Statistical Analysis of Structured Latent Attribute Models
dc.contributor.author | Gu, Yuqi | |
dc.date.accessioned | 2020-05-08T14:36:27Z | |
dc.date.available | NO_RESTRICTION | |
dc.date.available | 2020-05-08T14:36:27Z | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/155196 | |
dc.description.abstract | In modern psychological and biomedical research with diagnostic purposes, scientists often formulate the key task as inferring the fine-grained latent information under structural constraints. These structural constraints usually come from the domain experts' prior knowledge or insight. The emerging family of Structured Latent Attribute Models (SLAMs) accommodate these modeling needs and have received substantial attention in psychology, education, and epidemiology. SLAMs bring exciting opportunities and unique challenges. In particular, with high-dimensional discrete latent attributes and structural constraints encoded by a structural matrix, one needs to balance the gain in the model's explanatory power and interpretability, against the difficulty of understanding and handling the complex model structure. This dissertation studies such a family of structured latent attribute models from theoretical, methodological, and computational perspectives. On the theoretical front, we present identifiability results that advance the theoretical knowledge of how the structural matrix influences the estimability of SLAMs. The new identifiability conditions guide real-world practices of designing diagnostic tests and also lay the foundation for drawing valid statistical conclusions. On the methodology side, we propose a statistically consistent penalized likelihood approach to selecting significant latent patterns in the population in high dimensions. Computationally, we develop scalable algorithms to simultaneously recover both the structural matrix and the dependence structure of the latent attributes in ultrahigh dimensional scenarios. These developments explore an exponentially large model space involving many discrete latent variables, and they address the estimation and computation challenges of high-dimensional SLAMs arising from large-scale scientific measurements. The application of the proposed methodology to the data from international educational assessments reveals meaningful knowledge structures of the student population. | |
dc.language.iso | en_US | |
dc.subject | latent variable models | |
dc.subject | identifiability | |
dc.subject | psychometrics | |
dc.title | Statistical Analysis of Structured Latent Attribute Models | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Statistics | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Xu, Gongjun | |
dc.contributor.committeemember | Wu, Zhenke | |
dc.contributor.committeemember | Nguyen, Long | |
dc.contributor.committeemember | Wang, Naisyin | |
dc.subject.hlbsecondlevel | Statistics and Numeric Data | |
dc.subject.hlbtoplevel | Science | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/155196/1/yuqigu_1.pdf | |
dc.identifier.orcid | 0000-0002-4124-113X | |
dc.identifier.name-orcid | Gu, Yuqi; 0000-0002-4124-113X | en_US |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.