Exploring unobserved household living conditions in multilevel choice modeling: An application to contraceptive adoption by Indian women
Exploring unobserved household living conditions in multilevel choice modeling: An application to contraceptive adoption by Indian women
JoseÂ G. Dias 0 1
Isabel Tiago de Oliveira 1
0 Instituto Universit aÂrio de Lisboa (ISCTE-IUL), BRU-IUL , Lisboa, Portugal, 2 Instituto UniversitaÂ rio de Lisboa (ISCTE-IUL), CIES-IUL, Lisboa , Portugal
1 Editor: Karyn Morrissey, University of Exeter , UNITED KINGDOM
This research analyzes the effect of the poverty-wealth dimension on contraceptive adoption by Indian women when no direct measures of income/expenditures are available to use as covariates. The index±Household Living Conditions (HLC)±is based on household assets and dwelling characteristics and is computed by an item response model simultaneously with the choice model in a new single-step approach. That is, the HLC indicator is treated as a latent covariate measured by a set of items, it depends on a set of concomitant variables, and explains contraceptive choices in a probit regression. Additionally, the model accounts for complex survey design and sample weights in a multilevel framework. Regarding our case study on contraceptive adoption by Indian women, results show that women with better household living conditions tend to adopt contraception more often than their counterparts. This effect is significant after controlling other factors such as education, caste, and religion. The external validation of the indicator shows that it can also be used at aggregate levels of analysis (e.g., county or state) whenever no other indicators of household living conditions are available.
Data Availability Statement: This study used
globally authorized, publically available, and
nationally representative DHS data sets from India
collected in 2005 and 2006. All data used in this
study were obtained from DHS Program website
cfm). The data sets are publicly available free of
cost for research purposes upon registration and
request. The study used individual and household
files for the analysis. The DHS is a global program
supported by the United States Agency for
International Development and ICF International,
The modeling and understanding of social and health phenomena are heavily dependent on
socioeconomic measures, i.e., the economic resources available to individuals and households.
In most theoretical frameworks, the socioeconomic dimension needs to be controlled as a
covariate and methods are therefore required to estimate the economic resources available to
individuals and households. These resources can be divided into material wealth and
intangible resources such as education and skills [
]. Income and consumption data are the most
popular measures of material wealth or standards of living [
]. Income refers to the earnings from
productive activities and current transfers; consumption refers to resources actually consumed
and is expressed by expenditure data. Measured income often diverges from measured
and conducts surveys worldwide to collect
highquality data to measure demographic and health
status of various nations.
Funding: This research was supported by the
FundacËão para a Ciência e Tecnologia (Portugal),
Grant PTDC/CS-DEM/108033/2008, UID/GES/
00315/2013, and UID/SOC/03126/2013.
consumption as it is possible to save from income and to finance consumption from
]. Despite a lively debate on which is the best measure of material wealth, there is some
agreement that the smooth nature of consumption makes it the most suitable measurement of
the economic component of living standards [
]. Moreover, less developed countries often
report inaccurate income data, which are further masked by various forms of informal earning
mechanisms, such as self-employment and economic activities within and outside the
household, particularly in rural settings. In these contexts, it is generally far easier to measure
consumption than income .
Many surveys in developing countries do not collect data on income or expenditures as
they tend to be unreliable and lack standards for comparison between socioeconomic groups.
Nevertheless, the Demographic and Health Surveys (DHS) collect and disseminate accurate
and standardized data on household assets and dwelling characteristics for nationally
representative samples. In addition to these indicators, these surveys collect data on fertility,
reproductive health, maternal and child health from about 90 countries. The sampling design and
survey instruments are standard across countries, thus allowing for cross-country analyses.
Additionally, the DHS data sets are accessible to users including academic researchers and
those from national and international agencies, at http://dhsprogram.com/. As a result, the
DHS has become a standard source for international research on demography and health
(particularly maternal and child health) in developing countries. Notwithstanding, although
expenditure data is very useful, it is not widely collected in retrospective surveys. DHS is no
exception to this.
