Extending the reach of sequential regression multiple imputation
| dc.contributor.advisor | Raghunathan, T. E. | |
| dc.contributor.advisor | Schall, R. | |
| dc.contributor.advisor | Van der Merwe, A. J. | |
| dc.contributor.author | Von Maltitz, Michael Johan | |
| dc.date.accessioned | 2015-08-14T07:16:26Z | |
| dc.date.available | 2015-08-14T07:16:26Z | |
| dc.date.issued | 2015-06 | |
| dc.description.abstract | English: The purpose of this thesis is twofold. Firstly, it reviews a signi cant portion of literature concerning multiple imputation and, in particular, sequential regression multiple imputation, and summarises this information, thereby allowing a reader to gain in-depth knowledge of this research eld. Secondly, the thesis delves into one particular novel topic in sequential regression multiple imputation. The latter objective, of course, is not truly possible without the former, since the deeper the review of multiple imputation, the more likely it will be to identify and solve pressing concerns in the sequential regression multiple imputation sub eld. The literature review will show that there is room in imputation research for work on a robust model for the sequential regression multiple imputation algorithm. This thesis pays particular attention to this robust model, formulating its estimation procedure within the context of sequential regression multiple imputation of continuous data, attempting to discover a statistic that would show when to use the robust model over the regular Normal speci cation, and then implementing the robust model in another estimation algorithm that might allow for better imputation of ordinal data. This thesis contributes to `extending the reach of sequential regression multiple imputation' in two ways. Firstly, it is my wish for users of public data sets, particularly in South Africa, to become familiar with the (now internationally standard) topics presented in the rst half of this thesis. The only way to start publicising sequential regression multiple imputation in South Africa is to lay out the evidence for and against this procedure in a logical manner, so that any reader of this thesis might be able to understand the procedures for analysing multiply imputed data, or tackle one of the many research problems uncovered in this text. In this way, this thesis will extend the reach of sequential regression multiple imputation to many more South African researchers. Secondly, by working on a new robust model for use in the sequential regression multiple imputation algorithm, this thesis strengthens the sequential regression multiple imputation algorithm by extending its reach to incomplete data that is not necessarily Normally distributed, be it due to heavy tails, or inherent skewness, or both. | en_ZA |
| dc.description.abstract | Afrikaans: Die doel van hierdie tesis is tweeledig. Eerstens, gee dit 'n oorsig oor 'n beduidende gedeelte van die literatuur oor toerekening, en in die besonder, opeenvolgende regressie veelvuldige toerekening, en som hierdie inligting op, waardeur n leser in-diepte kennis van die navorsingsveld kan kry. Tweedens, die tesis vors 'n bepaalde nuwe onderwerp na in opeenvolgende regressie veelvuldige toerekening. Die laasgenoemde doelwit is natuurlik nie werklik moontlik sonder die voormalige nie, want hoe deegliker die oorsig oor veelvuldige toerekening, hoe meer waarskynlik sal dit wees om belangrike onderwerpe in die opeenvolgende regressie veelvuldige toerekening area te identi seer en op te los. Die literatuuroorsig sal wys dat daar ruimte in die navorsingsgebied oor toerekening is vir werk oor 'n robuuste model vir die opeenvolgende regressie veelvuldige toerekening algoritme. Hierdie tesis bestee besondere aandag aan hierdie robuuste model, naamlik die formulering van sy beramingsprosedure binne die konteks van opeenvolgende regressie veelvuldige toerekening van deurlopende data, en die tesis poog om 'n statistiek te vind wat aanwys wanneer die robuuste model moet gebruik word eerder as die gewone Normale spesi kasie; daarna word die robuuste model geimplementeer in 'n ander beramingsalgoritme wat moontlik ordinale data beter kan toereken. Hierdie tesis dra by tot die `uitbreiding van die aanreik van opeenvolgende regressie veelvuldige toerekening' op twee maniere. Eerstens, dit is my wens dat gebruikers van openbare data stelle, veral in Suid-Afrika, vertroud raak met die onderwerpe (wat nou die internasionale standaard is) wat in die eerste helfte van hierdie tesis hersien is. Die enigste manier om opeenvolgende regressie veelvuldige toerekening in Suid-Afrika bekend te stel is om sy voor- en nadele op 'n logiese manier uit te l^e, sodat enige leser van hierdie tesis in staat kan wees om die prosedures vir die ontleding van vermeerderde toegerekende data te verstaan, of poging kan maak om een van die vele navorsingsprobleme wat in hierdie teks voorgestel is op te los. Op hierdie manier sal die tesis die rykwydte van opeenvolgende regressie veelvuldige toerekening uitbrei na baie meer Suid- Afrikaanse navorsers. Tweedens, deur te werk op 'n nuwe robuuste model vir gebruik in die opeenvolgende regressie veelvuldige toerekening algoritme, verbeter hierdie tesis die opeenvolgende regressie veelvuldige toerekening algoritme deur die uitbreiding van sy aanreik oor onvolledige data wat nie noodwendig Normaal versprei is, of dit nou te danke is aan swaar sterte van die verdeling, of innerlike skeefheid daarvan, of albei. | |
| dc.identifier.uri | http://hdl.handle.net/11660/859 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | University of the Free State | en_ZA |
| dc.rights.holder | University of the Free State | en_ZA |
| dc.subject | Incomplete data | en_ZA |
| dc.subject | Thesis (Ph.D. (Mathematical Statistics and Actuarial Science))--University of the Free State, 2015 | en_ZA |
| dc.subject | Multiple imputation | en_ZA |
| dc.subject | Robust Bayesian regression model | en_ZA |
| dc.subject | Sequential regression multiple imputation | en_ZA |
| dc.subject | Skew Student t-distribution | en_ZA |
| dc.subject | Multiple imputation (Statistics) | en_ZA |
| dc.subject | Regression analysis | en_ZA |
| dc.subject | Bayesian statistical decision theory | en_ZA |
| dc.title | Extending the reach of sequential regression multiple imputation | en_ZA |
| dc.type | Thesis | en_ZA |