Introduction

This paper aimed to investigate whether husbands or partners influence South African women's choice of modern contraceptive use. In addition, the present paper explored this objective based on Tobler's (1970) first law of geography, to understand whether modern contraceptive use is explained by group effects within clusters where these women reside. Another objective was to determine whether group effects are spatially dependent among neighbouring clusters.

South Africa is one of the state parties to the Maputo Protocol. It continues to participate in development of other related continental instruments that seek, among others, to ensure an expansion of access to sexual and reproductive health services and to improve their quality. Access to modern contraceptives is crucial between these services because of its direct link with society's development. For instance, modern contraceptives empower married womenFootnote 1 to control births, potentially reducing fertility rates, which remain consistently high in sub-Saharan Africa as alluded to in many studies (Atake & Ali, 2019; Caldwell et al., 1990; Mbacké, 2017). Because of this link, one has to examine the determinants of modern contraceptive use. Although South Africa is amongst African countries with the highest level of contraceptive use, from a policy point of view, the analysis of its determinants remains vital for the government, which has committed itself to achieving the Maputo Protocol, as mentioned above.

Modern contraceptive use remains an area of continuous and pertinent research for African countries because, among others, of limited access available to users. For this reason, the literature abounds with studies on this topic that focus on sub-Saharan Africa, including South Africa. However, the present study was particularly interested in the male partners' role in South African women's modern contraceptive use.

First, married women's modern contraceptive use should be understood, to some extent, as a choice involving two partners who live as a couple. Therefore, the characteristics of the male partner should also be taken into account as determinants of modern contraceptive use. It is important from a policy point of view because policies, campaigns, and other interventions must include men to expand modern contraceptive use or any sexual and reproductive health services for women.

Second, few studies concerning this phenomenon have focused on sub-Saharan Africa, including South Africa, concerning this phenomenon (Abose et al., 2021; Blackstone et al., 2017; Izugbara et al., 2010; Palamuleni, 2013). This situation is an indication that there is limited knowledge regarding this relationship, and further research focusing on this region's different contexts is required. Third, Kriel et al. (2019) recently examined partners' influence on women's contraceptive use, but their scope of analysis was limited to the KwaZulu-Natal province. While their study shed light on aspects that explain women's contraceptive use, there are still limitations in understating understanding the situation in South Africa as a whole, with its varying regional contexts.

Furthermore, spatial analysis approaches are often overlooked in the literature when examining women's contraceptive use. For instance, the South African Demographic and Health Survey (SADHS) of 2016,Footnote 2 the source of data used in this paper, published information on women nested within clusters.Footnote 3 These clusters are characterizedcharacterised by a specific location in space, equivalent to Statistics South Africa's enumeration areas demarcated to collect demographic and other information on individuals. Nesting women's characteristics into clusters as spatial units may lead to a situation where the phenomenon under investigation is characterizedcharacterised by spatial heterogeneity and spatial dependence (Anselin, 1988). Spatial heterogeneity, in this context, describes a situation where there is dependence between modern contraceptive use within a cluster, which varies across clusters.

Consequently, as a social phenomenon, a woman's contraceptive use is susceptible to influences within the cluster in which she resides. These influences may arise from various channels, including social networks and geographical proximity. The effects from within clusters are often referred to as group effects. These effects differ from one cluster to another, and because clusters are spatial units, this phenomenon is referred to as spatial heterogeneity in this paper.

Spatial dependence, in this context, refers to a situation where there is the presence of autocorrelation of latent factors, also referred to as random effects among neighbouring clusters. While section three (the models) of this paper further elaborates on this issue, it is safe to say that the latent factors are among the right-side elements in the model specification of contraceptive use. If a model specification does not consider both spatial heterogeneity and spatial dependence, this can lead to biased parameter estimates and inconsistency (Anselin, 1988).

Based on the preceding, the hierarchical nature of the SADHS and because clusters are spatial units, make it is imperative to carefully consider the issue of spatial heterogeneity and the spatial autocorrelation that may characterizecharacterise the random effects of spatial units (i.e., clusters) in this paper. In other words, one cannot assume that contraceptive use within a cluster is independently distributed, whereby the error terms follow the same pattern across clusters and without interactions among neighbouring clusters regarding the latent factors.

This approach shows the importance of model specification accounting for the hierarchical nature of the data by incorporating the random effects on the right side of the equation as part of the unobserved component and determining whether these random effects are spatially independent or otherwise. Hence, non-spatial and spatial hierarchical logistic models were estimated to examine contraceptive use in South Africa. This specification is equivalent to what is also referred to as a hierarchical model with spatially structured random effects introduced by LeSage and Pace (2009).

The SADHS data covers all areas of South Africa, and the units used to sample households are based on the enumeration areas used by Statistics South Africa. Consequently, it is possible to consider South Africa as a study area instead of limiting the analysis to one province, as was the case with Kriel et al.'s (2019) research. This data also offers a variety of variables that can be selected to represent characteristics of a male partner's role in women's contraceptive use. In this regard, the selected predictors of interest were related to a partner's education level, employment status, age, fertility preferences, and the level of his involvement in the health decisions or choices of his wife, amongst others. It also provides the Cartesian coordinates of clusters' centroids, pertinent for spatial analysis.

