**INTRODUCTION**

**1.1 ****Background of the study**

Today’s healthy children can give tomorrow’s better world. So, health for children is indispensable for the development of the country. Infant and young child nutrition is essential for the foundation of human development.

Many people throughout the developing world remain vulnerable to food insecurity, under-nutrition, and ill health (World Development Report 2000). These problems tend to be particularly severe in developing countries struggling to emerge from the scourge of extreme poverty (United Nations System 5 ft report). In such countries, the health and nutritional benefits spawning from economic growth tend to be concentrated only among the economically-advantaged sectors of the population (Auerbach, JA; Krimgold, BK el al).

In Vanuatu, as in many other developing countries, under nutrition is one of the leading causes of childhood morbidity and mortality. Childhood under-nutrition affects physical and cognitive growth, impairs the immune system, and increases the risk of morbidity and mortality. Under-nutrition among children is often caused by the combined effects of improper or insufficient food intake, repeated episodes of infections, and inadequate care during sickness (Pelletier, DL). Additionally, under-nutrition affects somatic growth, impairs the immune system, and increases the risk of infection (Rice, AL; Sacco et al). In developing countries around the world, an estimated 46 million children are malnourished, 127 million are underweight, and 148 million children are adversely growth rate stunted [United Nations; 2004]. A recent comparative risk assessment by the World Health Organization estimates under-nutrition is by far the largest contributor to the global burden of disease [World Health Organization; 2002].

Previous research has associated childhood nutrition with a child’s multiple-birth status, a mother’s education and nutritional status, a father’s employment, the mother’s breastfeeding and feeding practices, access to safe drinking water and sanitation facilities, access to health care, prevalence of parasitic and infectious diseases, parent’s health-seeking behavior, race or ethnicity, rural residence, and social network and family support [Jacobs, B; Robertn et al]. Demographic characteristics such as a child’s age and gender, birth interval (both preceding and succeeding), and the mother’s age at childbirth, have also been associated with child nutrition status [Vella,VA; Tomkins, J; Marshall, T].

According to Kawachi, economic inequality is an independent determinant for childhood under-nutrition. Countries with a greater degree of economic inequality tend to have an overall poorer average population health status than countries with more economic equality [Ross, NA; Wolfson]. Suffice it to say that the relationship between economic inequality and under-nutrition is complex. This is in part due to the fact that greater national wealth does not necessarily translate into better health care for all. If that were the case, then the single best approach to improving health care would be to maximize economic growth [Wilkinson, RG]. Additionally, economic growth does not always benefit all sections of the society equally. A country’s social and economic inequality affects food availability, access to health services, and disease morbidity and mortality among the many sections of a society differently. In Japan, for example, a rapid improvement in life expectancy in the last few decades was associated not only with its rapid economic growth, but also with a low level of economic inequality [Hertzman, C; Frank,]A number of studies have illustrated that children from poorer households tend to be more undernourished than children in wealthier households [Larrea, Wang, Y et al]. Social deprivation has also been linked with a child’s nutritional status [Armstrong, J; Dorosty et al]. However, the relationship between economic inequality and a child’s nutritional status is not conclusive. A recent study in Mexico discovered that household poverty is not a necessary condition for children to be undernourished [Reyes, H]. Another recent study in Ecuador found inconsistent evidence to indicate any relationship between economic inequality and the nutritional status of children [Larrea, C; Kawachi].

Additionally, a study in Cambodia found that acute under-nutrition in children was associated with a mother’s feeding practices, parent’s health-seeking behaviour, and personal hygiene; however, there was no association with household food insecurity [Jacobs, B et al]. The primary objective of this study is to investigate the association between household wealth inequality and childhood under-nutrition in Vanuatu. We will also examine the effects of other potential risks and confounding factors on childhood under-nutrition

**1.2 ****LITERATURE REVIEW**

Malnutrition is a major public health concern in Bangladesh. It increases the risk of mortality in children by weakening the child’s defense mechanism, resulting in disease. The primary victims of malnutrition are infants. The nutrition coverage in Bangladesh has now been considered a topic of interest to population researchers because it has significant importance on child health. Only the relevant literature in the context of the present study is reviewed here.

Israt raihan (2002) estimated the determinants of malnutritional status among under five children in Bangladesh. Using multivariate technique Cox’s linear logistic regression model, he found that – mother age at birth , administrative division, mother’s education, type of housing, mother’s body mass index, breastfeeding status, father’s education, type of toilet facility, mass media exposure are significant predictors for morbidity among under five children.

In 1993, it was estimated that 67% of children aged 6–59 months were moderately-to-severely alnourished in Bangladesh (Helen Keller International, 1994).

Ricci and Becker (1996), analyzing in Philippines, showed that place of residence and child age are important risk factors for both stunting and wasting. Low birth weight and shot previous birth interval (24 months) were the two most important risk factors for stunting. Protective factors against stunting include breast feeding, more frequent parental care, being female and higher house hold socio-economic status.

