and the subsequent estimation of CS.

Methods: The article uses the general linear model and associated least squares means. Contrast analysis is being implemented through testing and estimating linear combinations of model parameters. Equations of estimable functions reveal how to interpret the results correctly.

Findings & value added: The article shows that contrast analysis is a valuable tool for segmenting policyholders in motor insurance. The segmentation's validity is statistically verifiable and is well applicable to the main effects. Suppose the significance of cross effects is proved during segmentation. In that case, the actuary must take into account the risk that even if the partial segmentation factors are set adequately, statistically proven, this may not apply to the interaction of these factors. The article also provides a procedure for segmentation in case of interaction of factors and the procedure for estimation of the segment's CS. Empirical research has shown that CS is significantly influenced by weight, engine power, age and brand of the car, policyholder's age, and district. The pattern of age's influence on CS differs in different categories of car brands. The significantly highest CS was revealed in the youngest age category and the category of luxury car brands.

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References

Agresti, A. (2015). Foundations of linear and generalized linear models. New York: John Wiley & Sons.
View in Google Scholar

Alemany, R., Bolancé, C., Rodrigo, R., & Vernic, R. (2020). Bivariate mixed Poisson and Normal Generalised Linear models with Sarmanov dependence?an application to model claim frequency and optimal transformed average severity. Mathematics, 9(1), 73. doi: 10.3390/math9010073.

DOI: https://doi.org/10.3390/math9010073
View in Google Scholar

Ayuso, M., Guillen, M., & Nielsen, J. P. (2019). Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data. Transportation, 46(3), 735?752. doi: 10.1007/s11116-018-9890-7.

DOI: https://doi.org/10.1007/s11116-018-9890-7
View in Google Scholar

Bae, J., Kim, Y. Y., & Lee, J. S. (2017). Factors associated with subjective life expectancy: comparison with actuarial life expectancy. Journal of Preventive Medicine and Public Health, 50(4), 240. doi: 10.3961/jpmph.17.036.

DOI: https://doi.org/10.3961/jpmph.17.036
View in Google Scholar

Bergelt, M., Fung Yuan, V., O?Brien, R., Middleton, L. E., & Martins dos Santos, W. (2020). Moderate aerobic exercise, but not anticipation of exercise, improves cognitive control. PloS One, 15(11), e0242270. doi: 10.1371/journal .pone.0242270.

DOI: https://doi.org/10.1371/journal.pone.0242270
View in Google Scholar

Burka, D., Kovács, L., & Szepesváry, L. (2021). Modelling MTPL insurance claim events: can machine learning methods overperform the traditional GLM approach? Hungarian Statistical Review, 4(2), 34?69. doi: 10.35618/hsr2021. 02.en034.

DOI: https://doi.org/10.35618/hsr2021.02.en034
View in Google Scholar

Byrne, K. M., Adler, P. B., & Lauenroth, W. K. (2017). Contrasting effects of precipitation manipulations in two Great Plains plant communities. Journal of Vegetation Science, 28(2), 238?249. doi: 10.1111/jvs.12486.

DOI: https://doi.org/10.1111/jvs.12486
View in Google Scholar

Cai, W. (2014). Making comparisons fair: how LS-means unify the analysis of linear models. SAS Institute Inc. Paper SA, S060-2014.
View in Google Scholar

Colin, T., Bruce, J., Meikle, W. G., & Barron, A. B. (2018). The development of honey bee colonies assessed using a new semi-automated brood counting method: CombCount. PLoS One, 13(10), e0205816. doi: 10.1371/journal.pone. 0205816.

DOI: https://doi.org/10.1371/journal.pone.0205816
View in Google Scholar

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: concepts, applications, and implementation. Guilford Publications.
View in Google Scholar

David, M. (2015). Auto insurance premium calculation using generalized linear models. Procedia Economics and Finance, 20, 147?156. doi: 10.1016/S2212-5671(15)00059-3.

DOI: https://doi.org/10.1016/S2212-5671(15)00059-3
View in Google Scholar

de Azevedo, F. C., Oliveira, T. A., & Oliveira, A. (2016). Modeling non-life insurance price for risk without historical information. REVSTAT-Statistical Journal, 14(2), 171?192. doi: 10.57805/revstat.v14i2.185.
View in Google Scholar

de Jong, P., & Heller, G. Z. (2008). Generalized linear models for insurance data. Cambridge Books.

