A Bayesian space varying parameter model applied to estimating fertility schedules.
We propose a spatial generalized linear model (GLM) to analyse the vital rates for small areas. In each small area, we have a response vector and covariates to explain its variability. The statistical methodology is based on a spatial Bayesian approach and it allows the covariates' parameters of the generalized linear model to vary smoothly on space. Hence, the effect of a covariate on the response varies depending on the random variables measurement location. Our model is an extension of disease mapping models allowing the space-covariate interaction to be modelled in a natural way and giving space a position of intrinsic interest. We introduce the model in the context of fertility curve estimation. In each small area, we have a curve describing the variation of fertility rates by age modelled by Coale's fertility model, which implies a GLM in each area. A simulation shows the advantages of our approach. In addition, the paper applies the procedure to census data used to study the diffusion of low fertility behaviour in Brazil.
UFMG, Departamento de Estatística, Caixa Postal 702, Belo Horizonte MG, 30161-970, Brazil. assuncao@est.ufmg.br
Renato M
RM
Assunção
Joseph E
JE
Potter
Suzana M
SM
Cavenaghi
D000293:Adolescent; D000328:Adult; D001499:Bayes Theorem; D001723:Birth Rate; D001938:Brazil; D003198:Computer Simulation; D005260:Female; D006801:Humans; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D017062:Small-Area Analysis