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- All Subjects: Actuarial
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Description
It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set.
ContributorsMilovanovic, Jelena (Author) / Young, Dennis (Thesis advisor) / Reiser, Mark R. (Thesis advisor) / Wilson, Jeffrey (Committee member) / Eubank, Randall (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2011
Description
Catastrophe events occur rather infrequently, but upon their occurrence, can lead to colossal losses for insurance companies. Due to their size and volatility, catastrophe losses are often treated separately from other insurance losses. In fact, many property and casualty insurance companies feature a department or team which focuses solely on modeling catastrophes. Setting reserves for catastrophe losses is difficult due to their unpredictable and often long-tailed nature. Determining loss development factors (LDFs) to estimate the ultimate loss amounts for catastrophe events is one method for setting reserves. In an attempt to aid Company XYZ set more accurate reserves, the research conducted focuses on estimating LDFs for catastrophes which have already occurred and have been settled. Furthermore, the research describes the process used to build a linear model in R to estimate LDFs for Company XYZ's closed catastrophe claims from 2001 \u2014 2016. This linear model was used to predict a catastrophe's LDFs based on the age in weeks of the catastrophe during the first year. Back testing was also performed, as was the comparison between the estimated ultimate losses and actual losses. Future research consideration was proposed.
ContributorsSwoverland, Robert Bo (Author) / Milovanovic, Jelena (Thesis director) / Zicarelli, John (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
AARP estimates that 90% of seniors wish to remain in their homes during retirement. Seniors need assistance as they age, historically they have received assistance from either family members, nursing homes, or Continuing Care Retirement Communities. For seniors not wanting any of these options, there has been very few alternatives. Now, the emergence of the continuing care at home program is providing hope for a different method of elder care moving forward. CCaH programs offer services such as: skilled nursing care, care coordination, emergency response systems, aid with personal and health care, and transportation. Such services allow seniors to continue to live in their own home with assistance as their health deteriorates over time. Currently, only 30 CCaH programs exist. With the growth of the elderly population in the coming years, this model seems poised for growth.
ContributorsSturm, Brendan (Author) / Milovanovic, Jelena (Thesis director) / Hassett, Matthew (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Economics Program in CLAS (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
A factor accounting for the COVID-19 pandemic was added to a generalized linear model to more accurately predict unpaid claims. COVID-19 has affected not just healthcare, but all sectors of the economy. Because of this, whether or not an automobile insurance claim is filed during the pandemic needs to be taken into account while estimating unpaid claims. Reserve-estimating functions such as glmReserve from the “ChainLadder” package in the statistical software R were experimented with to produce their own results. Because of their insufficiency, a manual approach to building the model turned out to be the most proficient method. Utilizing the GLM function, a model was built that emulated linear regression with a factor for COVID-19. The effects of such a model are analyzed based on effectiveness and interpretablility. A model such as this would prove useful for future calculations, especially as society is now returning to a “normal” state.
ContributorsKossler, Patrick (Author) / Zicarelli, John (Thesis director) / Milovanovic, Jelena (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05
Description
The objective of this study is to build a model using R and RStudio that automates ratemaking procedures for Company XYZ’s actuaries in their commercial general liability pricing department. The purpose and importance of this objective is to allow actuaries to work more efficiently and effectively by using this model that outputs the results they otherwise would have had to code and calculate on their own. Instead of spending time working towards these results, the actuaries can analyze the findings, strategize accordingly, and communicate with business partners. The model was built from R code that was later transformed to Shiny, a package within RStudio that allows for the build-up of interactive web applications. The final result is a Shiny app that first takes in multiple datasets from Company XYZ’s data warehouse and displays different views of the data in order for actuaries to make selections on development and trend methods. The app outputs the re-created ratemaking exhibits showing the resulting developed and trended loss and premium as well as the experience-based indicated rate level change based on prior selections. The ratemaking process and Shiny app functionality will be detailed in this report.
ContributorsGilkey, Gina (Author) / Zicarelli, John (Thesis director) / Milovanovic, Jelena (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05