Investigators have identified several variables related to infant and child malnutrition including low dietary intake, low birth weight, family size, lack of parental education, faulty infant feeding practices, incidence of diarrhea and delayed weaning (Bhuiya, Zimicki & D’Souza, 1986; Chowdhury & Bhuiya, 1993; Islam *et al.*, 1994; Victora *et al.*, 1984).

Inadequate nutrition of the mother may also be responsible for malnutrition in breast-fed infants and young children (Rahman *et al.*, 1993). It has been estimated that the prevalence of low body mass index in Bangladeshi adults ranges from 18·3 to 18·9% among poor women and from 1·8 to 2·1% among better-off women (Ahmed *et al.*, 1998; Baqui *et al.*, 1994).

Information on the effects of birth spacing on malnutrition in Bangladesh, however, is inadequate. Swenson (1984) reported that the proportion of Bangladeshi children in the severely malnourished category is almost twice as high among children born within 12 months.

Roy (1996) found that, among other factors, subsequent birth interval in Matlab has a significant effect on child nutritional status. The MCH–FP Extension Project (Rural) was originally launched in 1982, the objective of this study was to investigate the independent effect of the length of birth intervals on the nutritional status of infants and young children aged 6–39 months. WHO published Global Database on Child Growth and Malnutrition in ( 5 January 2009) on Bangladesh. Khurshid Talukder1 and A.K.M. Abdus Salam worked on Child Nutrition Survey of Bangladesh 2000.the object was Document the nutritional status of children and identify the determinants of malnutrition in Bangladesh. A. B. M. Khorshed Alam Mozumder work on child malnutrition.The aim of this study was to assess the economic difference in nutrition of under-five children. In this study, quintiles were calculated on the basis of asset and wealth score by use of principal component analysis. To understand the nutrition status and health inequality concentration index was also calculated.

Ellen Van de Poel et al had research on Inequality in malnutrition. The objectives of this study were to report on socioeconomic inequality in childhood malnutrition in the developing world, to provide evidence for an association between socioeconomic inequality and the average level of malnutrition, and to draw attention to different patterns of socioeconomic inequality in malnutrition (Bulletin of the World Health Organization 2008;86:282–291.).** **

Davidson R. Gwatkin, Shea Rutstein, Kiersten** **Johnson, Eldaw Suliman, Adam Wagstaff, and Agbessi Amouzou also work on Socio-Economic Differences in Health,Nutrition, and Population (HNP) within Developing Countries**.** Adam Wagstaff Naoko Watanabe also work on Socioeconomic Inequalities in Child Malnutrition in the Developing World . Rathavuth Hong, James E Banta, and Jose A Betancourt work on Relationship between household wealth inequality and chronic childhood under-nutrition in Bangladesh.

The Ministry of Health and Family Welfare of the People’s Republic of Bangladesh initiated the National Nutrition Programme (NNP), the largest nutrition initiative, to reduce malnutrition in children, adolescent girls, and women.

The National Nutrition Programme Baseline Survey carried out in 2004 was implemented through a collaborative effort of ICDDR,B: Centre for Health and Population Research, Institute of Public Health Nutrition (IPHN), and the National Institute of Population Research and Training (NIPORT). The objectives of the survey were to provide detailed information about nutritional status of children aged less than 5 years, adolescent girls and pregnant women, pregnancy weight gain, weight of the newborn, anemia and iodine status of pregnant women and adolescent along with socioeconomic data, feeding practices, access to and use of child health and nutrition services, and mothers’ nutrition knowledge and practices. Information about involvement in home gardening, poultry, household food security, participation in growth monitoring and promotion sessions, and adolescent girls’ forum were also obtained. ).

The Health Economics Unit (HEU) of ICDDR,B has been working as a resource unit for conducting policy-oriented research. In addition to economic evaluation of different health interventions, the Unit focuses on cost, efficiency, and equity of the interventions with a special focus on poverty and health.

**1.3. OBJECTIVES OF THE STUDY**

Health and nutrition status are sensitive indicator of communities health and nutrition .Thus the objectives of these study are:

* To describe the health, nutrition and health service facilities among children belonging to different the socio-economic classes and thus draw a picture of Inequalities in Child health and nutrition existing in different classes.

* To investigate the magnitude of association between household wealth inequality and childhood under-nutrition.

* To assess whether there is significant neighborhood variation in childhood malnutrition after control the effect of risk factors and confounders.

*To assess the neighborhood variation of health risk factors and confounders at the individual-level and community-level.

**1.4. RATIONALE OF THE STUDY**

Malnutrition severely affects the health of growing children and women of child bearing in most of the developing countries of the world like Vanuatu. In the study, malnutrition control by the maternal nutrition and other socio demographic factors which is correlated with household economic status. It has been well documented that malnutrition affects morbidity and mortality and is related to infection; its relation or effect on physical and mental development has also attracted considerable attention.

