CHAPTER ONE

1.1 Introduction

The term malnutrition, generally, refers both to under nutrition

and over nutrition, but in this study the term is used to refer

solely to a deficiency of nutrition. Nutritional status is the

result of complex interactions between food consumption and the

overall status of health and health care practices. Numerous

socio-economic and cultural factors influence patterns of feeding

children and the nutritional status of children and women as

well.

The period from birth to age two is especially important for

optimal growth, health, and development of children.

Unfortunately, this period is often marked by micronutrient

deficiencies that interfere with optimal growth. Additionally,

childhood illnesses such as diarrhea and acute respiratory

infections (ARI) are common. For women, improving overall

nutritional status throughout the life cycle is crucial to

maternal health. Women who become malnourished during pregnancy

and children who fail to grow and develop normally due to

1

malnutrition at any time during their life, including during

fetal development, are at increased risk of prenatal problems,

increased susceptibility to infections, slowed recovery from

illness, and possibly death. Improving maternal nutrition is

crucial for improving children’s health. The poor nutritional

status of children and women has been a serious problem in

Ethiopia for many years.

Not addressing malnutrition has high costs in lost GDP and higher

budget outlays while improving nutrition contributes to

productivity, economic development, and poverty reduction by

improving physical work capacity, cognitive development, school

performance and health by reducing disease and mortality. Besides

its important contribution to economic development and poverty

redaction, nutrition is recognized as a basic human right.

According to article 25 of the convention of universal

declaration of human rights, nutrition has long been recognized

as basic human right in 1948. The convention ensures that

“Everyone has the right to a standard of living adequate for the

health and well being of himself and his family….”(Benson, 2005).

2

As children and mothers are the primary victims of malnutrition,

this principle was reinforced in the 1989 convention of the

rights of child, ratified by the government of Ethiopia. Article

24 of the convention states that “states parties recognize the

right of children to enjoyment of the highest attainable standard

of health…”and shall act appropriately “to combat disease and

malnutrition through the provision of adequate nutrition foods,

clean drinking water and health care.”

Studies showed that in most countries where DHS have been

conducted, children born less than 24 months after the previous

child was born (a short birth interval) have a higher level of

stunting, wasting, and under nutrition. Although studies show

good progression in declining proportion of stunted and

underweight children intherecent past, there are problems to be

addressed and improved more, such as introduction of timely and

appropriate feeding of complimentary food and exclusive breast

feeding. Child malnutrition may lead to higher levels of chronic

illness and disability in adult life and these may also have

intergenerational effects as malnourished females are more likely

3

to give birth to low-weight babies. Malnutrition and/or child

death are the outcomes of a multisectoral development problem.

The different causes of malnutrition are interlinkedand include

immediate causes, underlying causes and basic causes (UNICEF,

2004). All factors operate together and not independently

(Williams, 2005).

In their effort to monitor the extent and distribution of

malnutrition so as to help the most affected by setting

priorities, for instance, of food targeting policies to the

severely malnourished groups, Smith and Haddad (2008) summarized

the regional levels and trends of child malnutrition prevalence

of 63 developing countries for the period of 1990s-2010s. They

categorized these countries into five regions. Based on their

order of underweight prevalence for the given period, the regions

are presented as: South Asia (61%), Sub-Saharan Africa (31%),

East Asia (23%), Latin America and the Caribbean (12%) and, Near

East and North Africa (11%) by using Bivariate and Trend

analysis.The authors reported that except for Sub-Saharan Africa,

there was some reduction in the level of malnutrition during the

4

given period.As part of welfare monitoring survey, the central

statistical authority of Ethiopia is permanently providing data

on nutritional status of children every two years since 1996.

According to WMS (2007) report, about 10.4 million children

(constituting 49% of female and 51% of male) children under-five

years of age are malnourished.

UNICEF (2004) classifies the immediate causes of childhood

malnutrition as insufficientdiet as well as stress, trauma,

disease (severe or frequent infections) and poorpsychosocial

care. Insufficient dietary intake may refer to poor breastfeeding

practices, early weaning, delayed introduction of complementary

foods and insufficient protein in thediet. The inadequate intake

can also be linked to neglect and abuse (UNICEF, 2004;Williams,

2005). Other factors that influence food intake include health

status,food taboos, growth and personal choice related to diet

(Vorster and Hautvast, 2002). The underlying causes of

malnutrition are household food insecurity, inadequate maternal

and child care, inadequate health services and health

environment.

5

Basic causes, also called national or root causes, of

malnutrition include poor availabilityand control of resources,

environmental degradation, poor agriculture, political

instability, urbanization, population growth, conflicts, natural

disasters, religious and culturalfactors (Torúnet al, 1994;

Vorster et al, 2003; UNICEF, 2004a;Torún, 2006).

