Study area
Namibia is a middle-income country located in the southwestern region of Africa. Its borders are the Atlantic Ocean on the west, Angola and Zambia on the north, Botswana on the east and South Africa on the south and east. The country is divided administratively into 13 regions with the capital at Windhoek in the Khomas region. Namibia’s population was about 2.1 million from the 2011 census with an intercensal growth rate of 1.5% [19]. The country’s economy relies on agriculture, tourism and mining; although there has been rapid urbanization, the population is mostly rural with about four in ten people living in rural areas [19].
Source of data and sample
Data used for this research was from the 2013–2014 Demographic and Health Survey (DHS) in Namibia. The request to use the data set was made to and permission obtained from Measure DHS. The DHS is a nationally representative cross-sectional survey which among other things monitors domestic violence and IPV, malaria, HIV, maternal and child health conditions as well as reproductive health issues. 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 domestic violence questionnaire was administered, for the first time in the Namibia Demographic Health Survey (NDHS) 2013 [19], to a nationally representative sample of women between 15 and 49 years. In total 2226 women consented and responded to the domestic violence survey questions. For our study, we used the variables specific to spousal violence. We generated a new binary variable, which measures IPV in three dimensions from the questions: 1. Ever experienced physical violence? 2. Ever experienced sexual violence? and 3. Ever experienced emotional violence? Background characteristic variables such as region, place of residence, age, respondent’s level of education, partner’s educational level and wealth index level were considered as covariates. In addition, we generated another variable, age difference, from the respective ages of partners/couples in the dataset. We used the couples’ dataset for our analysis in this study. Since IPV may be associated with location of residence, it is important to account for geographical and cultural differences. We used region level effects to allow expected spatial correlation and any other unknown regional heterogeneity of IPV [26].
Statistical model
Let \(y_{ij}\) be the intimate partner violence (IPV) status for a woman \(i\) in region \(j\). \(y_{ij} = 1\) if the woman \(i\) in region \(j\) experienced some form of partner violence and \(y_{ij} = 0\) otherwise. A vector \(X_{ij} = (x_{ij1} ,x_{ij2} , \ldots ,x_{ijp} )^{{{{\prime}}}}\) contains \(p\) continuous covariate random variables 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 an unknown \(E\left( {y_{ij} } \right) = p_{ij}\), being related to the covariates through the link function
$$g\left( {p_{ij} } \right) = X_{ij}^{\prime} \beta + Z_{ij}^{\prime} \theta$$
(1)
The link function in this equation is known as the logit link, \(\beta\) is the \(p\) dimensional vector of coefficients for the continuous random variables, and \(\theta\) is an \(r\) dimensional vector of coefficients for categorical random variables. In order to assess for both non-linear effects of continuous random variables and spatial autocorrelation in our data we employed a semi-parametric model which utilizes a penalized regression approach [23]. The penalized regression approach is a non-parametric method of ordinary least squares (OLS) which relaxes the highly restrictive linear predictor for a versatile semi-parametric predictor [23, 27]. The flexible semi-parametric predictor is defined by:
$$g\left( {p_{ij} } \right) = \mathop \sum \limits_{v = 1}^{p} f_{v} \left( {x_{ijv} } \right) + f_{spat} \left( {s_{j} } \right) + Z_{ij}^{\prime} \theta$$
(2)
where \(f_{v} \left( . \right)\) represents the non-linear twice differentiable smooth function for the 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 a convolution approach to the spatial effects. The assumption is that the spatial effects can be decomposed into two pure components, that is, spatially structured and spatially unstructured effects given as \(f_{spat} \left( {s_{j} } \right) = f_{str} \left( {s_{j} } \right) + f_{{unstr\left( {s_{j} } \right)}}\). The final model for our study then becomes:
$$g\left( {p_{ij} } \right) = \mathop \sum \limits_{v = 1}^{p} f_{v} \left( {x_{ijv} } \right) + f_{str} \left( {s_{j} } \right) + f_{unstr} \left( {s_{j} } \right) + Z_{ij}^{\prime} \theta$$
(3)
More details on the model formulation are available in Additional file 1: Appendix 1.