The planning and evaluation of public health activities and health facilities require knowledge of the extent of childhood malnutrition status under five children of Vanuatu . The Government of Vanuatu has implemented a number of priority programs in the health sector to improve the health condition of the people and to make the maximum utilization of the healthcare facilities.

This study is expected to improve our knowledge about the determinants of child health in Vanuatu and to justify the effectiveness of different health intervention programs existing in Vanuatu. It would also help policy planners in formulating programs to reduce malnutrition, which are the precursor to mortality.

**1.5 ORGANIZATION OF THE STUDY**

The present study is organized in six chapters. Chapter 1 is organized with the background of the study, objectives and the organization of the study and literature review.

Chapter 2 is about data and variables which gives the information about data source, sample profile and hierarchical structure of the data and about the variable used for analysis i.e. response variable and independent, control variables.

Chapter 3 is about the methodology used for analysis including health inequality in child.

Chapter 4 is about the analysis of this study.

Chapter 5 is the discussion and conclusion from overall result found from the study. In this part some policy implications of the findings are also suggested.

**2.1 INTRODUCTION**

Millions of children and women suffer from one or more forms of malnutrition, including: low birth weight (LBW), stunting, underweight, vitamin A deficiency, iodine deficiency disorders and anemia. Malnutrition passes from one generation to the next because malnourished mothers give birth to infants who struggle to thrive or grow well. If they are girls, these children often become malnourished mothers themselves. Malnutrition contributes to about one half of all child deaths, often by weakening immunity. Survivors of malnutrition are left vulnerable to illness, stunted and intellectually impaired.

In developing countries around the world, an estimated 148 million children are stunted, 127 million are under-weight, and 46 million are wasted. According to a recent comparative risk assessment by the World Health Organization (WHO), under-nutrition is estimated to be, by far, the largest contributor to the global burden of disease. Many people in developing countries still live in extreme poverty and in these countries economic growth tends to benefit only a small group of advantaged and affluent people and causes growing inequality in health and nutrition that affects particularly vulnerable groups of the population, such as children. Economic well-being at the household level operates mainly through availability of better food, more hygienic living conditions, and better access to health services in affecting the health and nutritional status of children .While there are numerous studies on childhood malnutrition in Vanuatu majority of these studies have looked at the contributions of individual-level (socio-economic and family planning) characteristics. A growing body of literature considers the importance of understanding of determinants of childhood malnutrition through an integrated analysis that considers linkages between demographic, household, and community structures. Thus, the contextual aspect of child malnutrition needs to be explored to understand the process of malnourishment as a whole. To expand our understanding of the effects of household wealth status on the risk of childhood malnutrition, the study argue that it is necessary to consider as additional risk factors the characteristics of the communities in which mothers and children live using multilevel analytic framework. Therefore, the purpose of this paper is to develop and test a model of childhood malnutrition that includes household wealth status, individual-level characteristics along with community-level characteristics. The second aim was to determine whether there is significant neighborhood variation in childhood malnutrition and whether neighborhood variation is explained by other factors at the individual-level and community-level.

**2.2 STUDY POPULATION AND SOURCES OF DATA:**

Vanuatu officially the Republic of Vanuatu is an island nation located in the South Pacific Ocean .It is 1,750 kilometers east of northern Australia, 500 kilometers north-east of New Caledonia, west of Fiji, and south of the Solomon Islands. Vanuatu has been divided into six provinces: Malampa, Penama ,Sanma, Shefa ,Tafea ,Torba . Port vila is the capital of Vanuatu. Its total area is 12,186 km and total population is 2,15,446. The economy is based primarily on small-scale agriculture, which provides a living for 65% of the population. Cattle farming and tourism (with about 50,000 visitors in 1997) are other mainstays of the economy.

The sample Multiple Cluster Survey for MICS Vanuatu is a probability-based, stratified cluster sample of 3000 households. They were selected in 120 clusters, each of size 25 households. The sample was designed with the intention of providing reliable estimates for the key MICS indicators at the national level and also for urban and rural separately. The sample was allocated to the Provinces and by urban-rural in an optimum fashion to secure enough sample cases in each domain for reliable estimates to be obtained.

A subset of the sample consisting of 60 clusters of 12 households each was selected for use in administering questionnaire modules on nutrition indicators including anthropometric measurements. The sample frame was the enumeration districts (EDs) that made up the 1999 Population Census of Vanuatu, which had been up-dated in the 2006 Agricultural Census. Primary sampling units, or PSUs, were defined as either single EDs or combinations of EDs. Combining EDs was necessary whenever an ED contained fewer than 25 households, because the cluster size to be interviewed was set at 25 households as mentioned above.

The sample was selected in two stages. The first stage consisted of first stratifying the PSUs by Province and within-Province by urban/rural and then selecting 120 PSUs with probability proportionate to size, or *pps*. At the second-stage, a fixed sample size of exactly 25 households was selected from each PSU, using systematic, equal-probability sampling, or *epsem*. Thus a total of 3000 households was selected (120 clusters times 25 households)The nutrition subsample was a systematically selected subset of the parent sample. Thus it was based on the same sample frame and allocated by Province and urban-rural as the parent sample.

