A multidimensional approach [18, 32], in which different dimensions of SEP are measured separately, provides a framework for disentangling socioeconomic inequalities in health in a way that is not possible with a composite index such as the widely used World Bank HWI. In Colombia, we show that inequalities in contraceptive behaviour by Physical capital were larger than by Public and Human capital dimensions of SEP. Inequalities in never use of modern contraceptive methods associated with Public and Human capital were also important, especially for women in rural areas. Importantly, the impact of education on contraceptive behaviour tended to be weaker for households with high access to Public capital and stronger in households with low access to Public capital. As far as the authors know, this is the first time this approach is used to analyse Colombian data. In low and middle income countries where monitoring poor-rich inequalities in health has become a central policy objective, for example in the context of the Millennium development Goals , a multidimensional approach provides an alternative theory-driven use of existing survey asset data that moves beyond a one-dimensional measure of SEP to provide understanding into the effects of multiple dimensions of SEP in health inequalities.
To construct the asset-based measures of SEP the composite HWI was divided into two dimensions: material (Physical capital) and publicly provided services (Public capital), and a third dimension was added based on the level of women's educational attainment (Human capital). Previous studies have used similar dimensions to construct asset-based measures of SEP in the absence of data on income and/or expenditure [18, 22, 32]. We found that for contraceptive behaviour, the magnitude of inequalities varied with each of the dimensions of SEP studied. Houweling et al.  explored the HWI and three alternative asset-based indices as measures of inequality in under-5 mortality and measles immunisation. They found that the observed poor-rich differences in both outcomes were sensitive to the measure used. The size and direction of change varied per country, index and health outcome. Others have observed similar results [14, 34].
We have found that grouping a large number of assets into coherent dimensions compared to the composite HWI, facilitates an intermediate level of analysis , by comparing the magnitude of inequalities in contraceptive behaviour for each dimension. In Colombia, our findings illustrate that for women in rural areas the magnitude of inequalities in contraceptive behaviour were larger in all SEP dimensions when compared to urban women. This approach is attractive because it can allow a different set of questions to be asked; instead of focusing exclusively on economic social class or women's level of education as determinants of contraceptive behaviour we can analyse the relative importance of different types of socioeconomic inequalities (e.g. Human, Physical and Public capital) and how these may vary in different places of residence [26, 32].
For the Public capital measure, there is clumping and truncation in the distribution, explained by the few indicators available. This gap makes it impossible to distinguish between the households in urban and rural samples that report access to all services (see Table S1 additional file 1) [17, 32]. Houweling et al  found a similar result and explained this phenomenon on the basis of the choice of variables included in the index. Our results suggest that additional indicators of public services e.g. access to public transport and road infrastructure at the household and community level should be considered to refine the stratification amongst the richer groups, both in urban and rural areas .
Women's level of education was selected as the only component of Human capital because information on education, either measured as years of education or achieved level of education, is the most widely used proxy for Human capital in Latin America [18, 20, 22]. Other possible indicators of Human capital include information on partner's level of education and occupation of household members. Our approach used Human capital as an individual level measure, whereas HWI, Physical and Public SEP dimensions correspond to household level information. The use of a household level measure of Human capital is a possible future direction in a multilevel framework .
Explaining socioeconomic inequalities in modern contraceptive use
This study shows that a multidimensional asset-based approach provides a theoretical advantage in health inequalities research. Separating different dimensions of SEP and studying their interaction effects enhance the extent to which we are able to explain these inequalities. This study found that measures of contraceptive use were strongly associated with SEP dimensions that reflect material pathways (Physical capital, Public capital) and psychosocial pathways (Human capital) as well as the composite HWI. These findings suggest that the well known effects of women's education on contraceptive behaviour  were confirmed in this study, particularly for women's lifetime prevalence of modern contraceptive use. The literature on the education-fertility relationship has consistently shown that the experience of education has a lasting impact for women's lives that serves as a resource of knowledge and empowerment, as a vehicle of socioeconomic mobility and as a modifier of attitudes that influence women's reproductive desires and behaviour [5, 7–10]. Importantly, in rural areas all three dimensions of SEP, Human, Public and Physical capital identified inequalities in contraceptive use. This finding suggests that in addition to education, material living conditions and access to publicly provided services play an important role in women's contraceptive behaviour, particularly for current non-use of modern contraceptive methods. These results do not undermine the importance of education, but point out to the cyclical relationship between disadvantaged living conditions, lower educational levels, and higher fertility trends observed in the region; mainly in rural areas and in urban slums with severe lack of public infrastructure [6, 11].
