### Defining and measuring socio-economic position

Socio-economic position (SEP) is a concept widely used in epidemiological research. Definitions vary, but commonly incorporate physical resources, social resources, and status within a social hierarchy[1]. Measurement of SEP is crucial not only for studies focusing on the social determinants of health, but also for the vast majority of observational health research, since SEP is likely to confound many relationships.

Traditionally, indicators of SEP have tended to be monetary measures such as income or consumption expenditure, based on the assumption that material living standards largely determine well-being[2]. Whilst it is now widely recognised that monetary measures of SEP fail to capture all of the diverse aspects of well-being, their use remains widespread, partially due to difficulties in measuring more complex conceptualisations of SEP, and because monetary measures may have clearer policy implications. There is longstanding debate about whether income or consumption expenditure is a better measure of SEP. Income is generally more variable than consumption; Friedman's permanent income hypothesis states that households are likely to base their consumption decisions on more than just their current income – people tend to 'smooth' their consumption in times of income fluctuation, for example by borrowing or drawing on savings in times of low income[3]. It is therefore widely asserted that consumption expenditure is a better marker of long-term SEP than income. This argument holds particularly strongly in low-income countries, where income may come from a variety of sources and may vary dramatically across seasons. Longer-term aspects of SEP are thought to be most relevant to many health outcomes, adding to the reasons for choosing consumption expenditure over income.

In low-income countries, measurement of consumption expenditure is fraught with difficulties. There are problems with recall and reluctance to divulge information. Additionally, prices are likely to differ substantially across times and areas, necessitating complex adjustment of expenditure figures to reflect these price differences[4]. Furthermore, collecting consumption expenditure data requires lengthy questionnaires that must be completed by skilled and trained interviewers. There are therefore both reliability and cost/time reasons why epidemiologists conducting health research in low-income countries may wish to use an alternative measure of SEP. Additionally there are existing datasets rich in health data, such as the Demographic and Health Surveys (DHS), which lack information on income or consumption expenditure.

### The asset-based approach to measuring socio-economic position

An asset-based approach to measuring household SEP is one alternative to income and consumption expenditure. This approach has arisen from demographic studies such as the DHS, which although lacking data on income or consumption expenditure, collect information on ownership of a range of durable assets (e.g. car, refrigerator, television), housing characteristics (e.g. material of dwelling floor and roof, toilet facilities), and access to basic services (e.g. electricity supply, source of drinking water). These items were all originally included in the surveys for their direct influences on health; for instance, television and radio ownership was of interest to identify households receiving public health messages. Researchers began to see that these assets could be used as indicators of living standards and have sought to construct wealth indices for that purpose[2, 5]. Wealth indices measure SEP at the household level and can only be used to assess relative SEP within a population.

Collection of asset data has been claimed to be more reliable than income or consumption expenditure, since it uses simple questions or direct observation by the interviewer and should therefore suffer from less recall or social desirability bias[6]. This claim has, however, been questioned by a recent study which demonstrated at best moderate inter-observer and between-test reliability for asset data collection[7].

An asset-based wealth index could be theorised to represent long-term SEP in a similar way to consumption expenditure; asset ownership is likely to be based at least partially on economic wealth and household assets are unlikely to change in response to short-term economic shocks. There is, however, continuing debate about the appropriateness of considering a wealth index as a proxy for consumption expenditure. Two separate studies have demonstrated weak correlation between consumption expenditure and wealth indices: a study in Mozambique showed a Spearman's rank correlation coefficient of 0.37[8], and a study using multiple datasets producing R^{2} values from regressions of consumption expenditure on a wealth index of ≤ 0.23[9]. A study using Indonesian data found that there was considerable re-ranking of households between a wealth index and consumption expenditure, with approximately 50% of households being misclassified when the population was split into the bottom 30%, middle 40% and top 30%[10]. Other studies have demonstrated considerable variation in the correlation across countries, with Spearman's rank correlation coefficients between 0.43–0.64 in one study and 0.39–0.71 in another[6, 11]. It could be argued that a wealth index captures a longer-term state of wealth than consumption expenditure; in times of economic shock, selling assets is likely to come subsequent to reductions in consumption expenditure. As both measures attempt to measure long-term SEP, and since it is useful to have a standard against which to judge wealth indices, we will consider consumption expenditure as a gold standard measure of long-term SEP, and explore the extent to which wealth indices agree with consumption expenditure.

### Weighting the items in a wealth index

When constructing a wealth index from a set of variables, a decision must be made about the weights to assign to each indicator. Principal Components Analysis (PCA) was recommended as a method for determining weights for components of a wealth index by Filmer and Pritchett[11]. Guidelines for the use of PCA for wealth indices were published by Vyas and Kumaranayake[12].