As alluded to in the first paragraph of this section, one aspect of the present paper's objectives stems from what is referred to as Tobler's (1970, p. 236) first law of geography, stipulating that "everything is related to everything else, but near things are more related than distant things". One can deduce that the similarity of characteristics that affect contraceptive use within clusters and autocorrelation of random effects among neighbouring groups are induced by social interactions between individuals, geographical proximity, or by missing spatially correlated latent factors.

Some studies consider social interaction as a factor that influences women's choices regarding fertility preferences, including contraceptive use (Balbo & Barban, 2014). These studies rely on measurable variables to determine social interaction or networking. In contrast, the present paper did not consider such variables in the analysis because of data limitations in the 2016 SADHS. Instead, this paper used Cartesian coordinates as variables to capture spatial effects.

This paper adopted an empirical strategy in line with Bivand et al.'s (2017) suggestion to ensure that four variants of hierarchical logistic models, that differ in the assumed behaviour of the random effects components, were estimated. The four hierarchical logistic models include a null model, a non-spatially structured random-effects model, and two models with spatially structured random-effects components (viz. the intrinsic conditional autoregression and the Besag-York-Mollié conditional autoregressive). Then, the best among these four models was selected based on the estimation procedure detailed in section three of this paper.

The present paper's hierarchical logistic model specification helped disentangle and estimate two sources of variability regarding modern contraceptive use. Given that the data are clustered, it is possible, on the one hand, to estimate the within-cluster variability of modern contraceptive use using a hierarchical logistical modelling framework. This type of variability can be translated into expected variability, regardless of whether a woman resides in a particular cluster. On the other hand, a hierarchical specification can estimate between-cluster variability regarding modern contraceptive use. The between-cluster variability is a crucial ingredient brought to the fore by a hierarchical specification because it offers an opportunity to examine whether, for instance, women residing in a particular cluster have similar patterns of modern contraceptive use and, at the same time, whether these patterns are assumed to be different from those of women in other clusters.

This paper is set out as follows: A discussion on the literature review is presented in section two, and the models to be estimated are discussed in section three. Section four discusses the data, while the results are discussed in section five. The concluding remarks are presented in section six.

Literature review

The literature is dominated by many demographic, population and health-related studies that have examined the relationship between socio-economic characteristics and contraceptive use in Sub-Saharan Africa (Addai, 1999; Ahinkorah et al., 2020; Avogo & Agadjanian, 2008; Blackstone, 2017; Blackstone et al., 2017; Oheneba-Sakyi & Takyi, 1997; Palamuleni, 2013; Tawiah, 1997). Therefore, while it is not practical to present a comprehensive discussion of all studies in this section, the main aim is to present studies for which some meaningful parallelism parallels can be drawn with the present study.

One can borrow from the earlier studies to understand the relevance of examining the relationship between male partners and women's contraceptive use, such as Abose et al. (2021), Izugbara et al. (2010), and Sarnak et al. (2021). For instance, Sarnak et al. (2021) stress that most empirical studies have a limited focus on male partners' involvement in women's contraception use. This situation occurs despite a theoretical framework put forward by Miller et al. (2004), understood in the context of the present study as suggesting that a woman's contraceptive use may be influenced by her fertility intentions and her male partner's fertility desires.

There are other (although few) empirical studies that have attempted to examine this aspect, including some that focused on Africa and South Africa in particular (Kopp et al., 2018; Kriel et al., 2019; Miller et al., 2007; Silverman et al., 2019, 2020). These studies used different variables to capture a male partner's influence on a woman's contraceptive use. This position can be explained partly by differences between data sources and the specific focus of each study. The present paper harnessed the richness of the 2016 SADHS data by capturing the male partner's role using a few variables representing education, employment status, age, fertility preference and involvement in a woman's health decisions. This, and the fact that it focuses on South Africa, is one contribution of the present paper.

Becker (1960) is among the researchers that developed a theoretical framework based on economic theories of demand and production to analyzeanalyse households' decision-making processes on fertility issues. Becker's work and this study are related because they both used the New Home Economics (NHE) hypothesis to explain the relationship between male partners (including other socio-economic characteristics) and women's contraceptive use.

Furthermore, most empirical studies used hierarchical models, mainly because of the hierarchical nature of data. As already elaborated in the introductory section, one can deal with the issue of spatial heterogeneity through the specification of hierarchical models. However, these models do not consider spatial dependence among the random effects. Although these studies examined contraceptive use, they did not focus on the present study's aspect, which incorporates both spatial heterogeneity and spatial dependence. Their inclusion is purely based on the methodological approaches they followed, and many focused on developing countries (Entwisle et al., 1986; Mutumba et al., 2018; Ngome & Odimegwu, 2014; Okigbo et al., 2017; Palamuleni, 2013; Stephenson et al., 2007). For instance, Okigbo et al. (2017) found a significant and positive relationship between a woman's employment and contraceptive use in urban Nigeria only when community and interaction variables were not considered.

In contrast, Ngome and Odimegwu's (2014) analysis determined that individual and community factors are significantly related to adolescent girls' contraceptive use. Mutumba et al. (2018) conducted a cross-country analysis of the relationship between individual and community factors and contraceptive use among women aged 15 and 24 years. Their findings confirm that young women's contraceptive use across the 52 middle-income countries considered is significantly related to community factors.