If issues related to the economic position of the family are

affected negatively, it caninfluence the chances of a child being

stunted and underweight (Grantham-McGregor, 1984; Zere and

McIntyre, 2003; UNICEF, 2004a). The degreeto which the three

underlying determinants are expressed, positively or negatively,

is a question of available resources. These include the

availability of food, the physical and economic access which an

individual or household has to that food, the caregiver’s

knowledge of how to utilize available food and to properly care

for the individual, the caregiver’s own health status, and the

control the caregiver has over resources within the household

that might be used to nourish the individual. Additionally, the

level of access to information and services for maintaining

6

health, whether curative services are available, and the presence

or absence of a healthy environment with clean water, adequate

sanitation, and proper shelter all contribute to determining the

nutritional status of an individual. The relative importance of

each must be assessed and analyzed in each setting in order to

define priorities for action (Benson, 2005).Failure to

effectively tackle the prevalence of malnutrition in children

under-five will also lead to the non-accomplishment of one of the

key targets of the first Millennium Development Goal, eradicating

extreme poverty and hunger.

1.2 Statement of the problem

To reduce malnutrition one must understand its causes. There is

a lack of agreement about the relative importance of factors

affecting nutritional status.

Ordinal logistic regression is not commonly used to assess the

nutritional status of children of under- five years of age;

particularly in the literatures from Ethiopia. The most commonly

used method is the bivariate logistic regression model. However,

some of the response variables can be multilevel ordinal so that

7

ordinal logistic regression model is more appropriate than the

multivariable logistic model. Therefore, this study focuses on

the alternative methodology, ordinal logistic regression, to

assess the nutritional status of under-five years of agechildren

in SNNPR.

1.3 Objectives of the study

General Objective

To identify and examine the correlatesof nutritional status of

under-five children in SNNPR state using ordinal logistic

regression model.

Specific objectives

Group children into categories of nutritional status of

children (severely malnourished, moderately malnourished and

nourished.

To identify the factors that are related to the nutritional

status of children under the age of five in SNNPR.

To investigate the different levels of the risk factors and

evaluate the probability of each risk level.

8

To recommend the concerned body to manage the problem

focusing on the most devastating factors of malnutrition.

Significance of the study

With the background described above and the literature related to

the study, there is no in-depth study to evaluate the potential

risk factors of under- nutrition of children of five years of age

specifically for SNNPR. For instance, some empirical studies

stress the importance of parental education and/or nutritional

knowledge, while others recommend the need to focus on improving

the poverty/wealth status of households. This question is not

only of academic interest but of considerable policy relevance,

both among national and international policy-makers. Thus, this

study would help to better understand the child, household,

community and policy level determinants of malnutrition

specifically for under-five children in SNNPR state. Such

knowledge will facilitate the development of effective policy

strategies in the region. Besides, the study aims at

investigating the most important determinants of malnutrition and

9

tries to check whether results agree with the findings of other

scholars with respect to the determinants of malnutrition.

CHAPTER TWO

2.1 Review of related literature

A variety of factors that are contributing to health problem and

malnutrition may differ among regions, communities and over time.

10

Identifying the immediate, underlying and basic/root causes of

health problem and/or malnutrition in a particular locality is

important to solve the nutritional and health problems. Various

studies on nutrition have been undertaken and conclusions were

reached by different scholars in the past regarding predictors of

health and nutritional status. The detailed literature review

presented below focuses on the socioeconomic, demographic, and

health and environmental determinants of malnutrition and health

problem in children.

Solomon et al (2006) used data from Gondar referral hospital in

Ethiopia by using logistic regression (both bivariate and

multivariable) to examine the risk factors of sever acute

malnutrition (SAM). The findings confirmed that there is

significant association between acute malnutrition of under-five

children and inappropriate feeding practice. Further analysis

with logistic regression revealed that the risk of acute

malnutrition was significantly associated with lack of exclusive

breastfeeding for the first six months of life (OR=3.22, 95% CI

1.31-7.91) and late initiation of complementary diet (OR=3.39,

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95% CI 1.20–9.57) after the effects of other significant risk

factors were controlled for.

Similarly, Pryer (2003) draw analysis on data collected from

panel survey conducted in Bangladesh by using binary logistic

regression model to compare children with better nutritional

status (height for age Z-score (stunting) >= -2) with that of

children with worst nutritional status (height for age Z-score

(stunting) < -2) and thereby to identify the potential

determinants/risk factors of malnutrition. The study shows that

age of child, educational status and sex of head of household,

household facility and area of residence are significantly

associated with malnutrition of children under five years of age.