DOI: https://doi.org/10.1017/CBO9780511755408
View in Google Scholar

de Sá, J. P. M. (2007). Applied statistics using SPSS, Statistica, MatLab and R. Springer Science & Business Media.
View in Google Scholar

Dean, A., Voss, D., & Draguljić, D. (2017). Design and analysis of experiments Springer, Cham.

DOI: https://doi.org/10.1007/978-3-319-52250-0
View in Google Scholar

Duan, Z., Chang, Y., Wang, Q., Chen, T., & Zhao, Q. (2018). A logistic regression based auto insurance rate-making model designed for the insurance rate reform. International Journal of Financial Studies, 6(1), 18. doi: 10.3390/ijfs6010018.

DOI: https://doi.org/10.3390/ijfs6010018
View in Google Scholar

Elswick Jr, R. K., Gennings, C., Chinchilli, V. M., & Dawson, K. S. (1991). A simple approach for finding estimable functions in linear models. American Statistician, 45(1), 51?53. doi: 10.1080/00031305.1991.10475766.

DOI: https://doi.org/10.1080/00031305.1991.10475766
View in Google Scholar

Ennour-Idrissi, K., T?tu, B., Maunsell, E., Poirier, B., Montoni, A., Rochette, P. J., & Diorio, C. (2016). Association of telomere length with breast cancer prognostic factors. PLoS One, 11(8), e0161903. doi: 10.1371/journal.pone.016 1903.

DOI: https://doi.org/10.1371/journal.pone.0161903
View in Google Scholar

Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.
View in Google Scholar

Frees, E. W., Derrig, R. A., & Meyers, G. (Eds.) (2014). Predictive modeling applications in actuarial science (Vol. 1). Cambridge University Press.

DOI: https://doi.org/10.1017/CBO9781139342674.001
View in Google Scholar

Frees, E. W., Lee, G., & Yang, L. (2016). Multivariate frequency-severity regression models in insurance. Risks, 4(1), 4. doi: 10.3390/risks4010004.

DOI: https://doi.org/10.3390/risks4010004
View in Google Scholar

Fung, T. C., Badescu, A. L., & Lin, X. S. (2021). A new class of severity regression models with an application to IBNR prediction. North American Actuarial Journal, 25(2), 206?231. doi: 10.1080/10920277.2020.1729813.

DOI: https://doi.org/10.1080/10920277.2020.1729813
View in Google Scholar

George, D., & Mallery, P. (2019). IBM SPSS statistics 26 step by step: a simple guide and reference. Routledge.

DOI: https://doi.org/10.4324/9780429056765
View in Google Scholar

Goldburd, M., Khare, A., Tevet, D., & Guller, D. (2016). Generalized linear models for insurance rating. Casualty Actuarial Society, CAS Monographs Series, 5.
View in Google Scholar

Goodnight, J. H, & Harvey, W. R (1997). SAS technical report R-103. Least Squares Means in the Fixed Effects General Model. Cary, NC: SAS Institute Inc.
View in Google Scholar

Haans, A. (2018). Contrast analysis: a tutorial. Practical Assessment, Research, and Evaluation, 23(1), 9. doi: 10.7275/7dey-zd62.
View in Google Scholar

Henckaerts, R., Antonio, K., Clijsters, M., & Verbelen, R. (2018). A data driven binning strategy for the construction of insurance tariff classes. Scandinavian Actuarial Journal, 8, 681?705. doi: 10.1080/03461238.2018.1429300.

DOI: https://doi.org/10.1080/03461238.2018.1429300
View in Google Scholar

Henckaerts, R., Côté, M. P., Antonio, K., & Verbelen, R. (2021). Boosting insights in insurance tariff plans with tree-based machine learning methods. North American Actuarial Journal, 25(2), 255?285. doi: 10.1080/10920277.2020.174 5656.

DOI: https://doi.org/10.1080/10920277.2020.1745656
View in Google Scholar

Henckaerts, R., & Antonio, K. (2022). The added value of dynamically updating motor insurance prices with telematics collected driving behavior data. Insurance: Mathematics and Economics, 105, 79?95. doi: 10.1016/j.insmath eco.2022.03.011.

DOI: https://doi.org/10.1016/j.insmatheco.2022.03.011
View in Google Scholar

Herberich, E., Sikorski, J., & Hothorn, T. (2010). A robust procedure for comparing multiple means under heteroscedasticity in unbalanced designs. PloS one, 5(3), e9788. doi: 10.1371/journal.pone.0009788.