As stated earlier, studies that used hierarchical models were related to the present study from a methodological perspective. By using hierarchical modelling, these studies assumed that the contraceptive use of a woman belonging to a region (i.e., cluster in the present study) is influenced by unobserved community-level factors, in the same way that other women's contraceptive use in that region is influenced. In other words, women belonging to an area will exhibit similarities regarding contraceptive use among themselves, while their behaviour is different from those belonging to different regions.

Nevertheless, the model specifications used in this study are different from the studies mentioned above in two ways. First, one limitation of (non-spatial) hierarchical modelling is its inability to consider the interrelationship between clusters. The present study differs from the studies mentioned above from this methodological perspective. Last, spatial dependence between clusters was investigated by estimating non-spatial hierarchical models. Then a comparison was made between these models and spatial hierarchical models, as further discussed in Sect. "Models" of the present paper.

Other empirical studies have incorporated some spatial or geographical dimensions in their analyses (Achana et al., 2015; Islam et al., 2020; Lakew et al., 2013). Achana et al. (2015) used household survey data for 66 census enumeration areas in seven rural districts of Ghana. They considered the spatial dimension component the distance between a woman's residence and a facility offering a community-based health-planning services programme (CHPS). One can deduce that the distance parameter was included in the model to assess the issue of accessibility. Their findings confirmed disparity regarding contraceptive use attributed to differences in accessing a CHPS. The model used by Islam et al. (2020) is a cross-sectional linear regression that incorporates regional fixed effects to account for variations in contraceptive use between regions. This modelling approach is different from the one applied in the present study for similar reasons as those provided for non-spatial hierarchical models.

Another collection of studies investigated the influence of social networks or interactions on contraceptive use (Behrman et al., 2001, 2002; Godley, 2001; Kohler, 1997; Kohler et al., 2001; Rutenberg & Watkins, 1997; Valente et al., 1997). As elaborated on in section one of this paper, these studies used measurable variables to determine social interaction or networking. These works are related to the present study from a conceptual point of view; however, the present study did not consider such variables in the analysis. Another advantage of the methodology applied in the present study is that it tests for spatial dependence in the non-spatial model. This could also have been done in the presence of variables representing social networks to ensure a correct model specification. Based on the above discussion, this paper attempted to close the spatial analysis gap in the literature by employing spatial hierarchical logistic models to investigate the relationship between a male partner's role and women's modern contraceptive use in South Africa.

Models

Setting the scene

This section starts by setting the scene to promote a straightforward interpretation of the equations and symbols used in the specifications. Regarding the study area (South Africa), it is essential to note that it is partitioned into \(P\) selected non-overlapping areal units whose geographical boundaries corresponded to 625 clusters in 2016. In addition, women are indexed by \(i \left(i=1,\ldots N\right)\) and clusters are symbolizedsymbolised by \(j (j=1,\ldots P)\). A total of 2243 women were considered in the analysis, suggesting that \(P<N.\)

The vector of the dependent variable and the matrix of independent variables are associated with women. The dependent variable is a binary indicator equal to 1 if a woman indicated that she used modern contraceptives \(\left({Y}_{ij}=1\right)\), and 0 if she did not \(\left({Y}_{ij}=0\right)\). The logistic transformation means one is predicting the probability of a woman falling into a target group using modern contraceptives. This is represented by \(Prob ({Y}_{ij}=1)\).

The logit is used in logistic regression instead of using the probabilities, which are bound to 0 and 1. It is important to note that the logit transforms the predicted likelihood of target group membership. The main reason for using the logit is to ensure the relationship between the independent variables and the probability of a woman using modern contraceptives is linear. Equation (1) represents the logit transformation of the likelihood of using modern contraceptives. In this specification, the \(logit\left({p}_{ij}\right)\) stands for the log-odds of a woman i in a cluster j using modern contraceptives. In addition, the vector of \(K\) independent variables is denoted by \({X}_{ij}^{T}=\left({X}_{ij1},\ldots ,{X}_{ijk}\right)\).

$$logit\left({p}_{ij}\right)=\mathrm{ln}\left(\frac{Prob\left({Y}_{ij}=1\right)}{Prob\left({Y}_{ij}=0\right)}\right)$$
(1)

Specification of spatial hierarchical models

After setting the scene, this section presents the model specifications considered for analysis in this paper. These model specifications are presented in line with the procedure often involved in the estimation of (spatial) hierarchical models. As such, this procedure involves multiple steps of estimating, testing, selecting, and interpreting the best-performing model. For instance, one must test whether the data are suitable for a single-level model. At the same time, the pertinence of a spatial model must be attested through a series of statistical tests.