On the other hand, Susmita et al (2009) assessed the spatial

distribution of nutritional status of Indian children and found

out that there are gender differences and spatial variations in

the weight-for-age (underweight) status of children in India.

Similarly, closely spaced pregnancies are often associated with

the mother having little time to regain lost fat and nutrient

stores (ACC/SCN, 2008). Higher birth spacing is also likely to

12

improve child nutrition, since the mother gets enough time for

proper childcare and feeding. Studies in developing countries

showed that children born after a short birth interval (less than

24 months) have higher levels of underweight in most countries

where DH Shave been conducted (Sommerfelt et al., 2008).

In 1995, WHO published a meta-analysis based on data sets from 25

studies that related maternal anthropometry to pregnancy outcomes

(WHO, 1995b).The meta-analysis reported that a pre-pregnancy body

mass index (BMI) below 20 kg/m2 was associatedwith a

significantly greater risk for intrauterine growth retardation

(IUGR) relative to a BMI above 24 kg /m2, with anoverall odds

ratio of 1.8 (95% confidence interval (CI): 1.7–2.0). In

developing countries, it has been estimated that poor nutritional

status in pregnancy accounts for14% of fetuses with IUGR, and

maternal stunting may account for a further 18.5%(ACC/SCN, 2000).

Afeworket al (2005) used data collected from the Central,

Eastern, Northwestern and Southern zones of Tigiray, Ethiopia,

and investigated the potential determinants of malnutrition on

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children under-five years of age by using analysis of variance

and multiple regressions. The study shows that age and

malnutrition are positively associated, i.e. both chronic and

acute childmalnutrition develop during the weaning period and

rise sharply thereafter. The retardation of growth, which

commences in the latter half of the first year, suggests problems

associated with child feeding practices and nutrient inadequacy

of the complementary foods. Studies have showed that long term

breast feeding adversely affects infant appetite and growth.

Breastfeeding beyond 12 months was very common in these

communities and such breast feeding practices might encourage

lower acceptance of non breast milk foods and lower energy intake

in children.

Ahmed et al (2012) performed bivariate and multinomial logistic

regression on data obtained from national nutrition program (NNP)

baseline survey conducted in rural Bangladesh in 2004. The14

results show that 40.5% of the children were stunted

(15.6%severely stunted), 35.4% were underweight (11.5% severely

underweight) and 17.8% were wasted (3%severely wasted).Female

children had 30% and 21% less odds to become moderately and

severely stunted than the male counterparts, respectively.

Femalechildren had 20% to 21% less odds of being underweight.

Moderately underweight children had greater number of aged, short

stature and malnourished mother.

Irena et al (2009) had applied the T-test, chi-square and

logistic regression to data collected from children aged 0-59

months with complicated acute malnutrition (AM) admitted to the

Zambia university teaching hospital’s stabilization center from

August to December 2009. The study shows that diarrhea is a major

killing cause of complication in children with severe acute

malnutrition (SAM). Within the said duration, diarrhea with sever

acute malnutrition was found to increase their odds of death

substantially irrespective of other factors.

Das et al (2011) had applied ordinal logistic regression (OLR)-

proportional odds model (POM) and partial proportional odds model

15

(PPOM) instead of traditional binary logistic regression to data

from the Bangladesh demographic and health survey (BDHS, 2004) to

assess the potential risk factors of malnutrition. According to

the findings of the author, household wealth status, child

feeding status, mother’s BMI, incidence of diarrhea, mother’s

antenatal and/or postnatal care status, mother’s education, child

feeding practice, birth interval and age of child are risk

factors that significantly affect the nutritional status of

children under-five years of age. The investigators also

recommended that ordinal logistic regression (OLR)-proportional

odds model (POM) or partial proportional odds model (PPOM) are

sound/appropriate to identify the potential risk factors of

malnutrition on children of five years of age than/to that of

traditional binary logistic regression.

Hien et al (2007) in Vietnam performed hierarchical logistic

regression on the data collected by employing cross-sectional

method to account the hierarchical relationships between

potential determinants of malnutrition. In the first step, they

found that the number of children and mother’s body mass index

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are significant risk factors of malnutrition (wasting and

stunting). Ethnic group and areas of residence are associated

with wasting while mother’s occupation with the stunting in the

second step. Meanwhile, they noted that being children of farmer

is significantly related to stunting. Furthermore, low birth

weights, duration of exclusive breast feeding and time of

initiation of breast feeding contribute significantly to

malnutrition. They also found that the prevalence of malnutrition

is increased with age and higher prevalence of malnutrition is

common on boys.

