METROPOLIS-HASTINGS BAYESIAN POISSON REGRESSION ANALYSIS WITH APPLICATION TO THE NATALITY OF MOTHERS IN LAGOS METROPOLIS
Abstract
This study modelled the natality of mothers in the Lagos metropolis of Lagos State using the
Bayesian Poisson Regression Analysis with the Metropolis-Hastings algorithm to sample the
expected posterior mean natality. The specific objectives were to compare the natality of mothers
by different predictors incorporating the prior knowledge about natality with a Poisson
distributed likelihood to obtain the posterior distribution. The study used nine different
categorical predictors to model the natality of mothers vis mother's age, highest education
qualification, religious affiliation, residence, use of contraceptives in between births, length of
breastfeeding babies, length of child spacing (birth gaps), mother age at first marriage, and the
Local government of residence. The prior distribution used was the normal prior on a Poisson
likelihood and obtained the posterior distributions. The data used comprised 2000 mothers
selected purposively and was extracted from Abe (2013), a city-wide study on infant mortality in
the presence of child spacing and migration and the data were analysed using the Bayesian
Poisson Regression with the help of code written in R programme environment. The study found
that the expected natality of mothers in the Lagos metropolis is 2.68 (95% CI 2.46 – 2.79). Also,
it found that the highest educational qualification, child spacing (birth gaps), age at first marriage
and Local Government of residence has a positive impact on the natality of mothers in Lagos
metropolis and while mothers’ age, residence, religious affiliation, use of contraceptives in
between birth, and breastfeeding length have a positive impact on natality of mothers. Also, it
found that the highest educational qualification, child spacing (birth gaps) and LGA of residence
have a significant impact on natality while the other predictors do not. The study therefore
concludes that the Bayesian Poisson Regression Model was a good model for the natality of
mothers in Lagos metropolis using the Metropolis-Hastings algorithm. It also concluded that the
model determined that the expected natality of mothers falls around 3 children.