This paper followed two main steps to estimate and test the hierarchical logistic models, as set out below. All models were estimated in the Bayesian context (Bivand et al., 2017) using the integrated nested Laplace approximation (R-INLA) algorithm programmed in the R-INLA package.Footnote 4

Step 1: Hierarchical null logistic model

Equation (2) is the hierarchical logistic model.

$$ \begin{aligned} & logit\left( {p_{ij} } \right) = \alpha_{ij} + u_{j} \\ & u_{j} \sim N\left( {0,\tau_{u} } \right) \\ & \pi \left( {\alpha_{ij} } \right)\sim N\left( {\mu_{\alpha } ,\sigma_{\alpha }^{2} } \right) \\ & \pi \left( {\tau_{u} } \right)\sim logGamma\left( {1,10^{ - 5} } \right) \\ \end{aligned} $$
(2)

where \(\alpha_{ij}\) is the overall intercept of log-odds of a woman using modern contraceptives across all clusters, and \({u}_{j}\) is the intercept specific for cluster j. Instead of the variance for the random effects, for computation purposes, the algorithm in R-INLA uses its inverse, \({\tau }_{u}=\frac{1}{{\sigma }_{u}^{2}}\), also referred to as precision. However, in the reporting of estimates in section four, the variance is shown for interpretation, not the precision. The term π indexes prior distributions of the relevant parameters to be estimated following the Bayesian approach (for more details on R-INLA priors, see Wang et al., 2018).

Equation (2) can be understood in this way. There are two components, notably the fixed-effects (\({\alpha }_{ij}\)) and the random-effects components (\({u}_{j}\)). For the latter component, the inverse of its variance (\({\tau }_{u}\)) is estimated, as it conveys useful information for analysis, as already indicated. Equation (2) is used to test the appropriateness of a hierarchical model against a single-level model. Technically, Eq. (2) tests whether the between-cluster variance is big enough to explain the log-odds of a woman using modern contraceptives. Therefore, after estimating Eq. (2), one has to calculate the interclass correlation coefficient (ICC), also known as the variance partition coefficient (VPC). An ICC indicates the relative magnitude of the between-cluster variance component. In other words, it quantifies the degree of homogeneity regarding the log-odds of a woman using modern contraceptives.

Equation (3) is the formula for calculating ICC from the estimated hierarchical null logistic model.

$$ICC=\frac{{\sigma }_{u}^{2}}{{\sigma }_{u}^{2}+\left(\frac{{\pi }^{3}}{3}\right)}$$
(3)

where \(\left({\pi }^{3}/3\right)\approx 3.29\) is the standard logistic distribution of the level 1 variance component. A higher ICC value implies there is dependence between women within clusters, whereas a lower ICC shows independence. The conventional threshold of 0.05 determines whether the between-wards variance is significant or not (Heck et al., 2014). Thus, if the estimated ICC is equal to or greater than 0.05, this paper concludes that a hierarchical logistic model is necessary, and one must proceed to the second step set out below.

Step 2: Hierarchical logistic models

After confirming the suitability of hierarchical over single-level logistic models, the next step was to estimate what is referred to as a random intercept logistic model. Equation (4) represents the specification of a random intercept logistic model.

$$ \begin{aligned} & logit\left( {p_{ij} } \right) = \alpha_{ij} + X_{ijk}^{T} \beta + u_{j} \\ & \pi \left( {\alpha_{ij} } \right)\sim N\left( {\mu_{\alpha } ,\sigma_{\alpha }^{2} } \right) \\ & \pi \left( \beta \right)\sim N\left( {\mu_{\beta } ,{\Sigma }_{\beta } } \right) \\ \end{aligned} $$
(4)

where the meaning of terms remains the same as in Eq. (2), except that the matrix of independent variables with their associated vector of K slopes (β) is now incorporated into the model. Equation (4) predicts the log-odds that a woman i in cluster j uses modern contraceptives as a function of the overall intercept (\({\alpha }_{ij}\)), with selected independent variables that include the variable of interest, and the vector of clusters' random effects (\({u}_{j}\)). This model allows the intercept to vary between clusters. For instance, the intercept of the log-odds that a woman in a specific cluster uses modern contraceptives is:\({\alpha }_{ij}+{u}_{j}\). As in Eq. (2), it is precision (\({\tau }_{u}\)) (or the variance) that is estimated.

Three variants of hierarchical specifications are derived from Eq. (4) based on the assumption made regarding the behaviour of the random effects component. The first assumption posits that random effects are independent, with 0 mean and a constant variance. Since the random effects are related to spatial units, which are clusters, the assumption of independence also means that the random effects are not spatially structured. In other words, there is no spatial dependence among neighbouring clusters. Equation (5) represents a model for which the random effects are identical and independent.

$$ \begin{aligned} & logit\left( {p_{ij} } \right) = \alpha_{ij} + X_{ijk}^{T} \beta + u_{j} \\ & u_{j} \sim N\left( {0,\tau_{u} } \right) \\ & \pi \left( {\tau_{u} } \right)\sim logGamma\left( {1,10^{ - 5} } \right) \\ \end{aligned} $$
(5)

The above-cited assumption implies that Eq. (5) is treated as a non-spatial hierarchical model. This model and the three spatial models discussed below were estimated and then compared using the deviance information criterion (DIC), as well as the Watanabe-Akaike information criterion (WAIC), to select a model that performs better.

