Bayesian semi-parametric spatial modeling of intimate partner violence in Namibia using data from the 2013 Demographic Health Survey | BMC Women’s Health

Study zone

Namibia is a middle-income country located in the southwestern region of Africa. Its borders are the Atlantic Ocean to the west, Angola and Zambia to the north, Botswana to the east and South Africa to the south and east. The country is administratively divided into 13 regions, the capital of which is Windhoek in the Khomas region. Namibia’s population was around 2.1 million according to the 2011 census with an intercensal growth rate of 1.5% [19]. The country’s economy is based on agriculture, tourism and mining; although there has been rapid urbanization, the population is predominantly rural with around four in ten people living in rural areas [19].

Data source and sample

The data used for this research came from the 2013-2014 Demographic and Health Survey (DHS) in Namibia. The request to use the dataset has been made and authorization obtained from Measure DHS. The DHS is a nationally representative cross-sectional survey that monitors domestic and domestic violence, malaria, HIV, maternal and child health conditions, and reproductive health issues, among others. The DHS Domestic Violence Module, from which our data is derived, used a shortened and modified Conflict Tactics Scale (CTS). [24] to measure different forms of IPV [25] and domestic violence in general. The questionnaire on domestic violence was administered, for the first time, as part of the Namibia Demographic Health Survey (NDHS) 2013 [19], to a nationally representative sample of women between 15 and 49 years old. A total of 2,226 women consented to and answered questions in the survey on domestic violence. For our study, we used variables specific to domestic violence. We generated a new binary variable, which measures IPV in three dimensions from the questions: 1. Have you ever been physically abused? 2. Have you ever experienced sexual violence? and 3. Have you ever experienced emotional abuse? Contextual characteristic variables such as region, place of residence, age, respondent’s education level, partner’s education level and wealth index level were considered to be covariates. In addition, we generated another variable, the age difference, from the respective ages of partners / couples in the data set. We used the couples dataset for our analysis in this study. Since IPV can be associated with place of residence, it is important to consider geographic and cultural differences. We used region-level effects to allow for the expected spatial correlation and any other unknown regional heterogeneity of IPV [26].

Statistical model

Let (y_ {ij} ) be the status of domestic violence (IPV) for a woman (I) in the region (j ). (y_ {ij} = 1 ) if the woman (I) in the region (j ) suffered some form of domestic violence and (y_ {ij} = 0 ) other. A vector (X_ {ij} = (x_ {ij1}, x_ {ij2}, ldots, x_ {ijp}) ^ {{{{ prime}}}} ) contains (p ) random variables with continuous covariates and (Z_ {ij} = (z_ {ij1}, z_ {ij2}, ldots, z_ {ijr}) ^ { prime} ) contains some r categorical variables. In our study, (p = 3 ) and (r = 5 ).

This study assumes that the dependent variable, (y_ {ij} ) is a Bernoulli distributed random variable with (y_ {ij} | p_ {ij} sim Bernoulli left ({p_ {ij}} right) ) with a stranger (E left ({y_ {ij}} right) = p_ {ij} ), being linked to the covariates by the link function

The link function in this equation is known as the logit link, (beta) is the (p ) dimensional vector of coefficients for continuous random variables, and ( theta ) is a (r ) dimensional vector of coefficients for categorical random variables. In order to assess both the nonlinear effects of continuous random variables and the spatial autocorrelation in our data, we used a semi-parametric model that uses a penalized regression approach. [23]. The penalized regression approach is a nonparametric ordinary least squares (OLS) method that relaxes the highly restrictive linear predictor for a versatile semi-parametric predictor [23, 27]. The flexible semi-parametric predictor is defined by:

or (f_ {v} left (. right) ) represents the twice-differentiable nonlinear smooth function for continuous covariates and (f_ {spat} left ({s_ {j}} right) ) is the variable that denotes the spatial effects for each region. In our study, as in Ngesa et al. [23], we consider an approach by convolution of spatial effects. The hypothesis is that the spatial effects can be decomposed into two pure components, i.e. spatially structured effects and spatially unstructured effects given by (f_ {spat} left ({s_ {j}} right) = f_ {str} left ({s_ {j}} right) + f _ {{unstr left ({s_ {j}} right)}}). The final model of our study then becomes:

More details on the formulation of the model are available in Supplementary File 1: Annex 1.