Binary and Ordinal Outcomes: Considerations for the Generalized Linear Model with the Log Link and with the Identity Link

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atmire.migration.oldid6076
dc.contributor.advisorFick, Gordon
dc.contributor.authorSingh, Gurbakhshash
dc.contributor.committeememberKopciuk, Karen
dc.contributor.committeememberSajobi, Tolulope
dc.contributor.committeememberLu, Xuewen
dc.contributor.committeememberHorrocks, Julie
dc.date.accessioned2017-09-29T15:21:33Z
dc.date.available2017-09-29T15:21:33Z
dc.date.issued2017
dc.date.submitted2017en
dc.description.abstractThere are gaps in the current literature on Generalized Linear Models (GLM) for binary outcomes with the log link. This dissertation explores a number of these gaps and presents specific results: (1) Uniqueness considerations for the Maximum Likelihood Estimate (MLE) are established from the conditions for the strict concavity of the log-likelihood. The full column rank of certain subsets of the covariate matrix is shown to be a condition for the strict concavity of the loglikelihood. (2) Conditions are established for the finiteness of components of the MLE. A method is proposed to address the possibility of non-finite components for the MLE, and it is based on determining directions of recession of the log-likelihood. In addition, it is established when the MLE will be in the interior of the parameter space and when the MLE will possibly be on a boundary of the parameter space. (3) Examples are presented of closed form expressions for the MLE. For a number of models with indicator variables and measured variables, closed form expressions for the MLE are presented. (4) There are considerations for the construction of confidence intervals when the MLE is close to a boundary of the parameter space. A new metric, called the “fraction within the parameter space”, is introduced for assessing intervals for MLEs close to a boundary. A simulation study is provided that offers support for Bootstrap Percentile Intervals having larger fractions when compared to Relative Likelihood Intervals and Normal Confidence Intervals. This dissertation continues by developing a proportional probability model using the log link for ordinal outcomes. For this model, similar results are presented for topics (1) and (3) above. In addition, there is the introduction of a score test to assess proportionality. The dissertation concludes with a discussion of future work. In particular, this discussion includes some preliminary work with the identity link GLM for binary and ordinal outcomes. Throughout this dissertation, there are many practical considerations and illustrations presented. The use of the log link and the identity link for binary and ordinal outcomes should now become a viable modeling option for researchers.en_US
dc.identifier.citationSingh, G. (2017). Binary and Ordinal Outcomes: Considerations for the Generalized Linear Model with the Log Link and with the Identity Link (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25118en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/25118
dc.identifier.urihttp://hdl.handle.net/11023/4170
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectBiostatistics
dc.subjectMathematics
dc.subjectStatistics
dc.subject.otherLog-Binomial Model
dc.subject.otherProportional Probability Model
dc.subject.otherAdditive Probability Model
dc.subject.otherIdentity-Binomial Model
dc.subject.otherGeneralized Linear Model
dc.subject.otherconstrained parameter space
dc.subject.otheruniqueness
dc.subject.othernon-finite
dc.subject.otherinterval estimation
dc.subject.otherRelative Likelihood Interval
dc.subject.otherBootstrap
dc.subject.otherMaximum Likelihood Estimate
dc.subject.otherOrdinal outcomes
dc.subject.otherBinary outcomes
dc.subject.otherlog link
dc.subject.othernon-canonical link
dc.subject.otheridentity link
dc.titleBinary and Ordinal Outcomes: Considerations for the Generalized Linear Model with the Log Link and with the Identity Link
dc.typedoctoral thesis
thesis.degree.disciplineCommunity Health Sciences
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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