Rayhan et al (2006) used Bangladesh demographic and health survey

1999/2000 to identify factors causing malnutrition among under-

five children in Bangladesh using Cox’s regression. The result

shows that 45 percent of the children under age five were stunted

(a condition reflecting chronic malnutrition), 10.5 percent were

wasted (a condition indicating acute or short-term food deficits)

and 48 percent were under-weight (which may reflect stunting,

wasting or both). In addition, children born with small size and

smaller than average size had respectively 1.89 and 1.69 times

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higher risk of being wasted as compared to those with larger size

at birth. Children with previous birth interval 0-23 and 24-47

months had respectively 1.4 and 1.2 times higher risk of being

under-weight as compared to children with previous birth interval

48 months and above. Babies, who were very small and smaller than

average, had respectively 3.93 times and 2.23 times higher risk

of being under-weight than those children who were average or

larger in size at birth. Children of nourished mother were 38

percent less likely to be under-weight as compared to children of

acutely malnourished mother. Father’s education and under-weight

were inversely related.

The results also identified that previous birth interval was

highly significant and had an inverse relationship with

prevalence of stunting. Children with previous birth interval 0-

23 months and 24-47 months had respectively 1.55 and 1.36 times

higher risk of being stunted as compared to children with birth

interval 48 months and above. Babies, who were very small in size

and smaller than average, had respectively 2.08 and 1.79 times

higher risk of being stunted than those children who were average

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or larger in size at birth. Risks of stunting were 11 percent and

37 percent lower according to children whose mothers had primary

education and secondary education, respectively, compared to

children of illiterate mother.

Children’s nutritional status is more sensitive to factors such

as feeding/weaning practices, care, and exposure to infection at

specific ages. A cumulative indicator of growth retardation

(height-for-age) in children is positively associated with age

(Anderson, 1995). Local and regional studies in Ethiopia have

also shown an increase in malnutrition with increase in age of

the child (Yimer, 2000; Genebo et al., 1999; Samson and Lakech,

2000).

According to the World Health Organization and UNICEF, mothers

should be helped to initiate breastfeeding within half an hour of

birth. Babies are normally in a quiet alert state in the first

hours after birth. This is the best time to begin bonding and

breast feeding. In 2001 the World Health Organization (WHO)

released global recommendations for infant feeding practices. It

recommends that infants be exclusively breastfed for the first

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six months using on-demand feeding and with initiation within the

first hour of life. Nutritionally appropriate and safe

complementary foods should be introduced after this time (six

month). Breastfeeding should be encouraged for up to two years of

age or longer (Kramer &Kakuma, 2002). However, exclusive

breastfeeding beyondthe recommended six months has been reported

to be associated with a higher risk ofmalnutrition (Fawzi et al

1998).

Inappropriate feeding practice is the principal risk factor which

brought about nutritional deprivation among under-five children

in food surplus areas of Ethiopia. Thus, the importance of

appropriate feeding during infancy and childhood cannot be

overstated even in food surplus areas. The high prevalence of

malnutrition in Ethiopia points out the need to revisit the

impression held by many people that malnutrition is not a problem

in food surplus areas. Development and implementation of

preventive policies aimed at addressing child malnutrition should

also consider food surplus areas of the country.

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A comparative study on maternal nutritional status in 16 of the

18 DHS conducted countries (Loaiza, 1997) and a study in the

SNNPR of Ethiopia (Teller and Yimar, 2000) showed that rural

women are more likely to suffer from chronic energy deficiency

than women in urban areas. These higher rates of rural

malnutrition were also reported by local studies in Ethiopia

(Zerihun et al., 1997; Ferro-Luzzi et al., 1990). Similarly,

studies on child nutrition (Sommerfelt et al., 1994; Yimer, 2000)

also showedsignificantly higher levels of stunting among rural

than urban children using multivariate analysis.

At the country level in Ethiopia, all the four welfare monitoring

surveys from 1996-2004 have revealed that boys are indicated to

be more vulnerable to malnutrition than girls with respect to the

three indices (wasting, stunting, and underweight). Various

reasons behind this gender differential are given in the

literature. Alemu et al. (2007)a, for example, argue that this

could be due to genetic differences between male and female

children and, due to girls’ greater access to food through their

gender-ascribed role in contributing to food preparation. In

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combination with other factors, high birth order and low birth

intervals are reported to have their share in poor childhood

malnutrition outcomes. According to Woldemariam & Timotiows

(2008) and Birhan (2010), high birth order and close spacing

imply uninterrupted pregnancy and breast feeding and, this

depletes women biologically and drains their nutritional

resources.