These international surveys collect systematic data on household assets and dwelling
characteristics (e.g., radio, TV, car, access to drinking water, type of toilet facility, roof material).
Although it is important to acknowledge the range of variables available for the measurement
of household wealth, it is often difficult to encapsulate all variables into a single score variable
and also measure each one with respect to the outcome variable. Some researchers have
proposed measures of material wealth [5±8]. While the variables considered in the construction
of a wealth index are not based on any valid theoretical foundations, they provide a proxy to
represent the socioeconomic dimension. It has been shown that this type of indicator is a
reliable measure of expenditures [9±11]. For instance, Tasciotti and Wagner [
] compare census
and survey data for Malawi and conclude that ªthe LSMS and DHS data are not only highly
comparable but also representative as demonstrated by the comparison with the 2008 censusº
(p. 23). Recently, Batana [
] took the broader perspective of Sen's definition of poverty rather
than using the poverty-wealth dimension. He goes beyond defining poverty on the basis of
material assets by adding other indicators such as schooling, BMI (body mass index), and
The literature offers at least two approaches in which a range of household assets and
related dwelling characteristics are weighted in the overall index: a) the a priori approach in
which the index results from a sum of indicator or dummy variables for whether a household
possesses certain assets [
]; b) the a posterior approach that deals with latent variables or
underlying dimensions and weights are factor loadings.
Different techniques have been applied to DHS data sets. The most common techniques
used to derive a posterior scores are: principal component analysis [
] and factor analysis
]. Booysen et al. [
] argue that multiple correspondence analysis is more appropriate for
the non-metric nature of observed data.
The DHS data set provides the Wealth Index (WI), originally introduced by Filmer and
]. This index measures the poverty-wealth dimension at the household level using
the first dimension/factor results from a principal component analysis (based on the
household assets and dwelling characteristics). An important feature of the DHS data is that the
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individual-level demographic information can be easily linked to household socioeconomic
data collected at the time of the survey. Additionally, DHS surveys make the WI available as an
indicator of households' socioeconomic dimension [
]. It has become usual to use this index
to address the poverty-wealth dimension in demographic and health research in developing
countries, because the WI is included in the Demographic and Health Surveys databases
available for scientific research.
Conceptually speaking, it is particularly interesting to assume that although household
living conditions cannot be observed directly, the level of this latent variable is reflected in a set of
manifest or observed variables [
]. Factor analysis is just one of these latent variable models but
it is inappropriate for modeling household living conditions because it assumes that both latent
and manifest variables are continuous. Indeed, most variables in the Demographic and Health
Surveys that measure dimensions of household living conditions are collected using nominal
and ordinal scales of measurement, and hence nonmetric (discrete) data. We conceptualize
Household Living Conditions (HLC) as a continuous latent variable that is measured by an item
response theory (IRT) model [18±19]. IRT focuses on the development of an accurate battery of
items to measure and score tests. It was first proposed in the field of psychometrics for the
purpose of ability assessment. It is used in social sciences (namely education and psychology) to
measure different kinds of ability (e.g., foreigner language skills) or more general traits (e.g.,
intelligence, consumer behavior, attitudes). The manifest variables are nonmetric (e.g., binary,
ordinal), which makes it a popular alternative to factor analysis and principal component
analysis in health and social sciences, for example [20±21]. The IRT methodology is also fundamental
in the assessment of international programs [
]. For example, in the context of poverty
measurement, IRT was applied in Spain and Malawi to measure household wealth [23±24].
This research combines latent variable modeling with choice modeling, taking Household
Living Conditions (HLC) as a latent covariate. Thus, our proposal integrates both analyses
into a single-step model using a probabilistic framework. Contrary to Oliveira and Dias [
and Oliveira et al. [
] in which the WI provided by the DHS database was used to capture the
poverty wealth impact on contraception adoption and to discriminate different contraceptive
methods, respectively, this paper estimates the household living conditions and the choice
model, simultaneously. Additionally, the latent variable HLC can be explained by covariates.