## 2.3 DESCRIPTION OF THE VARIABLES

## 2.3 .1 Response variable

### Malnutrition

Malnutrition is a condition that develops when the body does not get the proper amount of protein, energy (calories), vitamins, and other nutrients it needs to maintain healthy tissues and organ function. This state of malnutrition is often characterized by infections and disease. Malnutrition intensifies the effect of every disease. Severe malnutrition is most often found in developing countries. A child suffering from malnutrition is usually deficient in a variety of nutrients. The leading cause of death in children in developing countries is **protein-energy malnutrition**. This type of malnutrition is the result of inadequate intake of protein and energy. Children who are already undernourished can suffer from protein-energy malnutrition when rapid growth, infection, or disease increases the need for protein and essential nutrients. In worldwide malnutrition is measure by indicator, which is called Anthropometrics indicator. Anthropometrics indicators were constructed using data on the children’s age, height and weight. Three key anthropometrics measures were calculated using the new WHO reference standard: *stunting, wasting*, underweight.

The reference standards most commonly used to standardize measurements were developed by the US National Center for Health Statistics(NCHS) and are recommended for international use by the World Health Organization. The reference population chosen by NCHS was a statistically valid random population of healthy infants and children. Questions have frequently been raised about the validity of the US-based NCHS reference standards for populations from other ethnic backgrounds. References are used to standardize a child’s measurement by comparing the child’s measurement with the median or average measure for children pat the same age and sex. Taking age and sex into consideration, differences in measurements can be expressed a number of ways:

• standard deviation units, or Z-scores

• percentage of the median

• percentiles

To standardize reporting, USAID recommends that Cooperating Sponsors calculate percentages of children below cut-offs as well as other statistics using Z-scores. If Z-scores cannot be used, percentage of the median should be used. The **Z-score **or **standard deviation unit (SD) **is defined as the difference between the value for an individual and the median value of the reference population for the same age or height, divided by the standard deviation of the reference population. This can be written in equation form as:

Z-score (or SD-score) =

The cut-off points for different malnutrition classification systems are listed below. The most widely used system is WHO classification (Z-scores) are

**System Cut-off Malnutrition classification**

**WHO **< -1 to > -2 Z-score mild

< -2 to > -3 Z-score moderate

< -3 Z-score severe

** **

**Determinants of stunting Prevalence: **

** **% of children under five that fall below minus 2 standard deviations from the median height for age of the standard NCHS reference population (moderate & severe).we can define Numerator as: number of children under age five that fall below minus two standard deviations from the median height for age of the NCHS/WHO standard (moderate and severe); number that fall below minus three standard deviations (severe).Denominator as: Total number of children under age five measured

**Determinants of wasting prevalence: **

% of children under five that fall below minus 2 standard deviations from the median weight for height of the standard NCHS reference population (moderate & severe).

we can define Numerator as number of children under age five that fall below minus two standard deviations from the median weight for height of the NCHS/WHO standard (moderate and severe); number that fall below minus three standard deviations (severe) .Denominator as

Total numbers of children under age five that were weighed and measured

** Determinants of under-weight status prevalence:**

% of children under five that fall below minus 2 standard deviations from the median weight for age of the standard NCHS reference population (moderate & severe).we can define Numerator as number of children under age five that fall below minus two standard deviations from the median weight for age of the NCHS/WHO standard (moderate and severe); number that fall below minus three standard deviations (severe). Denominator as

Total numbers of children under age five that were weighed.

**2.3.2 Independent variables**

**Household socio-economic status**

Although father’s occupation serves as a proxy for socio-economic status, a more direct measure can be obtained by taking into consideration the index “wealth index”. However the original categories of this variable are collapsed into two categories as middle and rich group and poor group. An indicator of socioeconomic status was developed using principal component analysis. The indicator combined information on a set of household assets and living conditions: the ownership of a car, phone, TV, radio, fridge, bike and motorcycle; the availability of electricity, clean water and a toilet; and the material used to construct the wall, roof and floor of the household dwelling. Economic inequality is measured by dividing the wealth index into quintiles, with the lowest quintile representing the poorest households and the highest quintile representing the richest households in Vanuatu.

### Control variables

### Because household economic status is correlated with maternal nutrition and other socio-demographic factors that can also affect the nutritional status of children, the effects of household economic status on stunting are estimated after statistically controlling for the effects of these other potentially confounding factors. These factors include:

