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SUMMARY:Additive Density-on-Scalar Regression in Bayes Hilbert Spaces - So
 nja Greven (Humboldt-Universität zu Berlin)
DTSTART:20250509T081500Z
DTEND:20250509T091500Z
UID:TALK230497@talks.cam.ac.uk
DESCRIPTION:We present structured additive regression models to model dens
 ities given scalar covariates. To preserve nonnegativity and integration t
 o one\, we formulate our models for densities in a Bayes Hilbert space wit
 h respect to an arbitrary finite measure. This enables us to not only cons
 ider continuous densities\, but also\, e.g.\, discrete densities (composit
 ional data) or mixed densities. Mixed densities occur in our application m
 otivated by research on gender identity norms and the distribution of the 
 woman's share in a couple's total labor income\, as the woman's income sha
 re is a continuous variable having discrete point masses at zero and one f
 or single-earner couples. We discuss interpretation of effect functions in
  our model via odds-ratios. We consider two data situations: First\, where
  whole densities are observed and are directly used as responses. Second\,
  when only individual scalar realizations of the conditional distributions
  are observed\, we use our additive regression approach to model the condi
 tional density given covariates. We derive consistency and asymptotic norm
 ality of the proposed Bayes space (penalized) maximum likelihood estimator
 . To facilitate estimation\, we show approximate equivalence of the Bayes 
 space (penalized) likelihood to the (penalized) likelihood of a certain Po
 isson additive model. We apply our framework to the motivating gender econ
 omic data from the German Socio-Economic Panel Study (SOEP) to analyze the
  distribution of the woman's share in a couple's total labor income\, give
 n year\, place of residence and age of the youngest child.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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