Calibration Adjustment for Nonresponse in Sample Surveys To my parents Bernardo and Jacinta Örebro Studies in Statistics 8 BERNARDO JOÃO ROTA Calibration Adjustment for Nonresponse in Sample Surveys © Bernardo João Rota, 2016 Title: Calibration Adjustment for Nonresponse in Sample Surveys Publisher: Örebro University 2016 www.oru.se/publikationer-avhandlingar Print: Örebro University, Repro 09/2016 ISSN 1651-8608 ISBN 978-91-7529-160-4 Abstract Bernardo João Rota (2016): Calibration Adjustment for Nonresponse in Sample Surveys. Örebro Studies in Statistics 8. In this thesis, we discuss calibration estimation in the presence of nonre- sponse with a focus on the linear calibration estimator and the propensi- ty calibration estimator, along with the use of different levels of auxilia- ry information, that is, sample and population levels. This is a four- papers-based thesis, two of which discuss estimation in two steps. The two-step-type estimator here suggested is an improved compromise of both the linear calibration and the propensity calibration estimators mentioned above. Assuming that the functional form of the response model is known, it is estimated in the first step using calibration approach. In the second step the linear calibration estimator is con- structed replacing the design weights by products of these with the in- verse of the estimated response probabilities in the first step. The first step of estimation uses sample level of auxiliary information and we demonstrate that this results in more efficient estimated response proba- bilities than using population-level as earlier suggested. The variance expression for the two-step estimator is derived and an estimator of this is suggested. Two other papers address the use of auxiliary variables in estimation. One of which introduces the use of principal components theory in the calibration for nonresponse adjustment and suggests a selection of components using a theory of canonical correlation. Princi- pal components are used as a mean to accounting the problem of estima- tion in presence of large sets of candidate auxiliary variables. In addition to the use of auxiliary variables, the last paper also discusses the use of explicit models representing the true response behavior. Usually simple models such as logistic, probit, linear or log-linear are used for this pur- pose. However, given a possible complexity on the structure of the true response probability, it may raise a question whether these simple mod- els are effective. We use an example of telephone-based survey data col- lection process and demonstrate that the logistic model is generally not appropriate. Keywords: Auxiliary variables, Calibration, Nonresponse, principal com-ponents, regression estimator, response probability, survey sampling, two-step estimator, variance estimator, weighting. Bernardo João Rota, School of Business Örebro University, SE-701 82 Örebro, Sweden, [email protected] (cid:45)(cid:74)(cid:84)(cid:85)(cid:1)(cid:80)(cid:71)(cid:1)(cid:49)(cid:66)(cid:81)(cid:70)(cid:83)(cid:84) This(cid:1)thesis(cid:1)consists(cid:1)of(cid:1)four(cid:1)papers: • Rota,B.J.andLaitila,T.(2015)Comparisonsofsomeweightingmeth- odsfornonresponseadjustment. LithuanianJournalofStatistics,54:1, 69–83. • Rota, B. J. (2016). Variance Estimation in Two-Step Calibration for Nonresponse Adjustment. Manuscript • Rota,B.J.andLaitila,T.