**Child age**: the child’s age: in our study we consider under five child i.e. 0-59 mothers. There we measure the age in standard deviation. Malnutrition is height in this group.**Sex (boy, girl):**Several studies found significance association between malnutrition and sex of the indexed child. Therefore sex of indexed child is considered as a potential control factor for measuring malnutrition in our study.**Full immunization**: in our study we consider full immunization in two category, yes and no. this category was compiled on the basis of coverage of BCG, POLIO1 POLIO2, POLIO3, DPT1, DPT2, DPT3, measles(MMR). Complete immunization coverage among 12- to 23-month-old children was found to be significantly lower in study areas when compared with the national coverage levels.**Under-five child in household (3+) :**There we consider those household where the number of child is more than 3 of under-five children. we category this variable into two category yes and no.**Mothers education**: Mother’s education seams to be directly related with the life of a child (Caldwell, 1979). It helps her to be concern and to take the right decision. Maternal education influences child nutrition, (Chowdhury 1984, A. Bhuiya, s. zimichi and S.d’souza .1986). Among the socio-economic factors, education is the most influential factor in differentiating infant and child nutrition rates (Ahmed, 1986). So we include mother’s education as a risk factor in our study. The level of the mother’s education shows a distinct influence on child malnutrition, the rates being lower for mothers with some schooling. This phenomenon may be attributed to children of educated mothers enjoying better diets and better overall care than the children of non-educated mothers (Bairagi, 1980). Education is closely linked to the malnutrition. In this analysis education is measured as a three-category dummy variable, representing no education, primary, secondary and higher.**Area:**Place of residence is categorized as ‘Urban’ and ‘Rural’. The percent of respondent of current study is higher in rural than in urban areas, 44.3 versus 55.7 percent. Differentials in malnutrition levels between urban and rural populations are reported in various studies. For instance, in a study is found that babies born in rural areas were more likely to malnourished than babies born in urban areas. The increased malnutrition in rural areas was thought to be the result of biological influences operating after birth, and indirect family influence correlated with nutrition. Therefore, place of residence has been included in the analysis to capture the residual effect of community level influences that might directly or indirectly influence malnutrition.**Geographic region**: Region is one of the key background variables, which need no justification because the relevance of the geographical variations in nutrition is obvious relevance to policy priorities. Region is taken to be a potential risk factor for our study. In these data, Vanuatu is divided into eight regions: Malampa, Penama ,Sanma, Shefa ,Tafea ,Torba, Port vila, Luganville. The hierarchy of geographic and administrative units in Vanuatu. Malnutrition might be correlated with geographic region.

**2.4 SOFTWARE AND PACKAGES USED IN THIS STUDY**

All data analysis were done using the ‘SPSS’ 16 statistical software. Frequency for each * *variable, means and standard deviations and cross-tabulation of every variable compared* *with the malnutrition, among children under five years. The frequencies procedure used to get tables and descriptive statistics means. The crosstabs procedures produce tables showing the joint distribution of two or more variables that each has a limited number of distinct values. Cell counts, cell percentage and also chi-square were obtained through statistics. Finally the Logistic Regression procedure builds odds ratio which are use to estimate statistically significant effects on risk of malnutrition. Besides ‘SPSS’ other packages like Microsoft Word was used for word processing and Microsoft Excel was used for graphical representation.

## 3.1 Statistical analyses

**3.1.1 CROSS TABULATION**

Cross tabulation plays an important role in data analysis in more convenient way. This table displays the number of cases falling into each possible combination of different categories of two or more categorical variables and provides a measure of association. Independent variables are specified in the rows and dependent variables are specified in the columns.

**3.1.2 THE ****CONCENTRATION INDEX**

Inequality in childhood malnutrition was measured using the illness concentration index (*C*) proposed by Wagstaff *et al .*We measure a household’s living standards by equivalent consumption, but the method outlined below can be used for any socioeconomic ranking variable. We rank children by their household’s equivalent consumption. We also have a variable indicating whether or not a given child is malnourished. The curve labeled *L(p) *in Figure 1 is a malnutrition concentration curve. The concentration index is twice the area between the illness concentration curve (*L*(*S*)) and the diagonal with values ranging from +1 to -1.It plots the cumulative proportion of malnourished children (on the y-axis) against the cumulative proportion of children (on the x-axis), ranked by equivalent household consumption, beginning with the most disadvantage .If *L(p) *coincides with the diagonal, all children, irrespective of their household consumption, suffer from the same malnutrition rates. If, as is more likely, *L(p) *lies above the diagonal, inequalities in malnutrition favor the better-off children; we will call such inequalities *prorich. *If *L(p) *lies *below *the diagonal, we have *propoor *inequalities in malnutrition (inequalities to the disadvantage of the better-off). The further *L(p) *lies from the diagonal, the greater the degree of inequality in malnutrition across quintiles of living standards. If *L(p) *of country X is everywhere closer to the diagonal than that of country Y, then country X concentration curve is said to *dominate *that of country Y. It seems reasonable in such cases to conclude that there is unambiguously less inequality in malnutrition in country X than in country Y. Where concentration curves cross, or where, in any case, one wants a numerical measure of inequality in malnutrition, one can use the concentration index, denoted below by *C *and defined as twice the area between *L(p) *and the diagonal. This index, as has been shown elsewhere is related to the relative index of inequality (RII), used extensively by epidemiologists and others in analyses of socioeconomic inequalities in health and mortality takes a value of zero when L(p) coincides

with the diagonal and is negative (positive) when L(p) lies above (below) the diagonal. It can be calculated as (1) C *=-*1

where n is the sample size, xi is the malnutrition indicator for child i, mean level of malnutrition and *R _{i} , *is the relative rank in the consumption distribution of the ith child (the best-off child having a value of R of 1).

