Optimal Matching with Matching Priority
Matching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-03-01
|
| Series: | Analytics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2813-2203/3/1/9 |
| _version_ | 1797242353761648640 |
|---|---|
| author | Massimo Cannas Emiliano Sironi |
| author_facet | Massimo Cannas Emiliano Sironi |
| author_sort | Massimo Cannas |
| collection | DOAJ |
| description | Matching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important to reduce the number of drops to avoid unsatisfactory results. Greedy matching algorithms may not reach the maximum matching size, thus dropping more units than necessary. Optimal matching algorithms do ensure a maximum matching size, but they implicitly assume that all units have the same matching priority. In this paper, we propose a matching strategy which is order optimal in the sense that it finds a maximum matching size which is consistent with a given matching priority. The strategy is based on an order-optimal matching algorithm originally proposed in connection with assignment problems by D. Gale. When a matching priority is given, the algorithm ensures that the discarded units have the lowest possible matching priority. We discuss the algorithm’s complexity and its relation with classic optimal matching. We illustrate its use with a problem in a case study concerning a comparison of female and male executives and a simulation. |
| first_indexed | 2024-04-24T18:37:53Z |
| format | Article |
| id | doaj.art-926ab1dd27dc436399d56be0f38b2fa0 |
| institution | Directory Open Access Journal |
| issn | 2813-2203 |
| language | English |
| last_indexed | 2024-04-24T18:37:53Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Analytics |
| spelling | doaj.art-926ab1dd27dc436399d56be0f38b2fa02024-03-27T13:17:32ZengMDPI AGAnalytics2813-22032024-03-013116517710.3390/analytics3010009Optimal Matching with Matching PriorityMassimo Cannas0Emiliano Sironi1Department of Business and Economic Sciences, University of Cagliari, 09123 Cagliari, ItalyDepartment of Statistical Sciences, Catholic University of the Sacred Heart, 20123 Milan, ItalyMatching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important to reduce the number of drops to avoid unsatisfactory results. Greedy matching algorithms may not reach the maximum matching size, thus dropping more units than necessary. Optimal matching algorithms do ensure a maximum matching size, but they implicitly assume that all units have the same matching priority. In this paper, we propose a matching strategy which is order optimal in the sense that it finds a maximum matching size which is consistent with a given matching priority. The strategy is based on an order-optimal matching algorithm originally proposed in connection with assignment problems by D. Gale. When a matching priority is given, the algorithm ensures that the discarded units have the lowest possible matching priority. We discuss the algorithm’s complexity and its relation with classic optimal matching. We illustrate its use with a problem in a case study concerning a comparison of female and male executives and a simulation.https://www.mdpi.com/2813-2203/3/1/9comparative studiesoptimal matchingcausal inference |
| spellingShingle | Massimo Cannas Emiliano Sironi Optimal Matching with Matching Priority Analytics comparative studies optimal matching causal inference |
| title | Optimal Matching with Matching Priority |
| title_full | Optimal Matching with Matching Priority |
| title_fullStr | Optimal Matching with Matching Priority |
| title_full_unstemmed | Optimal Matching with Matching Priority |
| title_short | Optimal Matching with Matching Priority |
| title_sort | optimal matching with matching priority |
| topic | comparative studies optimal matching causal inference |
| url | https://www.mdpi.com/2813-2203/3/1/9 |
| work_keys_str_mv | AT massimocannas optimalmatchingwithmatchingpriority AT emilianosironi optimalmatchingwithmatchingpriority |