**1. Introduction**

544 Current Topics in Tropical Medicine

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Childhood undernutrition is amongst the most serious health issues facing developing countries. It is an intrinsic indicator of well-being, but it is also associated with morbidity, mortality, impaired childhood development, and reduced labor productivity (Svedberg 1996; UNICEF 1998; Sen 1999)

To assess nutritional status, the 2003 DHS obtained measurements of height and weight for all children below five years of age.(Survey 2003) Researchers distinguish between three types of malnutrition: wasting or insufficient weight for height indicating acute malnutrition; stunting or insufficient height for age indicating chronic malnutrition; and underweight or insufficient weight for age which could be a result of both stunting and wasting.

These three anthropometric variables are measured through z-scores for wasting, stunting and underweight, defined by

$$Z\_i = \frac{AI\_i - MAI}{\sigma},\tag{1}$$

where *AI* refers to the individual anthropometric indicator (e.g. height at a certain age), *MAI* refers to the median of a reference population, and refers to the standard deviation of the reference population. Each of the indicators measures somewhat different aspects of nutritional status. Note that higher values of a z-score indicate better nutrition and vice versa. Therefore, a decrease of z-scores indicates an increase in malnutrition. This has to be taken into account when interpreting the results. The reference standard typically used for the calculation is the NCHS-CDC Growth Standard that has been recommended for international use by WHO. (WHO 1999) The reference population are children from the USA. More precisely, the children, up to the age of 24 months are from white parents with a high socio-economic status, while children older than 24 months are from a representive sample of all US children. The selection of the reference populations can affect the results, for example a higher z-score can be caused by the change of the reference population.

**Latent variable model**: Previous analyses are often based on Demographic and Health Surveys (DHS) as a well-established data sources with reliable information on childhood

Associations Between Nutritional Indicators Using Geoadditive

information about the covariates considered in this study.

considered in the analysis to study child nutritional status.

reference population are considered short for their age or stunted.

distributed; thus in principle, could be applied.

for the nutritional status of a child.

see(Raach 2005; Khatab 2007)

**2. Data & methods** 

**3. Statistical analysis** 

**3.1 Geoadditive gaussian model** 

mentioned.

Latent Variable Models with Application to Child Malnutrition in Nigeria 547

To build a regression model for undernutrition, we first have to define a distribution for the response variable. In this application, it is reasonable to assume that z-score is Gaussian

The analysis started by employing a separate geoadditive Gaussian model to continuous response variables for wasting, stunting and underweight. The author then applied geoadditive latent variable models, based on these separate analyses results, which were reported in Khatab, 2007, where the three undernutrition variables were taken as indicators

All computations have been carried out with R Programs using the MCMC package;

DHS collects information on household living conditions such as housing characteristics, on childhood morbidity, malnutrition and child health from mothers in reproductive ages (15- 49). There were 6029 children's records in the 2003 survey of Nigeria. Each record consists of information on childhood malnutrition and diseases and the list of covariates that could affect the health and nutritional status of children. In the following, we provide some more information about the nutritional indicators, which were used as response variables and

**Stunting**. Stunting is an indicator of linear growth retardation relatively uncommon in the first few months of life. However it becomes more common as children get older. Children with *height-for-age* z-scores below minus two standard deviations from the median of the

**Wasting**. Wasting indicates body mass in relation to body length. Children whose *weight-forheight*'s z-scores are below minus two standard deviations (z-scores < 2 *SD* ) from the median of the reference population are considered wasted (i.e. too thin for their height)

**Underweight**. Underweight is a composite index of stunting and wasting. This means children may be underweight if they are either stunted or wasted, or both. In a similar manner to the two previous anthropometric incidences, children may be underweight when their z-score is below minus two standard deviations and they are severely or moderately so if their z-score is lower than two standard deviations. The included variables in Table 1 were

In the following, we focus on geoadditive Gaussian models for continuous response variables to analyze the effects of metrical, categorical, and spatial covariates on stunting, wasting and underweight response variables in latent variable analyses. Furthermore, we use "nutritional status" as the indicator in the analysis of the latent variable models as

In this analysis, we apply a noval approach by exploring regional patterns of childhood malnutrition and possible nonlinear effects of the factor within latent model framework using geoadditive Bayesian gaussian model for continuous response variable.The model

which implies that they are acutely undernourished otherwise they are not wasted.

undernutrition, and they rely on statistical inference with various forms of regression models. Because of methodological restraints, it is difficult to detect nonlinear covariate effects adequately, for example, age, and it is impossible to recover small-scale, districtspecific spatial effects with common linear regression or correlation analysis. Recent research has therefore applied geoadditive regression models (Fahrmeir L 2001; Fahrmeir 2004) .They have been used in regression studies of risk factors for acute or chronic undernutrition (e.g., Kandala et al., 2001; Adebayo 2003; Khatab, 2007) and for morbidity.(Kandala 2001; Adebayo 2003; Kandala, Magadi et al. 2006; Kandala, et al. 2007; Khatab 2007) These models can account for nonlinear covariate effects and geographical variation while simultaneously controlling for other important risk factors.

However, in all these studies regression analyses are carried out separately for certain types of undernutrition such as stunting, wasting or underweight, neglecting possible association among these response variables and without aiming at the detection of common latent risk factors. Because of common and overlapping risk factors, separate analyses may fail to give a comprehensive picture of the epidemiology for the malnutrition and the joint effects of childhood malnutrition at population level.

To asses the association between the the nutritional indicators, we applied the recently developed latent variable model. This model gives us the opportunity to study the association or interrelationship between the three types of malnutrition as indicators for nutritional status. The factor loadings describe the association between these indicators and their impact on the nutritional status of a child. Latent variable model permits modeling of covariate effects on the latent variables through a flexible geoadditive predictor

The objective of this study is to determine the associations between nutritional indicators among Nigerian children under 5 and also to examine the impact of socioeconomic and public health factors on the nutritional status.

Nutritional status is known to have various risk factors including geographical locations as a proxy of socioeconomic and environmental factors that affect the disease prevalence and incidence.

Spatial heterogeneity in these factors influences the nutritional status pattern. Consequently, efforts to reduce the burden of childhood undernutrition should include investigations into the influence of the associations between the different measurements of the malnutrition status of children and their distribution among the locations on child health.

Two approaches of latent variable models (joint model) analysis of malnutrition have emerged: the measurement model which accommodates and describes the effect of the latent variables and a set of observed covariates (e.g. child's sex, mother's educational attainment, working status, etc) on the nutritional indicators such as stunting, wasting and underweight.

The structural model is linking a set of observed covariates which have indirect effects (such as child and mother's age, etc), with the latent variables.

In the latent variables overall specific risks are estimated having adjusted for covariates, and in addition, the correlation of risk between measurements of the malnutrition can be quantified.

In this study, we considered the latent variable model to jointly analyse childhood stunting, wasting and underweight, with the objective of highlighting spatial patterns of these indicators.

To build a regression model for undernutrition, we first have to define a distribution for the response variable. In this application, it is reasonable to assume that z-score is Gaussian distributed; thus in principle, could be applied.

The analysis started by employing a separate geoadditive Gaussian model to continuous response variables for wasting, stunting and underweight. The author then applied geoadditive latent variable models, based on these separate analyses results, which were reported in Khatab, 2007, where the three undernutrition variables were taken as indicators for the nutritional status of a child.

All computations have been carried out with R Programs using the MCMC package; see(Raach 2005; Khatab 2007)