**3.1.3 HOUSEHOLD SOCIOECONOMIC STATUS**

This study uses a household wealth index, estimated from asset variables using principal components analysis (PCA) , as a proxy indicator for household economic status in this analysis. Economic inequality is measured by dividing the wealth index into quintiles, with the lowest quintile representing the 20% poorest households and the highest quintile representing the 20% richest households in Vanuatu.

**3.2 HIERARCHICAL ANALYSIS**

The statistical models used in multilevel analysis are known as hierarchical models. Multilevel models are often used synonymously. These models have previously appeared in different literature under a variety of names including random effect models or random coefficient models [Diggle et al (1994)], covariance components models or variance components models [Searle et al (1992)] and mixed models [Brown et al (2000)]. To provide a theoretical outline about the multi-level linear and multilevel logistic (non-linear) model along with their estimation techniques, we begin with a review of the logistic regression model.

**3.2.1 LOGISTIC REGRESSION MODEL**

Logistic regression is a popular modeling approach when the dependent variable is dichotomous. This model allows one to predict such outcomes, from a set of variables that may be continuous, discrete, dichotomous, or a mix of any of these. Hosmer et al (2000) has described logistic regression focusing on its theoretical and applied aspect. Let E(Y |x) = π(x) be the conditional mean of dependent variable, Y given explanatory variable, x. Then the logistic regression model defines π(x) as,

П(x)=^{ =………………………..}(1)

where β0 and β1 are the model parameters. The fact that the logistic functionπ(x) ranges between 0 and 1 is the major reason the logistic model is so popular. Besides, the curve results in an elongated S-shape (Figure 3.1) which can be seen in much binary response data analysis.

Figure 3.1: Logistic function curve

Rather than model (3.1) directly, the link function g(x), known as logit, allows the response variable to be modeled as:

g(x) =

= β0 + β1x (3.2)………………………..(2)

The logistic regression model is easily solved by the Eq. 3.2. The quantity is called odds and hence the logit is called log odds. There are two odds: one is when Y = 1 and the other is when Y = 0. The ratio of these two odds is known as odds ratio denoted by which is the base for interpretation of the coefficients the logistic regression model. This is the probability that Y will be a member of one class relative to the other class. For instance, for a binary independent variable (x: 0 or 1), can be expressed as below,

This odds ratio is the measure of how much more likely or unlikely it is for the outcome to be present among those with x = 1 than among those with x = 0.Hence, after estimating the parameters the effect of the independent variable on outcome variable can be measured through this odds ratio.

**3.3 MULTILEVEL ANALYSIS**

Multilevel analysis is applicable to a broad range of situations where units at a lower level are nested within units at a higher level. Normally these situations can be seen in the data collected by multistage stratified clustered sampling. The simplest multilevel model considers only two levels of analysis. The first and most elementary of these levels is usually referred to as level-1 and it is this level that the analysis is focused on. The remaining level is referred to as level-2 and provides the context for the level-1 units. For instance, level-1 units could be voters who are nested in different countries (level-2 units). The dependent variable is always measured for level-1 units, since this is the primary level of analysis. This model can be conceptualized as a two-stage system of equations in which the individual variation within each group of level-2 is explained by an individual-level equation, and the variation across groups in the group-specific regression coefficients is explained by a group-level equation. There are several straightforward ways to analyze such data where individuals are nested within groups. But these analyses do not take hierarchical effect into consideration. The first is to ignore group identity and focus exclusively on inter individual variation and on individual level attributes. This approach has the drawback of ignoring the potential importance of group level attributes in influencing individual level outcomes. Besides, if outcomes for individuals within groups are correlated, the assumption of independence of observations is violated, which results in incorrect standard errors and hence inefficient estimates. A second option is to focus exclusively on inter-group variation and on data aggregated to the group level. This approach considers the correlation between individuals within group but has the drawback of ignoring the role of individual level variables in shaping the outcome. A third approach is to define separate regressions for each group. This approach allows regression coefficients to differ from group to group, but does not examine how specific group-level properties may affect individual-level outcomes or interact with individual-level variables. In addition, it is not practical when dealing with large numbers of groups or small numbers of observations per group. A fourth approach is to include group identity in individual-level equations in the form of dummy variables. This approach is analogous to fitting separate regressions for each group and does not allow examination of exactly what group characteristics may be important in explaining the outcome. Besides, this approach treats the groups as unrelated. Multilevel analysis differs from the approaches mentioned above in the sense that, first: it allows the simultaneous examination of the effects of group-level and individual level predictors, second: the non independence of observations within groups is accounted for, third: groups are not treated as unrelated, but are seen as coming from a larger population of groups, fourth: both inter individual and inter group variation can be examined. Thus, multilevel analysis allows dealing with the micro-level of individuals and the macro-level of groups simultaneously.