Our application employs this new method to the study of the impact of household living
conditions on the most important long-term variable in population dynamics: fertility. The study of
fertility in India is crucial to the whole World. The United Nations Population Prospects [
estimate that India will soon become the most populated country in the World, surpassing China, as
a result of both a very young population structure and fertility above the replacement level.
Despite successive government efforts to promote family planning since the second half of the
20th century [
], India continues to have a comparatively high level of fertility even by Asian
standards. In fact, fertility in India is currently above the average for Asia and, notably, for China
(2.44 children per woman in 2010±15 vs. 2.20 and 1.60 respectively ).
This research aims to integrate a non-demographic complex and multidimensional factor
(the poverty-wealth dimension) with a demographic health outcome (fertility regulation by
means of contraception). The association of wealth and health is relevant in social sciences and
epidemiology. The specific relation between contraception and the socioeconomic dimension
is the subject of numerous studies in developing countries, frequently within the context of
maternal health research [30±32]. Studies on contraceptive behavior and the socio-economic
situation in developing countries reveal important differentials associated with the wealth
dimension, education, and other socio-economic characteristics. Overall, multivariate analyses
that simultaneously include women's education (a usual proxy for SES±Socioeconomic status)
and wealth (measured by the classic Wealth Index) demonstrate that both affect contraceptive
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adoption, even after controlling for other factors. The better off tend to adopt contraception
more frequently than their counterparts [30±33].
The paper is structured as follows. The next section describes the methodology for
estimating the impact of a latent covariate on the dependent variable, controlling other observed
covariates. A case study then addresses the impact of the socioeconomic context on the choice
of contraceptive methods by Indian women. The purpose of this analysis is to take a latent
variable approach based on household characteristics to estimate the impact of household living
conditions on contraception adoption. Results are validated by comparing our estimates with
official statistics from India. The paper concludes with further potential extensions and
applications of this integrated framework.
Multilevel choice modeling with a latent covariate
The proposed framework takes the form of a probit regression model with a latent covariate,
more specifically, the Household Living Conditions (HLC) indicator, measured by a set of
items using an Item Response Theory (IRT) model. Most surveys tend to collect data at
different levels of the hierarchy using complex sampling. For example, individuals may be clustered
within regions or countries. In this context, the traditional assumption of independence is
violated and this nesting structure needs to be addressed using multilevel modeling [34±36]. The
proposed multilevel probit regression model with a latent covariate is depicted in Fig 1 for
observation i in cluster j, where boxes show observed variables and the circle represents the
latent variable. The total number of units of the upper level is indicated by N and within cluster
j is designated by nj. The total sample size is PjN1 nj.