The type of caregiver employment was found to have a more mixed

impact while access to independent income was generally

positivein some communities, especially in Guraghe/ Worabe,

Ethiopia, where focus group discussants identified problems

linked to the arduous hours worked by women market traders. The

study is enhanced by multivariable logistic regression and the

data are obtained from 2002 young lives Ethiopia survey.

Results show that infants/children in such households are weaned

as early as three months and left in the care of older siblings

while the mother spends all day or even several days travelling

and selling goods at market. Not only is child health potentially

compromised by premature weaning and introduction of age-

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inappropriate foods, but in the absence of community child-care

mechanisms, this employment pattern reduces the amount of time

available for child-care (Save the Children, 2005).

Various studies reported maternal education to have a positive

and statistically significant coefficient (Barrera (2005), Thomas

et al. (2005) and Barrera (2007). For example, using data from

five regions of Brazil, Thomas et al. (2006)a found that in urban

north east, relative to having an illiterate mother, a child with

a literate mother will be about 1.6% taller, 2.5% taller if she

has completed elementary school and 4.2% taller if she has

completed secondary school. Other studies such as (Barrera et al

(2000), Barrera et al (2007)), Thomas et al (2006), Chaudhuri et

al (2008) and Escobal et al (2009) tried to see the role of

maternal schooling and its interaction with public health

programs in child health production using bivariate analysis.

Household resources such as income are believed to be among the

important factors in the prediction of child health and

nutritional status. Nevertheless, there is lack of consistency

across studies over the significance of these variables. For

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example, using data from the 2006 Brazilian Demographic and

Health Survey, Thomas et al. (2006b)found using multinomial

logistic regression that total income has a positive and

significant effect on child weight in both urban and rural

sectors and the effect is much larger in magnitude in the rural

sector. On the other hand, as household size gets larger there is

a big chance of having economically inactive members in the

household and this leads to an adverse impact on the available

resources and thereby on child nutrition outcomes.

Raj (2009) using Chi-square and t-test analysis in India found

that the risk of malnutrition is higher in young children born to

mothers married as minors (<18 years) than in those born to women

married at a mature enough age. The results also showed that the

majority of births (73%) were to mothers married early, that is

before 18 years. The bivariate analysis of this study also showed

that there are significant associations between maternal early

marriage and infant and child diarrhea, malnutrition, low birth

weight and mortality.

24

Crepinsek et al (2010) using binary Logistic regression analysis

underscored that employment of mothers can have both positive and

negative implication on children’s dietary intake.Small babies -

especially low-birth weight (LBW) babies - are effectively born

malnourished and are at higher risk of dying in early life. LBW

is defined as a birth weight of less than 2,500 g. This indicator

is widely used because it reflects not only the status (and

likely nutritional health risks) of the newborn, but also the

nutritional well-being of the mother. That is, while a low birth

weight results from many other factors (including smoking,

alcohol consumption during pregnancy, genetic background and

other environmental factors), it remains a good marker for a

mother's weight gain and the fetus' development during pregnancy.

The growth and development of babies are affected by their

mother's past nutritional history. Malnutrition is an

intergenerational phenomenon. A low-birth-weight infant is more

likely to be stunted (low height-for-age) by the age of 5 years.

Such a child, without adequate food, health and care, will become

a stunted adolescent and later, a stunted adult. Stunted women

25

are more likely to give birth to low-birth-weight babies,

perpetuating the cycle of malnutrition from generation to

generation. In addition, a low-birth-weight infant remains at

much higher risk of dying than the infant with normal weight at

birth. The proportion of low-birth-weight infants in a population

is the major determinant of the magnitude of the mortality rates

and a proxy indicator for maternal malnutrition (WFP, 2005).

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CHAPTER THREE

3.1 Methodology

3.1.1 Data and Variables

This study utilized the SNNPR’s data of EDHS 2011 where completed

and plausible anthropometric data are available. SPSS was used

as statistical package to analysis of this the data. The 2011

Ethiopia Demographic and Health Survey (EDHS) wasconducted by the

CentralStatistical Agency (CSA) under the auspices of the

Ministry of Health. The primary objective of the 2011 EDHS is to

provide up-to-date information for planning, policy formulation,

monitoring and evaluation of population and health programs in

the country. In the 2011 EDHS information on population and

health covering topics on family planning, fertility levels and

preferences, infant, child, adult and maternal mortality,

27

maternal and child health, nutrition, women’s empowerment, and

knowledge of HIV/AIDS were collected. Moreover, the 2011 EDHS

include blood sample collection from the respondents of the

survey. To this effect a nationally representative sample of

about 18,500 households was selected and all women aged 15-49 and

all men aged 15-59 in these households were eligible for the

individual interview module of the survey.