(2016)CalibratingonPrincipalComponents inthePresenceofMultipleAuxiliaryVariablesforNonresponseAdjust- ment. This paper is accepted in South African Statistical Journal • Rota, B. J. and Laitila, T. (2016). On the Use of Auxiliary Variables and Models in Estimation in Surveys with Nonresponse. Manuscript (cid:34)(cid:68)(cid:76)(cid:79)(cid:80)(cid:88)(cid:77)(cid:70)(cid:69)(cid:72)(cid:70)(cid:78)(cid:70)(cid:79)(cid:85)(cid:84) The(cid:1)path(cid:1)I(cid:1)have(cid:1)chosen(cid:1)does(cid:1)not(cid:1)end(cid:1)with(cid:1)achievement(cid:1)of(cid:1)a(cid:1)PhD(cid:1)degree;(cid:1) rather,(cid:1)it(cid:1)simply(cid:1)goes(cid:1)another(cid:1)way(cid:1)around(cid:1)to(cid:1)start(cid:1)another(cid:1)path.(cid:1)However,(cid:1)it(cid:1) is(cid:1)an(cid:1)amazing(cid:1)feeling(cid:1)to(cid:1)realize(cid:1)that(cid:1)you(cid:1)are(cid:1)capable(cid:1)of(cid:1)such(cid:1)achievement(cid:1)after(cid:1) a(cid:1)long(cid:1)journey(cid:1)on(cid:1)thorny(cid:1)ground.(cid:1)I(cid:1)would(cid:1)never(cid:1)be(cid:1)able(cid:1)to(cid:1)walk(cid:1)this(cid:1)thorny(cid:1) ground(cid:1)and(cid:1)succeed(cid:1)without(cid:1)support. I(cid:1)thank(cid:1)Professor(cid:1)Thomas(cid:1)Laitila,(cid:1)my(cid:1)Supervisor(cid:1)since(cid:1)I(cid:1)was(cid:1)a(cid:1)master(cid:1)stu- dent(cid:1)and(cid:1)mentor(cid:1)of(cid:1)my(cid:1)success(cid:1)in(cid:1)this(cid:1)endeavor.(cid:1)Thank(cid:1)you(cid:1)for(cid:1)being(cid:1)patient(cid:1) in(cid:1)your(cid:1)guidance,(cid:1)particularly(cid:1)in(cid:1)those(cid:1)moments(cid:1)when(cid:1)I(cid:1)wrote(cid:1)“senseless(cid:1)stuff”. I(cid:1)cannot(cid:1)forget(cid:1)Professor(cid:1)Sune(cid:1)Karlsson;(cid:1)thank(cid:1)you(cid:1)for(cid:1)your(cid:1)support(cid:1)which(cid:1) has(cid:1)been(cid:1)extended(cid:1)since(cid:1)I(cid:1)was(cid:1)a(cid:1)master(cid:1)student. My(cid:1)parents,(cid:1)aged(cid:1)as(cid:1)they(cid:1)are,(cid:1)were(cid:1)subjected(cid:1)to(cid:1)living(cid:1)years(cid:1)without(cid:1)seeing(cid:1) their(cid:1)son(cid:1)but(cid:1)had(cid:1)a(cid:1)strong(cid:1)belief(cid:1)in(cid:1)my(cid:1)success.(cid:1)I(cid:1)thank(cid:1)my(cid:1)brother(cid:1)Victor(cid:1)and(cid:1) my(cid:1)sister(cid:1)Bernardete(cid:1)and(cid:1)their(cid:1)respective(cid:1)families,(cid:1)my(cid:1)brothers(cid:1)Solano(cid:1)and(cid:1) Flaviano(cid:1)for(cid:1)everything.(cid:1) My(cid:1)nieces(cid:1)and(cid:1)nephews,(cid:1)you(cid:1)are(cid:1)always(cid:1)the(cid:1)reason(cid:1) for(cid:1)my(cid:1)happiness.(cid:1)Thank(cid:1)you(cid:1)for(cid:1)your(cid:1)tireless(cid:1)support. Mónica Mucocana thanks for everything. MygratitudeextendstotheÖrebroSchoolofBusinessadministrativeper- sonnel,thelistisextensive. Thankyouallofyouforbeingfriendlyandhelpful everymomentthatIneededyoursupport. Mycolleaguesfromdepartmentof Mathematics and Informatics at Eduardo Mondlane University. Thank you all. IalsoexpressmygratitudetoProfessorJoãoMunembe,co-supervisorfor themozambicanpart,ProfessorManuelAlvesIstillrememberyoursupport. My friends and fellow PhD colleagues, particularly Jose Nhavoto, with whom I started this journey and who witnessed my struggle day after day and Göran Bergstrand and Pari Bergstrand the best friendship I have made in Sweden. To all of you thank you very much. I would like to express my gratitude to the Swedish SIDA Foundation - International Science Program for the cooperation with Eduardo Mondlane University in Maputo and especially for funding and supporting my studies. For all who have been involved to tight this cooperation both from Swedish and Mozambican side, my deepest gratitude.