The binary dependent variable is Yij and is explained by the latent variable zij and a set of P
observed covariates (xijp). Let pij be the probability of success for observation i in cluster j, i.e.,
pij = P(Yij = 1 | xij, zij). This binary model defines a latent variable Yij and a threshold value of τ:
we observe a success if Yij > t, i.e., in this case Yij = 1. The linear component of the model is
given by Yij x0ijβ gzij uj ij, where xij is the vector that contains the P observed
covariates for observation i in cluster j, β is the vector of regression parameters (fixed effects), γ is the
parameter of the linear effect associated to the latent household living conditions indicator
(loading), zij is the latent household living conditions, uj is the random effect for cluster j, and
ij is the error term. The threshold replaces the intercept in the model, whereas the random
effect (uj) represents factors affecting Yij that are shared by all units within cluster j after
controlling individual covariates and the latent factor. The probit regression framework assumes
standard normal errors and random intercepts (uj) are independent of the errors ij and
normally distributed: uj N
This single-step approach is completed with the definition of the latent variable, household
living conditions (HLC), measured by a set of K observed items (vijk, k = 1,. . ., K). This model
can be interpreted as a factorial model with a continuous latent variable and discrete manifest
variables (see Fig 1) and when used autonomously, it is called the IRT model [
]. The IRT
specification here uses the factor-analytic parameterization, which is similar to the Yij
specification, i.e., it is given by the loading and threshold parameters for each item. The traditional
2-P definition of the IRT can be derived from this factor analytic specification . The
difficulty and discrimination of the item are given by the ratio threshold/loading and loading,
respectively. The difficulty parameter in the present context indicates how rare the item is in
the household. The discrimination parameter is a measure of an item's differential capability,
i.e., a high discrimination parameter value suggests an item that has a strong ability to
differentiate households. For each binary manifest variable k, we estimate the threshold and the
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loading parameters. Like in factor analysis, we assume that this latent variable score follows a
normal distribution. The variance of the latent variable is fixed at 1 to maintain the coefficients
of the latent variable identified (γ). Because the score may vary for different contextual
variables, this model allows distinct control variables wijl, where l = 1,. . ., L. Thus, zij has expected
value θ1wij1 + + θLwijL and unit variance, where θl measures the impact (slope) of
concomitant variables wl on the zij (HLC). Note that the intercept is zero so that the model remains
identified and the slopes provide the departure from the reference category. This submodel is
called the concomitant regression model.
The model was estimated using the maximum likelihood method using MPlus. This
computes maximum likelihood estimates with standard errors given by the sandwich estimator
that is robust to non-normality and non-independence of observations [39, p. 533]. The
complex design of the sample (weights) was taken into account [
A case study: Modeling contraceptive adoption in India
Population, sample, and variables
We apply the integrated model to data from the Indian National Family Health Survey
(NFHS) from 2005±06 (NFHS-3) [
]. The NFHS provides a representative nationwide sample
of Indian women. This data set was downloaded from the official website of the DHS program
(https://dhsprogram.com), after obtaining permission from the DHS team. The Demographic
Fig 1. The multilevel choice model with a latent covariate.
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and Health Surveys (DHSs) are free and public data sets. Researchers have to register with
MEASURE DHS and submit the request before access to DHS data is granted. This is the most
recent survey with a representative sample on the Indian population providing data for
research purposes (a new DHS is now ongoing in India, but no data are available yet). This
survey belongs to the DHS series and covers a large number of questions on women's fertility
and contraceptive practices, maternal and infant health, in addition to the usual individual
sociodemographic characteristics and the household assets and dwelling characteristics.
The original database with all women of fertile age was reduced to a smaller one with 31197
cases. The aim was to focus only on the women that may, or not, need to use family planning
methods. In many Asian countries, including India, contraception is largely an issue for
married women as unmarried women are not expected to engage in sexual relations [
instance, 99.3% of the women in the sample who answered questions on contraception were
married and only 0.7% unmarried women had sexual experience (own computation based on
values presented in [41, p. 121]). We select only fecund married women (with non-sterilized
husbands) with sexual experience and living in the household (excluding the ªnot the de jure
populationº). This new data set only includes unsterilized and recently sterilized women as the
association between the current socioeconomic situation and contraceptive behavior cannot
be established if sterilization took place a long time ago. On the other hand, the issue of
endogeneity must not be overlooked; in addition to the influence of household living conditions on
women's contraceptive adoption, contraceptive choices can also have reciprocal effects. This
selection of a subsample minimizes these effects.
The dependent variable, current use of contraception, is denoted by Yij and is coded as
either 1 (success: use of contraception) or 0 (failure: no use of contraception). Thus, it is
binary: the contraceptive users may have adopted any traditional or modern method and
nonusers used no form of family planning at the time of the survey. When examining the marginal
impact of the household living conditions on women's contraceptive adoption, we need to
control for the effects of other variables in the model. We examine the effects of life cycle
variables (age, number and sex composition of offspring), residence (urban vs. rural and nuclear
vs. joint households), and other socioeconomic and cultural factors (caste system, religion,
education and occupation). Thus, apart from material wealth, we control for other types of
wealth (e.g., social capital) that may have an impact on contraceptive adoption. For instance,
both education and wealth index tend to be included as covariates in the context of India (see,
]), and even in analyses with a broader geographical spectrum (see ).