The 2011 EDHS collected data on the nutritional status of

children by measuring the height and weight of all children under

age five which could be used to calculate three anthropometric

indicators—weight-for-age, height-for-age, and weight-for-

height.The three indices are expressed as standard deviation

units from the median for the reference group. The nutritional

status of children was calculated using new growth standards

published by the World Health Organization (WHO) in 2006.

This study will consider theanthropometric index of and weight-

for-age (Underweight) to measure children nutrition status. Child

28

nutrition status was categorized into three groups-severely

under-nourished (< -3.0 Z-score), moderately under-nourished (-

3.0 to -2.01 Z-score) and nourished (≥-2.0 Z-Score). Thus

nutrition status is an ordinal response variable grouped from a

continuous variable.

Explanatory variables are variables that are expected to

potentially affect/determine the response/dependent variables.

Several socio-economic, demographic and maternal and child health

characteristics are considered as the independent variables to

develop the proportional odds model(POM), partially proportional

ordinal model (PPOM), and separate binary logistic

regression(BLR) models. More generally, variables are listed in

the following table. The data are analyzed using SPSS package and

the descriptive results are shown in the following tables.

Dependent variables CodeY=nutritional status of

children under-five years of

age.

1=Severely Malnourished (<-3.0Z-score)

2=Moderately malnourished (-3.0to -2.01 Z-score)

3=Nourished (≥-2.0 Z-Score)

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Independent variables Code

Prenatal treatment by nurse/midwife

0 = No

1 = Yes Mother’s age at first birth 0= 15-20

1= 21-43

Size of child at birth

1= Below average

2=Average

3= Larger thanaverage

Preceding birth interval 0 = Below 24 months

1 = 24 & aboveSex of a child 0 = Male

1 = Female Received vitamin A 0 = No

1=YesDuring pregnancy given irontablet/syrup

0= No

30

1= Yes

Child age

1 =0-11 months

2 =12-23 months

3 =24-59 monthsArea of residence 0= Rural

1= UrbanMother’s highest education 0=No education

1=Primary/higherFather’s highest education 0=No education

1=Primary/higherBirth order 1 = 1-3

2 = 4-6

3 =>6

3.2 Statistical model

3.2.1Logistic regression model

Logistic regression is a technique that allows categorical

response variables which have binomial errors to bemodeled using

a regression analysis.Logistic regression analysis extends the

techniques of multiple regression analysis in which the outcome

variable is categorical. Logistic regression allows one to

predict a discrete outcome, such as group membership, from a set

of predictor variables that may be continuous, discrete,

31

dichotomous, or a mix of any of these (Gellman and Hill,

2007).Generally, when the dependent variable is dichotomous (such

as presence or absence, success or failure and etc) binary

logistic regression is used. The logistic regression is also

preferred to multiple regression and discriminant analysis as it

is mathematically flexible and easily used distribution and

requires fewer assumptions (Hosmer and Lemeshow, 1989). If the

response variable has more than two categories which are ordered

according to their importance, ordinal logistic regression (POM

or PPOM) should be applied to analyze the relationship between

the response and the independent variables. Unlike discriminant

analysis, logistic regression does not have the requirements of

the independent variables to be normally distributed,neither

linearly related nor of equal variance (homoscedasticity) within

each group (Tabachnick and Fidel, 1996). Logistic regression has

a peculiar property of easiness to estimate logit differences for

data collected both retrospectively and prospectively (McCullagh

and Nelder, 1983).The two main uses of logistic regression are

predicting group membership and providing knowledge of the

relationships and strengths among the variables.

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3.2.2 Binary logistic regression model description

Consider a random variable Y that can take on one of two

possible values. Given a data set with total sample size of n,

where each observation is independent, Y can be considered as a

column vector of n bernoulli random variablesyi. Let

Xi=(x0i,x1i,…xki)' be a vector of factors (explanatory variables)

corresponding to the i th subject, i=1,2,…n, wherex0i=1. Suppose

yi takes on the value 1 with probability∏(xi )=p (Yi=1׀Xi=xi ) and

the value 0 with probability1−∏(xi ). In logistic regression the

response probability ∏(xi ) is evaluated as:

∏(xi )=p (Yi=1׀Xi=xi )= eβ0+β1X1i+...+βkXki

1+eβ0+β1X1i+...+βkXki=

exp (β'Xi)1+exp (β'Xi)

(1)

whereβ=(β0,β1,β2,…,βk )'is a column vector of unknown regression

coefficients. The odds of success are defined as:

∏ (Xi )1−∏(Xi )

=exp {β'Xi} (2)

The log-odds (logit) are then given by:

33

log( ∏(xi )1−∏ (xi ) )=β'Xi,i=1,2,3,…,n (3)

An important feature of the multiple binary logistic regression

models is that the oddsthat an outcome will occur givena

particular category of a given covariate compared to the odds of

the outcome occurring given the reference category, adjusted for

all other covariates, can be calculated directly from the

logistic coefficients by ¿=exp(βk). However, this simple

relationship is true only if the relationship between the logit

and Xk is in fact linear and there are no interactions between

the covariates.