Equations (6) and (7) represent specifications where it is assumed there is a strong autocorrelation of random effects among neighbouring clusters. This assumption introduces the notion of spatial dependence in the random effects component. Thus, these equations are referred to as spatial hierarchical logistic models. It is also worth noting that the random effects in these models are represented with a conditional autoregressive prior to inducing spatial autocorrelation through the clusters' neighbourhood structure, as discussed below.

$$ \begin{aligned} & logit\left( {p_{ij} } \right) = \alpha_{ij} + X_{ijk}^{T} \beta + u_{j} \\ & \left. {u_{j} } \right|u_{ - j} ,W,\rho ,\tau_{u} \sim N\left( {\frac{{\rho \mathop \sum \nolimits_{i = 1}^{P} w_{ji} u_{j} }}{{\rho \mathop \sum \nolimits_{i = 1}^{P} w_{ji} + 1 - \rho }},\frac{{\tau_{u} }}{{\rho \mathop \sum \nolimits_{i = 1}^{P} w_{ji} + 1 - \rho }}} \right) \\ & \pi \left( {\tau_{u} } \right)\sim logGamma\left( {1,10^{ - 5} } \right) \\ \end{aligned} $$
(6)

where \(u_{ - j} = \left( {u_{1} , \ldots ,u_{j} , \ldots ,u_{j + 1} , \ldots ,u_{P} } \right)\) indexes the random effects, and \(W\) is a non-negative and symmetric P-by-P adjacency matrix. Its elements are denoted by \(w_{ji}\) to show the inverse Euclidean distance between cluster j and ward i.

The next section is related to the data and discusses the construction of the adjacency or spatial weight matrix. At this point, it can be said that the diagonal elements of \(W\) are set to 0 (\({w}_{jj}=0)\), as a non-overlapping areal unit cannot be a neighbour to itself. The spatial dependence parameter, \(\rho \), is set to 1 to indicate a strong autocorrelation. Because of the condition related to \(\rho \), Eq. (6) is referred to as the intrinsic conditional autoregressive (ICAR) model. If the spatial dependence parameter is set to 0 in Eq. (6), this is equivalent to assuming that the random effects are independent, as discussed for Eq. (5).

Equation (7) considers two sets of random effects. It is referred to as the Besag-York-Mollié (BYM) conditional autoregressive model (Besag et al., 1991), and is the most used in empirical studies.

$$ \begin{aligned} & logit\left( {p_{ij} } \right) = \alpha_{ij} + X_{ijk}^{T} \beta + u_{j} \\ & u_{j} = \varphi_{j} + \theta_{j} \\ & \varphi_{j} \left| {\varphi_{ - j} ,W,\tau_{u} \sim N\left( {\frac{{\mathop \sum \nolimits_{i = 1}^{P} w_{ji} \varphi_{i} }}{{\mathop \sum \nolimits_{i = 1}^{P} w_{ji} }},\frac{{\tau_{\varphi } }}{{\mathop \sum \nolimits_{i = 1}^{P} w_{ji} }}} \right)} \right. \\ & \theta_{j} \sim N\left( {0,\tau_{\theta } } \right) \\ \end{aligned} $$
(7)

All symbols in Eq. (7) are the same as in the preceding equations, except that the assumption regarding the behaviour of the random effects changes. In effect, the assumption entails segregating the random-effects component into two parts, as follows:

$${u}_{j}={\varphi }_{j}+{\theta }_{j},$$
(8)

where \({\varphi }_{j}\) is the spatially structured part of the random effects, andeffects and is equivalent to the random effects defined for the ICAR model in Eq. (6), whereas \({\theta }_{j}\) is assumed to follow a Gaussian distribution, as is the case in Eq. (5).

To end this section, it should be noted that, in addition to the null model that must prove the relevance of hierarchical modelling for the data at hand, two sets of three hierarchical logistic models were first estimated. Second, the DIC and WAIC statistics were used to select (for each set of hierarchical multilevel logistic models) the model that performed the best. Third, the estimates of the best-performing model were then used to address the set research objective. The next section is a discussion of the data used in this paper.

Data

Spatial data

The first set of information includes the longitudes and latitudes of the centroids of 625 out of 750 clusters, as they were defined in 2016. This data was sourced from the SADHS 2016 file called “ZAGE71FL”. This data was used to construct the adjacency matrix, \(W\), to estimate Eqs. (6) and (7), which require the identification of each cluster's neighbours' inverse Euclidean distance. This is critical in explaining the spatial dependence among random effects. In this regard, this paper first uses the clusters' longitudes and latitudes to Euclidean pairs of distances, as depicted below.

$$ d_{ji} = \left\| {\sqrt {\left( {u_{j} - u_{i} } \right)^{2} + \left( {v_{j} - v_{i} } \right)^{2} } } \right\|, $$
(9)

where \({d}_{ji}\) is the distance in kilometres between cluster j and cluster i, and \(\left({u}_{j},{v}_{j}\right)\) and \(\left({u}_{i},{v}_{i}\right)\) are geographical coordinates (latitudes and longitudes) for cluster j and cluster i, respectively. Second, based on the estimated distances, the spatial weight is constructed in a manner that its element, \(w_{ji}\), is determined as follows:

$$ w_{ji} = \left\{ {\begin{array}{*{20}l} {d_{ji}^{ - 1} ,} \hfill & {j \ne i} \hfill \\ {0,} \hfill & {j = i} \hfill \\ \end{array} } \right. $$
(10)

Equation (10) shows that the spatial weight matrix takes two values; 0 for elements on the diagonal, and the inverses of centroid distances between clusters for other elements. The particular feature in the spatial weight matrix is that each municipality is neighbour to all other municipalities in the sample. Moreover, the consideration of the inverse distance criterion for the construction of the spatial weight matrix aligns with Tobler's first law of geography. This is because the weight of cluster i or j decays as the distance between the two decreases. In other words, things that are far apart are less similar than those that are nearby.