DOI: https://doi.org/10.1371/journal.pone.0009788
View in Google Scholar

Huzar-Novakowiski, J., & Dorrance, A. E. (2018). Genetic diversity and population structure of Pythium irregulare from soybean and corn production fields in Ohio. Plant Disease, 102(10), 1989?2000. doi: 10.1094/PDIS-11-17-1725-RE.

DOI: https://doi.org/10.1094/PDIS-11-17-1725-RE
View in Google Scholar

Kafková, S., & Křivánková, L. (2014). Generalized linear models in vehicle insurance. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 62(2), 383?388. doi: 10.11118/actaun201462020383.

DOI: https://doi.org/10.11118/actaun201462020383
View in Google Scholar

Kafková, S. (2015). Bonus-malus systems in vehicle insurance. Procedia Economics and Finance, 23, 216?222. doi: 10.1016/S2212-5671(15)00354-8.

DOI: https://doi.org/10.1016/S2212-5671(15)00354-8
View in Google Scholar

Kim, K., & Timm, N. (2006). Univariate and multivariate general linear models: theory and applications with SAS. Chapman and Hall/CRC.

DOI: https://doi.org/10.1201/b15891
View in Google Scholar

Kim, J. H. (2019). Multicollinearity and misleading statistical results. Korean Journal of Anesthesiology, 72(6), 558. doi: 10.4097/kja.19087.

DOI: https://doi.org/10.4097/kja.19087
View in Google Scholar

Kuznetsova. A., Brockhoff. P. B., & Christensen. R. H. B. (2017). lmerTest package: tests in linear mixed effects models. Journal of Statistical Software. 82(13), 1?26. doi: 10.18637/jss.v082.i13.

DOI: https://doi.org/10.18637/jss.v082.i13
View in Google Scholar

LaMotte, L. R. (2020). A formula for Type III sums of squares. Communications in Statistics-Theory and Methods, 49(13), 3126?3136. doi: 10.1080/03610926.201 9.1586933.

DOI: https://doi.org/10.1080/03610926.2019.1586933
View in Google Scholar

Lee, S., & Lee, D. K. (2018). What is the proper way to apply the multiple comparison test? Korean Journal of Anesthesiology, 71(5), 353. doi: 10.4097/kj a.d.18.00242.

DOI: https://doi.org/10.4097/kja.d.18.00242
View in Google Scholar

Lenth, R., V. (2016). Least-squares means: the R package lsmeans. Journal of Statistical Software, 69(1), 1?33. doi: 10.18637/jss.v069.i01.

DOI: https://doi.org/10.18637/jss.v069.i01
View in Google Scholar

Lenth, R., Buerkner, P., Herve, M., Love, J., Miguez, F., Riebl, H., & Singmann, H. (2022). Estimated marginal means, aka least-squares means. R package ?emmeans?, version 1.7.2. Retrieved from https://cran.r-project.org/web/packag es/emmeans/emmeans.pdf (15.03.2022).
View in Google Scholar

Littell, R. C., Stroup, W. W., & Freund, R. J. (2010). SAS for linear models. Cary, NC: SAS Institute Inc.
View in Google Scholar

McFarquhar, M. (2016). Testable hypotheses for unbalanced neuroimaging data. Frontiers in Neuroscience, 10, 270. doi: 10.3389/fnins.2016.00270.

DOI: https://doi.org/10.3389/fnins.2016.00270
View in Google Scholar

O?Brien, R. M. (2014). Estimable functions in age-period-cohort models: a unified approach. Quality & Quantity, 48(1), 457?474. doi: 10.1007/s11135-012-9780-6.

DOI: https://doi.org/10.1007/s11135-012-9780-6
View in Google Scholar

Olivera-La Rosa, A., Chuquichambi, E. G., & Ingram, G. P. (2020). Keep your (social) distance: pathogen concerns and social perception in the time of COVID-19. Personality and Individual Differences, 166, 110200. doi: 10.1016 /j.paid.2020.110200.

DOI: https://doi.org/10.1016/j.paid.2020.110200
View in Google Scholar

Ordaz, J. A., del Carmen Melgar, M., & Khan, M. K. (2011). An analysis of Spanish accidents in automobile insurance: the use of the Probit model and the theoretical potential of other econometric tools. Equilibrium. Equilibrium. Quarterly Journal of Economics and Economic Policy, 6(3), 117?134. doi: 10.12775/EQUIL2011.024.