A set of items is used to measure the latent variable. The items include dwelling
characteristics i.e. type of flooring, type of toilet facility, cooking fuel, household electrification, glass
windows, as well as household assets such as a pressure cooker, telephone, color television,
refrigerator, computer, car, and motorcycle/scooter. The binary variable, urban/rural, was
added to the model as a concomitant variable. It has been shown that there is a difference in
the distribution of the Wealth Index in rural and urban environments in many countries, and
India is no exception (e.g., [
The community or place of residence (Primary Sampling Unit (PSU)) constitutes the upper
level in this multilevel model taking into account the hierarchical structure of data and
adjusting for the community effects. Sample weights at the household level are included in the NFHS
data and are based on the complex sample design of the survey.
The sample description (Table 1) shows that the large majority of women in the sample live in
rural areas. Contraceptive prevalence is clearly lower in rural than urban settings. A relatively
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high proportion of women from nuclear families use contraception, but these women
comprise less than half of the sample. Women in the middle of the fertile ages are the most typical
users of contraception and family planning methods; this is closely linked with the number
and sex composition of offspring. Religion is another important factor, and Muslim women
use contraception less frequently. Contraceptive prevalence is also lower among women from
scheduled castes, tribes, and other backward classes than for women that do not classify
themselves in any of these categories. For female education, there is a strong gradient for the
adoption of family planning methods: contraceptive prevalence rises as the level of women's
Measurement of Household Living Conditions (HLC)
Contraceptive choice results
The tendencies observed in this first description are analyzed by means of a multilevel probit
regression model with a latent covariate. This probit model estimates the impact of HLC and
controls for other factors (e.g., life cycle variables and residence factors). We note that the
impact of age and HLC on Yij is specified to be quadratic. Thus, for instance, for HLC (zij)
we have glinearzij gquadraticzi2j in the linear component of the model. These joint effects of
household living conditions on the regression model are particularly important. If we fail to reject H0:
γlinear = γquadratic = 0, HLC, which is measured by a set of indicators and explained by the
concomitant variable urban, cannot explain the dependent variable. A second model under the null
hypothesis was estimated. Based on the likelihood ratio statistic that follows the qui-square
distribution, the p-value is <10−6. And the decision is to reject the null hypothesis. Thus, HLC has
a joint effect on the contraceptive adoption.
Results from the multilevel probit model for contraceptive adoption in India reveal the
impact of HLC plus a set of covariates on contraceptive use (Table 3). More specifically, the
latent variable HLC has a significant and linear impact on contraceptive adoption: as HLC
increases, the probability of adopting contraception also increases. The non-linear impact is
Previous research on the contraceptive behavior of Indian women reveals that
contraceptive use is quite sensitive to the number and sex composition of previous births [46±48] and
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aNumber of respondents are based on unweighted data.
bPercentages are sample weight-adjusted.
Other backward class [OBC]
None of them
Less than 25 yr
35 yr or more
No formal schooling
that Muslim women adopt contraception less frequently [
] as do those from
disadvantaged social groups [
], those living in non-nuclear households [
], and those living in
rural areas [
]. On the other hand, socioeconomic factors, e.g. wealth [
] and women's
], proved important to the adoption of family planning.