Attributes

The second set of information includes what is often referred to in spatial econometrics as attributes, as reported in Table 1. This data was sourced from the file named “ZAIR71DT” of the SADHS, which contains the characteristics of women of reproductive age nested within clusters (ICF, 2018). Information related to women and their husbands/partners in the sample was selected from this file. This means that for every woman of reproductive age (15–49 years) selected, her husband's or male partner's characteristics (i.e., education attainment, employment status, etc.) were also selected to ensure dyad observations.

Table 1 Data description.
Full size table

First, the dependent variable "contraceptive" was reconstructed based on the original variable that indicated the current contraceptive method being used by a woman. This variable was multinomial but was transformed into a binomial for ease of interpretation in this paper.

Second, focusing on the three independent variables of interest in this paper, symbolizedsymbolised by “Both”, “Education partner” and “Fertility with partner”, it can be seen in column 2 of Table 1 that each captures the male partner's role in a woman's modern contraceptive use. For instance, the variable “Both” indicates whether a woman usually takes decisions regarding her health together with her husband or partner. This shows a certain degree of male partners' involvement in their female partners' health decisions. Hence, the specified models seek to understand whether the fact that male partners are involved in their female partners' health decisions indeed can explain a woman's modern contraceptive use.

Moreover, this paper attempted to discover whether there is a significant association between women's modern contraceptive use and their partner's socio-economic and demographic characteristics. In this respect, education is the first characteristic considered. One must note that the 2016 SADHS publishes education in two formats. In the one format, education is given in the number of years, and in the second, it is given as a categorical variable grouped into four—no education, primary education, secondary education, and higher education. Most studies that use the second format tend to include all categories in the regression model. For this reason, in the present study, education in number of years is used. In this respect, “Education partner” was another variable of interest in this paper.

By considering “Education partner”, this paper hypothesizes that male partners who are educated are predisposed to understanding the benefits of modern contraceptive use for their partners. As a result of this predisposition, rational, educated male partners are expected to positively influence their female partners to use modern contraceptives. As Degraff et al., (1997, p. 391) explain: "Husband's education also reflects permanent income but, in addition, may affect attitudes toward the number of children desired". Thus, it can be concluded that the expected relationship between the male partner's education level and a woman's modern contraceptive use is positive. Chacko (2001) is among the researchers that considered a partner's literacy instead of education as a determinant of women's contraceptive use. However, in view of this study, education is more relevant than just literacy.

Since this paper focused on women in the reproductive age group, fertility preference becomes one important determinant of contraceptive use that requires examination. In this regard, this paper considered “Fertility with partner” as another variable through which a male partner's influence on his wife's use of modern contraceptives is captured. Unlike the variable “Both”, which thus far has often been overlooked in the literature, one can note that the partner's fertility preference is employed in Sarnak et al.'s (2021) analysis, although represented by different variables than those used in the present paper. For instance, these authors considered the variable “partner desiring a child within two years”. The difference between the present paper and that of Sarnak et al. (2021) can be explained partly by the difference in sources of data.

Third, two other independent variables of interest were considered in this paper to capture a husband or partner's influence on a woman's modern contraceptive use, notably “Working partner” and “Age partner”. Based on Cazzola et al.'s (2016) findings, one would assume that the relationship between "Working partner" and "Contraceptive" is negative. This is because it is argued that a husband's or partner's employment status is positively related to his low fertility preference, which is ultimately associated with his wife's desire not to use modern contraceptives. The inclusion of “Age partner” illustrates whether, as the husband's age increases, there is a greater influence on their partners' use of contraceptives.

Control variables were selected in conformity with the literature and the availability of data. First, "Age woman" was selected as a control variable by assuming that it is plausible to expect differences in fertility preferences between young married women and older ones. Second, a woman's education level, "Education woman", was used in the present paper. This variable or literacy level features in most studies (Ahinkorah et al., 2020; Beson et al., 2018; Hounton et al., 2015; Palamuleni, 2013). It is argued in these studies that a woman's education or literacy is positively associated with her contraceptive use. The third control variable was the number of women in a cluster who indicated that they were working ("Working woman"). Becker's theory, referred to as the NHE, supports the inclusion of "Working woman" as one control variable (Becker, 1960). In this respect, this paper hypothesizes that modern contraceptive use is positively associated with "Working woman" because of the opportunity cost related to time and other factors required for working women to raise children.

While this paper took an economic view to analyzeanalyse the relationship between women's employment and contraceptive use, some demographic studies view women's employment as a mechanism that increases women's control over household decisions, including the demand for children (Gage, 1995; Hogan et al., 1999). Consequently, these studies argue that, because of this control in the decision-making process, it is logical to expect a positive relationship between contraceptive use and women's employment.

