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.
Assunção
Renato M
RM
UFMG, Departamento de Estatística, Caixa Postal 702, Belo Horizonte MG, 30161-970, Brazil. assuncao@est.ufmg.br
Potter
Joseph E
JE
Cavenaghi
Suzana M
SM
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