A.03.Robertson

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1. Hazard group
Collection of workers compensation classifications that have relatively similar expected XS loss factor over a broad range of limits
2. 1993 NCCI review
• used principal components analysis on 3 yrs
• serious clm freq / total clm frq by class / statewide
• serious clm indemnity severity by class / statewide
• serious PP by class / statewide
3. 2007 NCCI review
• based on class ELF & cluster analysis
• ELF vary by state, but not hazard group
• Rj(L) = Σ wi,j si (L / μi,j)
• wi,j = % loss due to injury type i
• Si = state normlized xs ratio function
• L / μi,j = entry ratio point
• XS ratio vector = RC = (RC(L1), ..., RC(Ln))
4. Corro & Engl
A distribution is characterized by its excess ratios and so there is no loss of information in working with xs ratios rather than w size of loss
5. Robertson hazard group credibility
• z = min(n / n+ k * 1.5, 1), k = mean clm cnt
• 1 - z given to RHG (previous hazard group)
• k - using median: too low, z too high
• exl medical only
• incl only serious claims
• k = mean of all classes w some minimum threshould → rejected, k was too high
6. Building hazard groups - Limits
• how to choose n and actual limits
• correlation btwn neighboring XS ratios is high
• looked at more limits, but they weren't gaining much info due to strong correlation for closer limits
7. Euclidian distance btwn vectors (L2)
8. Cluster method
• if 2 objects are in diff clusters in the k cluster partition, then they will be in different clusters in all partitions w more than k elements
• k-mean: for k clusters, group classes into k groups as to minimize the euclidian distance between elements
• centroid: avg xs ratio vector for ith group
•  |HGi| = # of classes in hazard group i
9. Optimal # of clusters
• Calinski & Harabasz statistic = [trace(B) / (k -1) / [trace(W)] / (n - k)]
• n = # of classes, k = # of clusters
• maximize it (high means higher btwn & lower within)
• Cubic Clustering Criterion (CCC): compares amt of variance explained by a given set of clusters to rdm clusters
• (-) less reliable when data is elongated (variables are highly correlated)
10. Reasons why NCCI kept 7 hazard groups
• Calinksi & Harabasz gave right answer more time than CCC on control data
• CCC less reliable when var are highly correlated
• both test indicated 7 when only class w high cred were used
• 9 HG sln produces crossovers
11. NCCI update - why B & E have many classes
• XS ratios were credibility weighted w prior HG
• low cred classes have similar vectors → end up together
 Author: Exam8 ID: 162734 Card Set: A.03.Robertson Updated: 2012-08-14 01:35:36 Tags: NCCI hazard group excess ratio cluster Folders: Description: NCCI's 2007 Hazard Group Mapping Show Answers: