• Login
    View Item 
    •   DSpace Home
    • Stony Brook University
    • Stony Brook Theses & Dissertations [SBU]
    • View Item
    •   DSpace Home
    • Stony Brook University
    • Stony Brook Theses & Dissertations [SBU]
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsDepartmentThis CollectionBy Issue DateAuthorsTitlesSubjectsDepartment

    My Account

    LoginRegister

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Power analysis of the likelihood ratio test for logistic regression mixtures

    Thumbnail
    View/Open
    Lee_grad.sunysb_0771E_10432.pdf (570.4Kb)
    Date
    1-May-11
    Author
    Lee, Minyoung
    Publisher
    The Graduate School, Stony Brook University: Stony Brook, NY.
    Metadata
    Show full item record
    Abstract
    Finite mixture models emerge in many applications, particularly in biology, psychology and genetics. This dissertation focused on detecting associations between a quantitative explanatory variable and a dichotomous response variable in a situation where the population consists of a mixture. That is, there is a fraction of the population for whom there is an association between the quantitative predictor and the response and there is a fraction of individuals for whom there is no association between the quantitative predictor and the response. We developed the Likelihood Ratio Test (LRT) in the context of ordinary logistic regression models and logistic regression mixture models. However, the classical theorem for the null distribution of the LRT statistics can not be applied to finite mixture alternatives. Thus, we conjectured that the asymptotic null distribution of the LRT statistics held. We investigated how the empirical and fitted null distribution of the LRT statistics compared with our conjecture. We found that the null distribution appears to be well approximated by a 50:50 mixture of chi-squared distributions with respect to the critical values. Based on this null distribution, simulation studies were conducted to compare the power of the ordinary logistic regression models to the logistic regression mixture models. The logistic regression mixture models resulted in the improvement in power to detect the association between the two variables, compared with the ordinary logistic regression models. We found the significant factors in the improvement of the power by modeling the odds ratio in the improvement (logistic mixture model vs. ordinary logistic regression model). Essentially, the only factors that affected improvement in power were slope and mixing proportion. In addition, we compared the precision of these two approaches. This mixture model can be widely applied in large sample surveys with non-response and in missing data problems.
    URI
    http://hdl.handle.net/1951/56048
    Collections
    • Stony Brook Theses & Dissertations [SBU] [1955]

    SUNY Digital Repository Support
    DSpace software copyright © 2002-2023  DuraSpace
    Contact Us | Send Feedback
    DSpace Express is a service operated by 
    Atmire NV
     

     


    SUNY Digital Repository Support
    DSpace software copyright © 2002-2023  DuraSpace
    Contact Us | Send Feedback
    DSpace Express is a service operated by 
    Atmire NV