Besides asking which socioeconomic dimensions are important for women with respect to their contraceptive behaviour, we also investigated how these dimensions may interact and for which social groups. Our findings of an interaction between Human capital and Public capital in rural areas suggests that provision of public services to the household has a compensatory effect for women with lower levels of Human capital with respect to contraceptive behaviour. Similarly, a study in Peru found an interaction between Public service availability at household level and maternal years of education with respect to their children's nutritional status. Nutritional status was higher among children in households with access to public services compared to those without them when mothers had less years of education, but this contrast was not evident among more educated mothers . These important observations emphasize that public provision of infrastructure could substitute or complement the effect of level of education among women who lacked educational opportunity in relation to many aspects of personal and family health [22, 24, 25].
The interaction between level of education and Public capital in relation to contraceptive behaviour in DHS 2005 takes the expected form. Among households with high Public capital the education gradient is smaller, while among households with low Public capital it is larger. There may be two explanations for our findings. First, women in households with high Public capital may have better access to family planning through health insurance , yet the inclusion of health insurance cover had no effect in the interaction model. Second, better living conditions may influence contraceptive use through higher physical wealth and resources in the household . Households with high Public capital do differ from low Public capital households particularly in terms of physical wealth (ownership of durable goods and housing quality) in urban and rural areas. However, we demonstrate that the interaction remains after adjusting for household wealth (Physical capital) consistent with an independent effect of public services provision.
On the other hand, the combined effects of low levels of education (Human capital) and low Public capital may operate as a bottleneck for family planning interventions in deprived urban and rural areas in Colombia. The evidence that higher provision of Public capital compensates for low levels of Human capital suggests that government investment in public services is even more necessary in areas where women with lower levels of education are clustered . The socioeconomic gap in contraceptive use documented in Colombia in the past decade  is likely to decrease with improvement of household living conditions and community infrastructure. Other dimensions such as availability and accessibility to family planning programmes, domestic violence, ethnicity, religious attitudes and cultural norms about sexual and reproductive health, could be key to understanding our findings, especially in rural areas in Colombia where the Catholic Church remains a strong influence on family planning [12, 37].
Future studies could investigate two other possible mechanisms. First, Public capital could be a proxy for local economic development, with better public infrastructure and social organisation such as health programmes or services in those areas that have mains water, sewage and electricity . Households with higher Public capital may be more exposed to family planning campaigns, closer to pharmacies and hospitals and other factors associated to family planning uptake [6, 12]. Second, higher levels of Public capital could benefit women in their household chores (e.g. household access to water, garbage collection) and indirectly provide women with autonomy that may translate into spare time to participate in activities that enhance women's health and status e.g. social activities and use of health services .
The results of this study should be carefully interpreted for the Colombian population as some marginalized groups, such as the internally displaced population, are likely to be underrepresented in the sample. Another limitation is the restriction on asset data for the construction of the asset-based measures of SEP. The DHS for Colombia 2005 was not designed for collecting information on assets, and although the indicators included cover a wide range of assets, information on other type of assets, such as livestock and land ownership, relevant for assessing SEP are absent from the data [14, 15, 17]. Secondly, health insurance coverage is a poor proxy for access to family planning as the most common sources of contraceptive methods in Colombia are pharmacies and Profamilia, a private family planning agency . Finally, the definition of 'being at risk of pregnancy' for single women on the basis of women's report of recent sexual activity is debatable i.e. highly educated single women might be less likely to report sexual activity. The exclusion of single women with a non-response to sexual activity in the month of interview could lead to biased results.