DOI: https://doi.org/10.12775/EQUIL2011.024
View in Google Scholar

Poline, J. B., Kherif, F., Pallier, C., & Penny, W. (2007). Contrasts and classical inference. In W. D. Penny, K. J. Friston, J. T. Ashburner, S. J. Kiebel & T. E. Nichols (Eds.) (2011). Statistical parametric mapping: the analysis of functional brain images (126?139). Elsevier.

DOI: https://doi.org/10.1016/B978-012372560-8/50009-7
View in Google Scholar

Rafter, J. A., Abell, M. L., & Braselton, J. P. (2002). Multiple comparison methods for means. Siam Review, 44(2), 259?278. doi: 10.1137/S0036144501357233.

DOI: https://doi.org/10.1137/S0036144501357233
View in Google Scholar

Rivers, J. W., Newberry, G. N., Schwarz, C. J., & Ardia, D. R. (2017). Success despite the stress: violet?green swallows increase glucocorticoids and maintain reproductive output despite experimental increases in flight costs. Functional Ecology, 31(1), 235?244. doi: 10.1111/1365-2435.12719.

DOI: https://doi.org/10.1111/1365-2435.12719
View in Google Scholar

Rahardja, D. (2020). Multiple comparison procedures for the differences of proportion parameters in over-reported multiple-sample binomial data. Stats, 3(1), 56?67. doi: 10.3390/stats3010006.

DOI: https://doi.org/10.3390/stats3010006
View in Google Scholar

Quigley, M. Y., Rivers, M. L., & Kravchenko, A. N. (2018). Patterns and sources of spatial heterogeneity in soil matrix from contrasting long term management practices. Frontiers in Environmental Science, 6, 28. doi: 10.3390/stats3010006

DOI: https://doi.org/10.3389/fenvs.2018.00028
View in Google Scholar

SAS Institute Inc. (2017). The four types of estimable functions. In SAS/STAT? 14.3 User?s Guide. Cary, NC: SAS Institute Inc.
View in Google Scholar

SAS Institute Inc. (2018). SAS/STAT? 15.1 User?s Guide. The GLM Procedure. Cary, NC: SAS Institute Inc.
View in Google Scholar

Schad, D. J., Vasishth, S., Hohenstein, S., & Kliegl, R. (2020). How to capitalize on a priori contrasts in linear (mixed) models: a tutorial. Journal of Memory and Language, 110, 104038. doi: 10.1016/j.jml.2019.104038.

DOI: https://doi.org/10.1016/j.jml.2019.104038
View in Google Scholar

Searle, S. R., & Gruber, M. H. J. (2017). Linear models. John Wiley & Sons.
View in Google Scholar

Searle, S. R., Speed, F. M., & Milliken, G. A. (1980). Population marginal means in the linear model: an alternative to least squares means. American Statistician, 34(4), 216?221. doi: 10.1080/00031305.1980.10483031.

DOI: https://doi.org/10.1080/00031305.1980.10483031
View in Google Scholar

Shi, P., Feng, X., & Ivantsova, A. (2015). Dependent frequency?severity modeling of insurance claims. Insurance Mathematics and Economics, 64, 417?428. doi: 10.1016/j.insmatheco.2015.07.006.

DOI: https://doi.org/10.1016/j.insmatheco.2015.07.006
View in Google Scholar

Singh, N., Wang, C., & Cooper, R. (2015). Role of vision and mechanoreception in bed bug, Cimex lectularius L. behavior. PLoS one, 10(3), e0118855. doi: 10.1371/journal.pone.0118855.

DOI: https://doi.org/10.1371/journal.pone.0118855
View in Google Scholar

Spilbergs, A., Fomins, A., Krastins, M. (2021). Impact of Covid-19 on the dynamics of MTPL insurance premiums and claims paid in Latvia. WSEAS Transactions on Computer Research, 9, 33?42. doi: 10.37394/232018.2021.9.5

DOI: https://doi.org/10.37394/232018.2021.9.5
View in Google Scholar

Spilbergs, A., Fomins, A., & Krastins, M. (2022). Road traffic accidents risk drivers' analysis ? multivariate modelling based on Latvian motor third party liability insurance data. In D. Tipuric, A. Krajnovic & N. Recker (Eds.). Economic and social development: book of proceedings (pp. 246?264). Varazdin, Croatia: Varazdin Development and Entrepreneurship Agency.
View in Google Scholar

Statgraphics Technologies Inc. (2017). General linear models. Statgraphics centu-rion 18.
View in Google Scholar

Staudt, Y., & Wagner, J. (2021). Assessing the performance of random forests for modeling claim severity in collision car insurance. Risks, 9(3), 53. doi: 10.339 0/risks9030053.

