Latent Regression Analysis.

Statistical Modelling
Thaddeus Tarpey, Eva Petkova

Abstract

Finite mixture models have come to play a very prominent role in modelling data. The finite mixture model is predicated on the assumption that distinct latent groups exist in the population. The finite mixture model therefore is based on a categorical latent variable that distinguishes the different groups. Often in practice distinct sub-populations do not actually exist. For example, disease severity (e.g. depression) may vary continuously and therefore, a distinction of diseased and not-diseased may not be based on the existence of distinct sub-populations. Thus, what is needed is a generalization of the finite mixture's discrete latent predictor to a continuous latent predictor. We cast the finite mixture model as a regression model with a latent Bernoulli predictor. A latent regression model is proposed by replacing the discrete Bernoulli predictor by a continuous latent predictor with a beta distribution. Motivation for the latent regression model arises from applications where distinct latent classes do not exist, but instead individuals vary according to a continuous latent variable. The shapes of the beta density are very flexible and can approximate the discrete Bernoulli distribution. Examples and a simulation are pro...Continue Reading

References

Jun 1, 1978·Computers and Biomedical Research, an International Journal·M A WoodburyA Garson
Aug 11, 2000·The Journal of Clinical Psychiatry·P J McGrathC M Beasley
Mar 29, 2001·Journal of Clinical Psychopharmacology·A Khan, W A Brown
Apr 21, 2001·Biometrics·S BartolettiD G Nel
Apr 25, 2001·Biometrics·B Muthén, K Shedden
Apr 10, 2002·JAMA : the Journal of the American Medical Association·B Timothy WalshMadelyn Gould
Aug 5, 2005·Biostatistics·Jia GuoYasuo Amemiya

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Citations

Dec 27, 2017·Statistical Methods in Medical Research·Rob KesselsJos Bloemers
Jan 1, 2019·The American Statistician·Thaddeus Tarpey, Eva Petkova

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