Women in a cluster who indicated during the survey that they wished to have another child ("Fertility woman") were considered as a control variable that captured one aspect of fertility preference. Intuitively, a negative relationship between this variable and the use of modern contraceptives is expected. Moreover, the number of poor women ("Wealth") was considered in this paper to assess the relationship between income and modern contraceptive use. According to Becker (1960, p. 219), "it is well known that rich families use contraception earlier and more frequently than poor families", and one would therefore expect a negative relationship between poor women and modern contraceptive use. This view is counterintuitive based on the NHE hypothesis; Becker's view is substantiated in the context of women accessing and/or affording contraceptives. This is understandable, sinceunderstandable since Becker's analysis was carried out in 1960. Since then, governments have made significant progress in increasing access to contraceptives as part of population policies. Also, it is the view of this paper that the cost of raising children is high for poor parents, and one can therefore expect a positive relationship between poor women and contraceptive use.

Table 2 depicts the summary of categorical variables. The first column of this table shows a variable, while the second describes categories associated with the variable. The reference categories are displayed in bold font. The number of married women that fall within each category is shown in column three, and while the fourth column shows the same information in percentages. For instance, one can read the second row of Table 2, which is related to the variable "Contraceptive", as follows: 1117 out of 2243 married women indicated that they used modern contraceptives. This represents 50%. It also means that 1126 women in the sample did not use modern contraceptives. It is also noted that 56% of women took decisions on their health care together with their husbands. Disparities between women and men concerning work or labour market participation in South Africa should be considered. Table 2 also shows that only 39% of married women versus 76% of husbands or partners in the sample were working at the time of data collection. It can also be seen that women wanted more children than their husbands.

Table 2 Summary of categorical variables
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Table 3 presents some summary statistics of the continuous variables. There is little difference between women and men regarding the reported variable, except that the maximum age of a husband or partner in the sample was 95 years. It is also evident that the minimum age for women and men was 15 years. However, after checking the data, there was only one woman and two men aged 15 in the sample. It was decided to include them in the analysis.

Table 3 Summary statistics
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Discussion of results

Before discussing the results of estimated models, it is essential to note that a hierarchical null logistic model was first estimated. An ICC of 0.05 that coincided with the threshold was found in this model. With this ICC, one can conclude that 5% of the variability in the log-odds of a woman using modern contraceptives is caused by differences between clusters. Based on this finding, the data are suitable for hierarchical logistic models.

The next stage was to estimate and determine which of these three models—the non-spatial hierarchical logistic model, ICAR or BYM—was suitable based on the DIC and WAIC criteria. Table 4 reports the parameter estimates of these models, including their respective DIC and WAIC. First, Models 1–3 in this table refer to non-spatial hierarchical logistic, ICAR and BYM models, respectively. Second, the reported DIC and WAIC for the non-spatial model are smaller than that of spatial hierarchical models. This finding indicates that the non-spatial hierarchical model is suitable for the data. Based on these findings, it is possible to conclude that according to the 2016 SADHS data, space matters as far as group effects are concerned. In other words, there is a similarity of modern contraceptive use within a cluster, whereas it differs between clusters. This finding also suggests the existence of spatial heterogeneity, which, as discussed in section three, is taken care of through the specification of a hierarchical logistic framework. It is the view in this paper that this behaviour is partly attributable to possible social networks and cluster-wide cultural similarities that may influence the women's decisions regarding modern contraceptive use.

Table 4 Posterior mean estimates
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It also is essential to note that space does not matter as far as the spatial dependence among random effects is concerned. This conclusion is drawn since neither ICAR nor BYM specifications that deal with spatial dependence are deemed suitable for the data at hand. However, the rejection of ICAR and BYM does not necessarily mean there is no spatial dependence per se. The reported statistically significant variances of random effects of ICAR and BYM in Table 4 is another way to emphasize this point. Instead, the sound interpretation is that even if there was spatial dependence among random effects, its effect is negligeable in explaining the relationships between a male partner's characteristics and a woman's modern contraceptive use. This conclusion is also confirmed as the estimates of the fixed effect component for all three models were not significantly different, as further discussed in the following sections.

Though the discussion of the results (as set out in the following paragraphs) focuses only on Model 1, it is essential at this stage to first compare the posterior mean estimates of this model to those of Models 2 and 3. There are no significant differences between posterior mean estimates for all three models in Table 4. This observation shows that spatial models (i.e., ICAR and BYM) do not change the estimates of the non-spatial hierarchical model, confirming that spatial dependence among random effects does not matter for the data. In contrast, as discussed throughout this paper, spatial heterogeneity exists as confirmed by the reported ICC.

Starting with the coefficients of the independent variables of interest, the reported posterior mean of "Both: Yes" for Model 1 is negative and significant. This finding suggests that for a couple that takes decisions about a woman's health care together, the expected log-odds of her using modern contraceptives is − 0.279, regardless of the cluster in which she resides, all other things being equal. As can be seen, this interpretation is not necessarily straightforward.

A better way to interpret estimates of logistic models, particularly their magnitude, is to use the exponential of coefficients. For instance, the exponential of − 0.279 equals 0.75 for “Both: Yes”; this result implies that the odds that a woman in a couple that takes decisions together on a woman's health care will use modern contraceptive is 0.75 lower compared to a couple that does not take these decisions together. This finding is fascinating as it shows that a husband or partner has little influence on a woman's use of modern contraceptives in South Africa.