DOI: https://doi.org/10.3390/risks9030053
View in Google Scholar

Su, X., & Bai, M. (2020). Stochastic gradient boosting frequency-severity model of insurance claims. PloS one, 15(8), e0238000. doi: 10.1371/journal.pone.0238 000.

DOI: https://doi.org/10.1371/journal.pone.0238000
View in Google Scholar

Suzuki, M., Taniguchi, T., Furihata, R., Yoshita, K., Arai, Y., Yoshiike, N., & Uchiyama, M. (2019). Seasonal changes in sleep duration and sleep problems: a prospective study in Japanese community residents. PLoS One, 14(4), e0215345. doi: 10.1371/journal.pone.0215345.

DOI: https://doi.org/10.1371/journal.pone.0215345
View in Google Scholar

Šoltés, E., Zelinová, S., & Bilíková, M. (2019). General linear model: an effective tool for analysis of claim severity in motor third party liability insurance. Statistics in Transition New Series, 20(4), 13?31, doi: 10.21307/stattrans-2019-032.

DOI: https://doi.org/10.21307/stattrans-2019-032
View in Google Scholar

Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Boston, MA: Pearson.
View in Google Scholar

Tattar, P. N., Ramaiah, S., & Manjunath, B. G. (2016). A course in statistics with R. John Wiley & Sons.

DOI: https://doi.org/10.1002/9781119152743
View in Google Scholar

Thompson, P. A. (2006). The ?handy-dandy, quick-n-dirty? automated contrast generator-A SAS/IML R ? macro to support the GLM, MIXED, and GENMOD procedures. SUGI 31 Statistics and data Analysis. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.176.736&rep=rep1&type=pdf (11.12.2021).
View in Google Scholar

Ugarte, M. D., Militino, A. F., & Arnholt, A. T. (2008). Probability and statistics with R. CRC press.

DOI: https://doi.org/10.1201/9781584888925
View in Google Scholar

Wang, B., Wu, P., Kwan, B., Tu, M. X., & Feng, Ch. (2018). Simpson?s paradox: examples. Shanghai Archives of Psychiatry, 30(2), 139. doi: 10.11919/j.issn.10 02-0829.218026.
View in Google Scholar

Westfall, P. H., & Tobias, R. D. (2007). Multiple testing of general contrasts: Truncated closure and the extended Shaffer?Royen method. Journal of the American Statistical Association, 102(478), 487?494. doi: 10.1198/0162 14506000001338.

DOI: https://doi.org/10.1198/016214506000001338
View in Google Scholar

Wicklin R. (2018). Generalized inverses for matrices. Retrieved from https://blogs.sas.com/content/iml/2018/11/21/generalized-inverses-for-matrices. html (23.02. 2022).
View in Google Scholar

Wilcox, R. R. (2003). Applying contemporary statistical techniques. Elsevier.
View in Google Scholar

Wooldridge, J. M. (2013). Introductory econometrics: a modern approach. Mason: South-Western.
View in Google Scholar

Zahi, J. (2021). Non-life insurance ratemaking techniques. International Journal of Accounting, Finance, Auditing, Management and Economics, 2(1), 344?361. doi: 10.5281/zenodo.4474479.
View in Google Scholar

Zhao, J., Wang, C., Totton, S. C., Cullen, J. N., & O?Connor, A. M. (2019). Reporting and analysis of repeated measurements in preclinical animals experiments. PloS one, 14(8), e0220879. doi: 10.1371/journal.pone.0220879.

DOI: https://doi.org/10.1371/journal.pone.0220879
View in Google Scholar

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2022-09-30

How to Cite

Reiff, M. ., Šoltés, E. ., Komara, S. ., Šoltésová, T. ., & Zelinová, S. . (2022). Segmentation and estimation of claim severity in motor third-party liability insurance through contrast analysis. Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 803–842. https://doi.org/10.24136/eq.2022.028

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