3.2.3 Ordinal logistic regression

There are several occasions when the outcome variable is multi-

level. Such outcome variable can be classified into two

categories-multinomial and ordinal. When the dependent variable

is classified according to some order of magnitude, one cannot

use the multinomial logistic regression model. A number of

34

logistic regression models have been developed for analyzing

ordinal response variables. Moreover, when there is a need to

take several factors into consideration, special multivariate

analysis for ordinal data is the natural alternative.There are

various approaches, such as the use of mixed models or another

class of models, probit for example, but the ordinal logistic

regression models have been widely used in most research works.

There are several ordinal logistic regression models such as

proportional odds model (POM), two versions of the partial

proportional odds model-without restrictions (PPOM-UR) and with

restrictions (PPOM-R), continuous ratio model (CRM), and

stereotype model (SM). The most frequently used ordinal logistic

regression model in practice is the constrained cumulative logit

model called the proportional odds model. The POM is widely used

in epidemiological and biomedical applications but POM relies on

strong assumptions that may lead to incorrect interpretations if

the assumptions are violated.

If the data fail to satisfy the proportional odds assumption, a

valid solution is fitting a partial proportional odds model.35

Another simple and valid approach to analyze the data is to

dichotomize the ordinal response variable by means of several

cut-off points and use separate binary logistic regression models

for each dichotomous response variable. However, some scholars

suggested that the second procedure should be avoided if possible

because of the loss in statistical power and the reduced

generality of the analytical solution.

3.4.3.1 The cumulative logit model

As discussed briefly, ordinal logistic regression refers to the

case where the dependent variable has an order. The most common

ordinal logistic model is the proportional odds model, also

called cumulative probabilities of the response categories. If we

pretend that the dependent variable is really continuous, but is

recorded as ordinal having ‘C’ categories (as might, for

instance, happen if income were asked about in terms of ranges,

rather than precise numbers), then the application of ordinal

logistic model is the appropriate method.

Attempts to extend the logistic regression model for binary

responses to allow for ordinal responses have often involved

36

modeling the cumulative logit. Consider a multinomial response

variable Y with categorical outcomes denoted by 1, 2, 3… C, and

letXi denote a k-dimensional vector of covariates for the ith

subject,i=1,2,…,n. The cumulative logit model was originally

proposed by Walker and Duncan (1944) and later called the

proportional odds model by McCullagh (1980). Suppose the response

variable Y has C ordered categorieswith probabilities

p(Yi=j׀Xi)=∏(j)(Xi )forj=1,2,…,C (4).

In multinomial logistic model, we have(C-1) ratios:

p(Yi=j׀Xi)

p (Yi=1׀Xi)=

∏(j )(Xi )∏(1 )(Xi )

forj=2,3,…,C;i=1,2,…,n (5 )

and the respective model for each can be estimated. Unlike

multinomial logistic model, we will consider the C-1 cumulative

probabilities:

γ(j )(xi)=p (Yi≤j׀Xi )=∏(1 )(Xi )+…+∏(j) (Xi),for j ¿1,2,…,C−1,i=1,2,…,n (6)

and write down a model for each of them. Note that

γ(C )(xi)=p (Yi≤C׀Xi )=1and hence, it need not be modeled.

The following holds for γ(j )(xi)=p (Yi≤j׀Xi ),for each subject

i=1,2,…,nand for each categoryj=1,2,…,C−1:

37

log( γ(j )(xi)1−γ(j)(xi ) )=log( p (Yi≤j׀Xi)

1−p (Yi≤j׀Xi ) )=α(j)−(β1X1i+β2X2i+,…+βkXki )=α(j )−Xi'β,

whereβ=(β1,β2,…,βk )'andXi=(X1i,X2i,…Xki)'.(7 )

That is, the ordinal logistic model considers a set of

dichotomies, one for each possible cut-off of the response

categories into two setsof ‘high’ and ‘low’ responses. This is

meaningful only if the categories of Y do have an ordering. A

binary logistic model is then defined for the log-odds of each of

these cuts.