The second independent variable of interest is "Education partner". Its reported posterior mean coefficient is positive and significant. Based on this finding, it can be deduced that an increase of one year of education for a husband or partner corresponds to a 14% (exponential of 0.114 = 1.143) increase in the odds that a woman is using modern contraceptives, all other things being equal. Previous studies, including Addai (1999), Blackstone (2017), and Tawiah (1997) have also considered the education level of a husband or partner as a determinant of a woman's contraceptive use. For instance, Addai’s (1999) finding is similar to this paper. This author confirms that husband's education increases the likelihood of contraceptive use by his wife, all other things being equal. This finding is intuitively in the sense that education predisposes a husband or partner to understand the intricacy of family planning and its benefits for their household. Therefore, one can expect that as the education level of a husband increases, the likelihood of using modern contraceptives also increases. However, it is important to note that Tawiah (1997) found that a husband's education is not a determinant of a woman's contraceptive use.

In contrast, the reported posterior mean of “Fertility with partner” is not significant. This result suggests that a woman who desires to have more children than her husband has little influence as far as modern contraceptive use is concerned. Regarding other independent variables of interest in this paper, notably “Working partner” and “Age partner”, the former is significant, while the latter is not. For a woman who indicated that her husband was working, the odds of using modern contraceptives are 1.47 higher than that of a woman whose husband was not working. But Tawiah (1997) found that a husband's occupation is not a determinant of a woman's contraceptive use in Ghana. As demonstrated in the preceding discussions, the male partner's role is essential to explain women's modern contraceptive use, but only through education, employment status and not necessarily through their fertility preferences or involvement in their female partners' health issues.

Turning now to posterior means of control variables, the coefficients related to “Education woman” is positive and significant. For instance, an increase (decrease) by one year in a woman's education corresponds to a 20% (i.e., exponential (0.183) = 1.20) expansion (drop) in the odds of that woman using modern contraceptives, irrespective of the cluster in which she resides. Ultimately, these empirical findings highlight the crucial role of education as a path for policies or interventions that seek to encourage modern contraceptive use and other sexual and reproductive health services in South Africa. Previous studies have cited the relevance of education of a woman as determinant such that as education level increases there is also the likelihood that contraceptive use will increase (Asekun-Olarinmoye et al., 2013; Audu et al., 2008; Blackstone et al., 2017; Bukar et al., 2013; Kamal, 2015; Onwujekwe et al., 2012; Orji et al., 2007; Palamuleni, 2013; Paz Soldan, 2004; Teye, 2013).

Moreover, the reported posterior mean of "Working woman: Yes" is not statistically significant. This finding refutes the NHE hypothesis that there is a positive relationship between women's employment and contraceptive use based on the cost in terms of the time required to raise children. This finding contradicts many other studies, including Shapiro and Tambashe (1994).

The coefficients of “Fertility woman: Yes” is are negative, as intuitively expected, and statistically significant, which is an indication of their strong relationship with the log-odds of women's modern contraceptive use across clusters in South Africa. Therefore, if a woman indicates that she desires to have another child, the odds for her using modern contraceptives are 0.44 lower than for a woman not wanting another child. This finding is in line with any rational behaviour. Also, as mentioned in section four, according to Becker's (1960) hypothesis regarding the relationship between socio-economic factors and contraceptive use, this paper considered “Wealth” among control variables in the specification. In this regard, the reported posterior mean for “Wealth: Richest” is negative and significant. This finding suggests that the odds of women using modern contraceptives is 0.55 lower if a woman's household is classified as rich compared to women from poorer households. It appears that this finding refutes Becker's (1960) hypothesis. One implication of this deduction is that women who belong to poor households tend to use modern contraceptives, all other things being equal. A negative relationship was also found between a woman's age and her choice of modern contraceptive use.

It is worth noting that while the present study harnessed the richness of the 2016 SADHS, one limitation of this data set is cross-sectional. One cannot explore the trends regarding the relationships between the variable of interest and modern contraceptive use. Another limitation resides in the inability of the data to disentangle couples and those male and female partners that reside together male and female partners. Based on this, the results presented in this paper should be interpreted with caution.

Concluding remarks

This paper gathered data from the 2016 SADHS to investigate the research objectives as alluded to in the introductory section. Information related to women and their partners' characteristics, notably education, fertility preference, wealth index, health decisions, employment status, age, and their clusters' longitudes and latitudes, were explicitly selected for analysis. After estimating hierarchical logistic models using the information mentioned above, a rigorous analysis of the results ensued. First, the findings illustrated that the choice of modern contraceptive use was best explained through a hierarchical logistic than single-level logistic modelling. This finding also led to the conclusion that spatial heterogeneity matters. Second, the empirical results suggest that space does not count as far as modelling the random-effects component is concerned. It also meant that the non-spatial hierarchical model is suitable in explaining the relationship between male partners' influence on a woman's choice to use modern contraceptives in South Africa. Third, the results pointed out that male partners' education level and employment status are determinants of South African women’s modern contraceptives use. This finding highlights the importance of male partners' education in contraceptive use. Of course, further research is needed to elucidate the dynamics of the relationship between the role of maale partners and women's modern contraceptive use.