Our results show that age has a non-linear effect on contraceptive adoption: there is almost
an inverted U shape relation, with the greatest likelihood of adopting contraception coming in
the most fecund ages. The number and sex composition of offspring are important factors for
the adoption of family planning methods. The residence is also a significant factor: the
probability of women living in urban areas and in nuclear households using contraception is higher
than that of their counterparts. Turning to India's traditional socioeconomic and cultural
differences, it is clear that women from scheduled tribes and other backward classes were less
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likely to adopt family planning than women in the reference category. On the other hand, both
Muslim women and women from other religious affiliations have a lower probability of using
contraception than Hindu women. Additionally, female work and education both increase the
odds of adopting family planning methods. As expected, the education gradient is very clear.
To sum up, Hindu women and women not belonging to marginal communities are the most
likely to control their fertility. On the other hand, women living in nuclear households are
more likely to use contraception than their counterparts as are women living in urban settings.
Nevertheless, it should be noted that women living in rural settings constitute the biggest
group in the Indian population.
The intraclass correlation (ICC) corresponds to the proportion of the total variability that is
explained by cluster level: ICC s2u=
1 s2. The upper level (PSU) explains 18.8% of the
Fig 2 depicts the boxplot of the PSU effects grouped by state. We notice that random effects
control the spatial dependency in the multilevel structure. Its impact on the linear component
of the model either adds or subtracts a common factor to all observations from the same PSU
and corrects the impact of the fixed effects. States from Northeast India tend to have high
absolute medians of the estimated random effect (e.g., Tripuna, Meghalaya, Assam, Nagaland). The
same happens with states from Eastern India such as Jharkhand and West Bengal. These
results show that these regions of India have specific characteristics (e.g., houses built with
different materials) that are corrected by the random effect in this two-level structure.
Finally, Fig 3 shows the distribution of the HLC in each Indian state. We observe
withinand between-state heterogeneity in terms of median and interquartile range, respectively.
Some states, such as Bihar, Assam, Jharkhand, Orissa, and Chhattisgarh, have particularly
poor HLC at the household level (median level), while others e.g. Delhi, Goa, Kerala, Sikkim,
and Maharashtra, have a better median HLC than most Indian states. In Central and East
states, scores of HLC are particularly heterogeneous (Uttar Pradesh, Assam, West Bengal,
Jharkhand, Orissa, Madhya Pradesh, Rajasthan and Bihar), whereas HLC in the North and
Northeast states (Delhi, Tripura, Manipur, Nagaland, Sikkim, Punjab, Himachal Pradesh) and
Kerala and Chhattisgarh (in the South and in the East) are the most homogeneous. In short,
the Central and Eastern states tend to be poor and more heterogeneous than the West states
and some of the Northeast and North Indian states.
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External validation of the HLC
As an illustration and external validation, we compare the HLC score (aggregated at the state
level) with the respective Net State Domestic Product (NSDP) per capita at constant prices
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Fig 2. Distribution of the estimated random effects grouped by state.
(2004±2005) for each Indian state. External validation is important as it provides a measure of
the predictive ability and generalizability of the indicator in a different (external) context [
Data on NSDP are provided by the Government of India [
]. Table 4 summarizes the mean
scores and ranking for both indicators.
Overall, we conclude that there is general agreement between the two indicators despite
their conceptual difference. The HLC tends to be broader in scope than an income-based
indicator. Fig 4 allows a more precise understanding of the relationship between these two
variables. With the exception of the two small Indian states of Goa and New Delhi, which have the
Fig 3. Distribution of Household Living Conditions (HLC) by Indian state.
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highest values, there is a strong linear relationship and Bihar occupies the bottom position.
The Pearson correlation between the HLC and the NSDPpc of 0.794 indicates a strong
association between these variables. In terms of rankings, the ordering of Indian states by the two
indicators is also strongly associated (Spearman's rho correlation = 0.853).
This paper proposes an integrated choice modeling framework which adds covariates that are
not measured directly. This is particularly important as most studies need to include control
variables, e.g. the socioeconomic dimension of the phenomenon being explained. The model
is embedded in a multilevel setting that takes the complex survey design into account.