Reason for using multilevel analysis:

Suppose the data has n clusters with T observations in each cluster. The de- pendent variable for the ith cluster is yi and we are interested in knowing what is the mean of the dependent variable in each cluster, μi ; i = 1, 2, …, n. Thencan be calculated as an unbiased estimate of μi, with standard error for the ith cluster. In this case the standard error increases to the extent that the clusters are heterogeneous. But there are other estimators available. We could pool units, and estimate μi with the grand mean. This estimator is based on all the data and so has a small standard error. But this grand mean, y, will be a biased estimator of any the cluster-specific means. The bias increases to the extent that the clusters are heterogeneous. On the other hand, if the clusters are less heterogeneous or there is little between cluster variation, then estimating the mean of each cluster by the grand mean is worthwhile. Between these two estimators one might prefer the pooled estimator on mean square error grounds (trading off some bias for small standard errors), depending on the relative size of the between cluster variation to the within cluster variation. We can see, at one extreme, that we have no pooling and zero bias in the estimates of μi. But these estimates could have large standard errors, for instance, if the within-cluster variation is large (if T is small). At the other extreme, we can see that we have complete pooling and potentially lots of bias if the between-cluster variation is large, but potentially big gain in efficiency (if n is large relative to T).Thus, choosing any one of the above estimators results in either biased or inefficient estimation. Now, the question is whether there is any estimator that makes b μi close to the no-pooling estimator if the between-cluster variation is large, but close to the grand-mean if the between-cluster variation is small. The answer to the above question is yes, which is known as a random effect estimator. The estimator dominates the fixed effects (no pooling estimator) in terms of mean square error, by buying just the right amount of bias relative to the efficiency gain, cluster-by-cluster. The related model of this fixed effect estimator is a multilevel model through which an unbiased and efficient estimate can be obtained.

**3.4 MULTILEVEL LINEAR MODEL**

The multilevel linear model and its application had been described by various authors in the past [Mason et al (1983), Goldstein (1987, 1995, 2003), Bryk et al(1992)]. We describe below the multilevel linear model and its basic properties. We first consider a simple linear model for the data with hierarchical structure(with two levels) with a single explanatory variable,

where yij is the outcome variable for the ith unit at level-1 and the jth unit atlevel-2, αj is the intercept for the j th unit at level-2 (i.e. it varies across level-2 but has the same value for all the units within each level-2), xij is the explanatory variable for the ith unit at level-1 and the jth unit at level-2, _β1 is the effect of xij and and eij is the level-1 random effect. Here, αj is a random variable rather than a constant and can be written as

where, β0 is the intercept (constant across level-2) and uj is a random effect accounting for the random variation at level-2.

Combining both equations and the two level linear model can be written as

In equation, uj and eij are random quantities which follow normal distributions,N(0, ) and N(0, ) respectively. The equation (3.5) has the properties: E[uj ] = E[eij ] = 0, var(uj) = _ var(eij) = , cov(uj , eij ) = 0 and cov(uj , uj′) = 0 for j ≠= j′. In this model, β0 and β1 are known as fixed parameters and _2 and are known as random parameters. Equation (3.5) is also known as variance component model since the variance of the response, about the fixed components (β0 & β1), the fixed parameter, is

which is the total variation obtained summing level 1 and level 2 variance. The covariance between two units of level 1 (say, i1, i2) can be defined as,

The within level-2 or intra-level 2 correlation after controlling the explanatoryvariable can be obtained from

**3.5 MULTILEVEL LOGISTIC REGRESSION MODEL**

We shall start considering first a two level logistic regression model with a singleexplanatory variable, with both fixed and random effect.

**Two Level Model**

Basically, the two level logistic model is equivalent to model except for the outcome variable. Let yij be the binary outcome variable, coded ‘0’ or ‘1’, associated with level-1 unit i nested within level-2 unit j. Also let pij be the probability that the response variable equals 1, and pij = Pr(yij= 1). Here, y_{ij} follows a Bernoulli distribution. Like logistic regression the pij is modeled using link function, logit. The two level logistic regression model can be written as,

where uj is the random effect at level 2. Without uj , Eq. (3.6) can be considered as a standard logistic regression model. Therefore, conditional on uj , the yij ’s can be assumed to be independently distributed. Here, uj is a random quantity and follows N(0, )The model (3.6) can be written as follows splitting up into two models: one for level 1 and the other for level 2.

The multilevel logistic regression model can not be derived in the way simple logistic regression model is derived. This mode can be derived through a latent or hidden variable conceptualization. Let us suppose y′ij to be a continuous variable such that And however we cannot observe y _{ij }directly but only the binary outcome y_{ij} . In terms of the continuous latent variable y′ij the model can be written equivalently to as below,

Conditional on the random effect uj at level two, a multilevel logistic model can be derived from (3.7) depending on the standard logistic distribution of eij . This conceptualization or threshold concept illustrates the close connections between the multilevel models for linear data and those for binary data [McCullagh &Nelder (1989)]. Conditional on uj , the conditional density function for cluster j for model (3.6) is identical to that for the logistic regression

where, yj and xj denote the responses and explanatory variables in cluster j respectively.