PCA is a 'data reduction' procedure. It involves replacing a set of correlated variables with a set of uncorrelated 'principal components' which represent unobserved characteristics of the population. The principal components are linear combinations of the original variables; the weights are derived from the correlation matrix of the data or the covariance matrix if the data have been standardised prior to PCA. The first principal component explains the largest proportion of the total variance. If the first few principal components explain a substantial proportion of the total variance, they can be used to represent the original items, thus reducing the number of variables required in models[13].

For constructing a wealth index, the first principal component is taken to represent the household's wealth[14]. The weights for each indicator from this first principal component are used to generate a household score. Assets that are more unequally distributed across the sample will have a higher weight in the first principal component[12]. The relative rank of households using the score generated from the first principal component is then used as a measure of relative SEP, enabling calculation of a single estimate of the effect of wealth[15]. The use of a single principal component in this way could be questioned, since the first principal component from PCA of a set of assets frequently explains a low proportion of the total variation in those assets (often less than 20%)[11, 12, 16]. It could be the case that the theoretical 'wealth' construct is multi-dimensional, with the first few principal components each capturing a specific aspect of wealth. Using only the first principal component would, in this case, not capture the entire wealth effect. However, the aim of using PCA to generate a wealth index is to define a single indicator of SEP, and using multiple principal components would not be compatible with this. If the first principal component explains a small proportion of the total variance, each subsequent higher order component will explain a smaller proportion still, so using two or three principal components may not drastically improve the proportion of the total variance explained. It is also not generally straightforward to identify which aspects of wealth higher order principal components might represent, since there is not usually a clear pattern of which assets are assigned positive/negative or higher/lower weights. Furthermore, there is some evidence that utilising higher order principal components is unnecessary. McKenzie demonstrated that the standard deviation of higher order components was not associated with consumption expenditure, whereas that of the first principal component was[16]. Filmer and Pritchett noted that multivariate analyses of the association between the wealth index and school enrollment were robust to the inclusion of higher order components[11].

After the paper by Filmer and Pritchett, the use of PCA for wealth index construction was quickly adopted by the World Bank and Macro International Inc. for analysis of inequalities within DHS datasets[5, 17–19]. The approach is now also more widely used. Nevertheless, this application of PCA is not fully justified and requires further investigation. PCA is designed for use with continuous, normally-distributed data. Its application to the predominantly discrete data in a wealth index is therefore inappropriate. The use of binary dummy variables for each category of categorical variables (as recommended by Filmer and Pritchett[11]) is particularly problematic. The linear dependence between the dummy variables may lead to incorrect estimates of the wealth index; the PCA method is affected by collinearity, with variation in the data arising both from the underlying concept of wealth and from the linear dependence between dummy variables of categorical variables. This approach has been shown to be inferior to several alternative methods of dealing with categorical data[20]. The alternative methods explored were using ordinal variables, using group means, and using polychoric correlations. These methods, whilst being preferable in terms of the data assumptions of PCA, do require strong assumptions about the ordinal nature of the data. It is not necessarily straightforward, for instance, to rank different sources of drinking water, and to assume that they are equally spaced from each other in terms of their relationship with SEP.

The limitations of PCA for the construction of wealth indices are thus twofold: i) PCA is problematic with the discrete data commonly included in a wealth index, and ii) the first principal component frequently explains only a low proportion of the total variation in asset data. Furthermore, PCA is a fairly complex method. It is likely to be unfamiliar and poorly understood by less technical readers of papers. It could therefore be argued that simpler, more familiar and easily understood methods for weighting the items in a wealth index would be preferable. Using an equal weights approach (simple sum) was used in several early studies using wealth indices[21, 22]. Although simple, this approach could be criticised for being arbitrary and simplistic, since different assets are unlikely to have equal meaning in terms of SEP. The literature comparing indices constructed using PCA and using an equal weights approach is not consistent. There is some evidence that PCA performs no better as a proxy for consumption expenditure than an equal weights approach[23]. In contrast, Bollen *et al*. showed that a PCA-based wealth index and an equal weights index had considerably different regression coefficients with consumption expenditure[24]; another study also demonstrated that a PCA-based wealth index had a stronger relationship than an equal weights index with a latent variable of permanent income (planned and anticipated income, a long-term concept of SEP that both consumption expenditure and wealth indices have been claimed to be measuring)[25].