The case study illustrates the approach by simultaneously estimating Household Living
Conditions (HLC) as a latent covariate that explains a choice process in a probit regression. It
addresses the association between contraceptive adoption and the women's household
Note: NSDPpcÐNet State Domestic Product per capita (Indian rupees); Weighted mean score.
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Fig 4. Relation between NSDPpc and Household Living Conditions (HLC) for Indian states (see Table 4 for the
meaning of acronyms of Indian states).
position in terms of the poverty-wealth dimension in India. This relation is analyzed by
allowing a latent covariate, the HLC indicator, into the model as an alternative to the standard
wealth index (WI). The new indicator is estimated as part of the model simultaneously with
the probit model for contraception. This research confirms that the household characteristics
and assets are important predictors of women's contraceptive behavior in India. Validation of
the indicator by external data from a different source (Net State Domestic Product) shows that
this new proxy is a valid measure of the material wealth. It also shows a promising application
of the household-level scores to obtain an aggregate, for instance, at county- or state- level
indicators that can be used to track poverty and inequality development goals where more
specific data is lacking. This new single-step method to obtain indicators is more consistent at a
methodological level than the usual WI and can be applied to other contexts, especially in
empirical research using DHS or similar surveys. In particular this procedure overcomes the
limitation of a lack of income/expenditure data to measure the socioeconomic dimension in
surveys that collect household assets and dwelling characteristics (e.g., DHS and MICS
(Multiple Indicator Cluster Surveys)).
From an empirical standpoint, the model can be used whenever the household living
conditions construct is conceptualized as an unobserved covariate in social and health research. The
fact that the model explicitly takes the socioeconomic dimension into account minimizes the
problem of endogeneity between the dependent and the errors that may have biased the
estimates in the model.
This model can be applied to contexts other than modeling the choice of contraception, e.g.
to measure the impact of socioeconomic status on child undernutrition [
], HIV prevalence
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[60±62], women's empowerment [
], and domestic violence [
]. Thus, this framework is a
one-step alternative to the use of WI as an external covariate. Additionally, the definition of
living conditions can be an extension of HLC by adding non-material items [
]. The IRT
structure, measuring the HLC, could also be added to more complex contraception choice
This integrated choice modeling has several advantages, particularly in dealing with the
endogeneity problems associated to the interrelated processes of wealth and health as it
estimates LHC jointly. On the other hand, two limitations must be mentioned. First, this is a
complex and sophisticated methodology and, consequently, is less accessible to a direct application
by most researchers. Second, these indicators are specific to each application and embedded in
the choice modeling with a specific dependent variable. Thus, this type of indicator should not
be used in a different context, i.e., with another dependent variable; even with the same set of
items, a new model should the estimated in a one-step approach.
Future research can also explore the application of this model to address highly correlated
covariates. Aguilera et al. [
] proposed a logistic regression model with an embedded
principal component structure for highly correlated covariates. It can be hypothesized that highly
correlated covariates are manifestations of the same latent variable or construct. In this case,
we can define an integrated factorial structure underlying the correlated covariates instead of
using an external index construction based on the principal component analysis.
The authors would like to thank the editor and three anonymous reviewers for their
constructive comments, which helped us to improve the manuscript.
Conceptualization: JoseÂ G. Dias.
Data curation: JoseÂ G. Dias, Isabel Tiago de Oliveira.
Formal analysis: JoseÂ G. Dias.
Funding acquisition: JoseÂ G. Dias.
Methodology: JoseÂ G. Dias.
Project administration: JoseÂ G. Dias.
Resources: JoseÂ G. Dias.
Software: JoseÂ G. Dias.
Supervision: JoseÂ G. Dias.
Validation: JoseÂ G. Dias, Isabel Tiago de Oliveira.
Visualization: JoseÂ G. Dias, Isabel Tiago de Oliveira.
Writing ± original draft: JoseÂ G. Dias, Isabel Tiago de Oliveira.
Writing ± review & editing: JoseÂ G. Dias, Isabel Tiago de Oliveira.
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