**5.1 MAIN FINDINGS OF THIS STUDY**

The results of present study have shown that childhood under-nutrition is a serious problem in Vanuatu and have provided evidence of concentration of childhood malnutrition among the poorest, poorer and middle households.

.*These findings are consistent with preponderance of evidence from other developing countries and provide further evidence that household economic status is an important determinant of childhood under-nutrition in developing countries.

*However, household wealth status functions mainly through better access to food and health care in affecting childhood nutritional status, for example more wealthy households can afford better food in terms of quality.

*Poverty affects child nutritional status through insufficient food intake, greater exposure to infections, and lack of access to vaccinations and basic health care.

*It is noted that income-related inequalities are the strongest in stunting, an indicator of chronic malnutrition that is often associated with socio-economic deprivation.

*It also find that socio-economic inequalities are observed in wasting, as income has a little effect on the stochastic conditions (unforeseen environmental factors and diseases) which usually precipitate wasting

*The positive association between wealth index and underweight is considerably diminished and non-significant when underlying factors are taken into account. These results indicate that much of the positive association between and underweight is due to underlying factors.

*The study find that child’s sex, age, mother’s education are important determinants of a child’s nutritional status, which is consistent with the findings of most studies in this study.

*A number of studies from Vanuatu suggest that malnutrition among boys is consistently higher than malnutrition among girls.

*In previous research, it has been suggested that a mother’s education is one of the more important factors in promoting a family’s health and nutrition, increasing household income. However, in our analysis, maternal education is found to have little to no effect on adverse childhood growth-stunting; even when we control for a mother’s education, this does not significantly alter the effect of household wealth status on growth-stunting.

*Of particular interest in this investigation are possible effects of neighborhood context on childhood malnutrition. Neighborhood constitutes a key determinant of socioeconomic disparities in health, as they shape individual opportunities and expose residents to multiple risks and resources over the life course.

*Using multilevel framework, this study that has shown that both individual-level and community-level characteristics are important predictors of childhood malnutrition in Vanuatu, and demonstrates significant neighborhood variation in chronic childhood malnutrition.

*The individual- and community-level characteristics included in the model are able about 50% of these observed variations

**5.2 RECOMMENDATION**

The study findings have some important and relevant policy messages. There is a need for scaling up strategies for reducing economic inequality and raising the relative income of the poorest sections of the population, and these could include:

(i) the development of relatively poor rural areas,

(ii) awareness should be increased about male malnutrition

(iii) reducing health service fees for poor ,

(iv) identifying and tackling the demographic and socioeconomic characteristics which affects malnutrition of poor and vulnerable groups, and

(v) With the models the study is able to explain only half of the neighborhood variations in childhood malnutrition. These findings have important implications for targeting policy as well as the search for left-out variables that might account for this unexplained variation.

**5.3 STUDY LIMITATIONS AND STRENGTHS**

There are a number of caveats to be considered when interpreting these results. They are:

*The data which are used in this study are cross-sectional nature which may have limits ability to draw casual inferences.

*Limitations related to sample design remain in the data.

*Another limitation of this study worth mentioning is that measuring wealth is problematic

*The study can be criticized for using an indirect measure of household wealth.

*However, due to the fact that in developing countries like Vanuatu it is hard to obtain reliable income and expenditure data, an asset-based index is generally considered a good proxy for household wealth status.

*Another potential limitation of this analysis is that it does not control for diet and other health care indicators.

*For time consuming could not be examined some important factors as like father’s education, occupation.

*However, household wealth status functions mainly through better access to food and health care in affecting childhood nutritional status, for example more wealthy households can afford better food in terms of quality, which may not always true.

*Despite these limitations, the study strength is significant. It is a large, population-based study with national coverage.

**5.4 CONCLUSION**

Using an explicit multilevel analytic framework, the study has demonstrated that household wealth status is an important determinant of chronic childhood malnutrition, and that there is significant neighborhood variation in childhood malnutrition, even after controlling for effects of both individual- and community-level characteristics. Future studies should investigate other factors that may account for the unexplained neighborhood variation in childhood malnutrition. Future research also should address the mechanisms that connect the individual and neighborhood levels, that is, the means through which deleterious neighborhood effects are transmitted to children. These mechanisms are crucial to the design of community-based interventions because these processes are more amenable to change than entrenched structural properties of neighborhoods (e.g., concentrated poverty). Although this study does not investigate these mechanisms, the findings clearly provide evidence that social context is associated with health independent of individual-level health risk factors, challenging a purely individualistic approach to health, and pointing to the importance of health promotion and disease prevention at the community level. Scholars trying to understand variation childhood malnutrition should pay attention to the characteristics of both children and place of residence.

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