Another potentially simpler and more easily understood alternative to PCA is to use the inverse of the proportion of households that own an asset as its weight. This is based on a method originally suggested by Townsend[26]. The underlying assumption is that assets owned by a smaller proportion of households are indicative of higher household wealth and are therefore assigned a higher weight[27]. A problem with methods using inverse proportion weights is that not all assets show a linear relationship with living standards, e.g. ownership of a motorbike may tend to increase up to a certain income and subsequently decrease in richer households[5]. A similar method was applied by Morris *et al*., who calculated weights by using the inverse of the proportion of households that owned each item, multiplying that by the number of units of asset owned by the household, and summing this quantity for all assets[28]. Both the equal weights and the inverse proportion weighting methods can only be applied to binary data.

Multiple Correspondence Analysis (MCA) is analogous to PCA, but is for discrete data[29]. Whilst this method does not remove the complexity and unfamiliarity of PCA, nor the problems of the first dimension explaining a small proportion of the total variance, it is appropriate for the analysis of the categorical data commonly collected on most assets[30]. Booysen *et al*. utilised MCA to construct wealth indices for seven sub-Saharan African countries. They found that the index was very highly correlated with one constructed using PCA, and that although households were not always in the same quintile by the two indices, movement was in most cases limited to one quintile in either direction. They also showed that the weights assigned to index items were generally similar by the two methods[30].

Other methods for weighting items in a wealth index do exist, but in general offer neither more simplicity than PCA, nor more suitability for discrete data. For instance, latent variable approaches have been proposed[31, 32]. In his 2005 paper, Montgomery constructs a wealth index using a latent variable approach called MIMIC; this model specifies which variables are determinants of living standards (e.g. education and occupation) and which are indicators of living standards (e.g. consumer durables). In other methods of wealth index construction, both determinants and indicators of the underlying socio-economic construct may be included without distinction. For instance, producer durables such as farm equipment are sometimes included in a wealth index in the same way as consumer durables, whereas these should in fact be considered as determinants of the socio-economic construct and not treated in the same way as indicator variables[31]. Latent variable methods, despite offering some theoretical advantages over PCA, are far more complex and arguably even less easily understood by a wide readership than PCA. A further option could be to assign weights based on the price of an item, but this requires detailed information allowing for date of purchase, area of purchase, and current condition of the item. There is also some evidence that price-based indices are less reliable than alternatives; one study showed a price-based index to have implausible relationships with health outcomes[33] and a further study demonstrated that two price methods had weaker relationships with a permanent income latent variable than alternative weighting methods[25]. In contrast, however, Morris *et al*. showed high correlation between wealth indices constructed using the inverse proportion method and weights based on the current value of each item[28]. The issue of prices is a crucial one. Consumption expenditure measures are adjusted for the variability of prices across regions. In contrast, the variability in prices is generally ignored when pooling data across regions to construct a wealth index. The methods currently used in the literature to incorporate prices into weights for wealth index indicators (typically relying on self-reported current sale value) do not, however, appear to be appropriate, and more complex methods involving regional price data calculation similar to the approach used for consumption expenditure data would probably be too costly for the majority of epidemiological studies.

### Which concept of long-term SEP does a wealth index represent?

Both consumption expenditure and wealth indices are measured using household-level data. Equivalence scales are generally applied to consumption expenditure data in order to allow for household size and composition. The most frequently used equivalence scales are per capita (i.e. divided by the total number of household members), per adult or per adult equivalent (where each child is considered to require a pre-determined proportion of the consumption of one adult). Wealth indices, however, are not generally adjusted for household size or composition. There is some evidence that adjusting a wealth index for household size results in implausible relationships with health outcomes[5]. It has also been argued that while consumption needs and patterns will obviously be strongly affected by household size and composition, the benefits of most items included in a wealth index are at the household level[5]. It has, however, been demonstrated that wealth indices and per capita expenditures produce very different patterns in household size; in 11 low-income countries, the poor-rich difference in average household size was consistently greater when using per capita expenditures compared with a wealth index[34]. This indicates that households with a greater number of members, a factor often associated with poverty, would not always end up in the lower quintiles of a wealth index.

In considering the appropriateness of a wealth index as a proxy for consumption expenditure, it has been suggested that the choice of equivalence scale may have a substantial impact on the observed relationship. Sahn and Stifel suggested that the correlation of a wealth index would be highest when total household expenditures were considered, intermediate when a per adult equivalence scale is used, and lowest when per capita consumption expenditure is used[6]. There is, however, no evidence of this presented in the current body of literature.

### Aim

The aim of these analyses is to compare wealth indices constructed using different weighting methods to identify whether PCA offers an advantage over either simpler, more transparent methods (equal weights and inverse of the proportion of the population owning the asset) or methods more appropriate for discrete data (MCA). Furthermore, the agreement of a wealth index with consumption expenditure measures adjusted for household size and composition in different ways will be examined to identify which aspect of long-term SEP a wealth index best represents.