3.4.3.2 Parameters of the model

The model for the cumulative probabilities is

γ(j )(xi)=p (Yi≤j׀Xi )=exp [α(j)−(β1X1i+β2X2i+,…+βkXki)]

1+exp [α(j )−(β1X1i+β2X2i+,…+βkXki )]=

exp (α(j )−Xi'β )

1+exp (α(j)−Xi'β)(8)

The intercepts α(1 ),α(2),….,α(C−1) must satisfy the condition that

α(1 )≤α(2)≤…≤α(C−1) to guarantee thatγ(1 )≤γ(2)≤…≤γ(C−1 ). The parameters

β1,β2,…,βk are the same for each value of j. There is thus only

one set of regression coefficient, not C-1 as in multinomial

38

logistic model. McCullagh (1944) calls this assumption of

identical log- odds ratio across C-cut points proportional odds

assumption, hence the name ‘proportional odds’ model. The

validity of this assumption can be checked based on a Chi−square

score test. The model that relaxes the proportional odds

assumption can be represented aslogit[γ(j )(xi) ]=α(j)−Xi'β(j), where the

regression parametersβ(j )are allowed to vary with j.The usefulness

of this latter model is to test the assumption of the

proportionality that there is perfect homogeneity within the

categories collapsed.

The probabilities for individual responses are:

p (Yi=1׀Xi )=γ(1 )(xi)=exp [α(1)−(β1X1i+β2X2i+,…+βkXki) ]

1+exp [α(1)−(β1X1i+β2X2i+,…+βkXki)](9)

p (Yi=j׀Xi )=γ(j )(xi)−γ(j−1)(xi)=exp [α(j)−(β1X1i+β2X2i+,…+βkXki) ]

1+exp [α(j)−(β1X1i+β2X2i+,…+βkXki) ]−

exp [α(j−1)−(β1X1i+β2X2i+,…+βkXki) ]1+exp [α(j−1)−(β1X1i+β2X2i+,…+βkXki) ]

(10)

for j=1,2,…,C−1 and

p (Yi=C׀Xi )=1−γ(C−1) (xi )=1−exp [α(C−1)−(β1X1i+β2X2i+,…+βkXki) ]

1+exp [α(C−1 )−(β1X1i+β2X2i+,…+βkXki ) ](11)

39

3.4.3.3The proportional odds assumption

The proportional odds assumption is thatβs are independent of j (

j=1,2,…,C−1). In other words, if we look at binary logistic

regressions of category 1 vs. 2, category 2 vs. 3, and so on,

then the intercepts inthe equations might vary, but the other

parameters would be identical for each model. Tocompare the

ordinal model with the binomial models, determine whether the

slopes are meaningfully different.

3.4.3.4 Score statistics and test

To understand the general form of the score statistics, let g (θ )

be the vector of first partial derivatives of the log likelihood

with respect to the parameter vectorθ, andletH (θ )be a matrix of

second partial derivatives of the log likelihood with respect toθ

. That is,g (θ ) is the gradient vector and H (θ ) is the Hessian

matrix. Let I (θ ) be either −H (θ) or the expected value of−H (θ).

Consider the null hypothesisH0:θ=θ¿. Let θ̂be the MLEofθ. The chi-

square score statistic for testing H0 is defined by:

g' ( θ̂−θ¿ )I−1 (θ̂−θ¿)g (θ̂−θ¿)

(12)40

This test statistic has an asymptotic chi−square distribution

with r degrees of freedom, where r is the number of restriction

imposed onθ byH0(SAS Institute Inc., 2008).

Test of Parallel Lines (proportionality assumption)

When fitting an ordinal regression we assume that the

relationships between the independent variables and the logits

are the same for all the logits. That means the results are a set

of parallel lines or planes—one for each category of the outcome

variable. We can check this assumption by allowing the

coefficients to vary, estimating them, and then testing whether

they are all equal.

For this test, the number of response levels (C¿ is assumed to be

greater than two. Let Y be the response variable taking the

values1,…,C, and suppose there are k explanatory variables.

Consider the general cumulative model without making the parallel

lines assumption:

g (p (Yi=j׀Xi ))=(1,Xi )θj,

whereg (. )is the link function, and θj=(α(j),βj1,βj2,…,βjk )'is a

vector of unknown parameters consisting of an intercept α(j ) and

41

K slope parameters(βj1,βj2,…,βjk )'. The parameter set for this

general cumulative model isθ=(θ'1,θ'2,…,θ'

C−1 )'. The null

hypothesis of parallelism is thatHo:β(1 )=β(2 )=…=β(C−1) , whereβ(j )the

vector of parameters in jth category, that is, there isa single

common slope parameter for each of the explanatory variables. Let

β1,β2,…,βk be the common slope parameters. Let α̂1,α̂1,…,α̂C−1 and

β̂1,β̂2,…,β̂k be the MLEs of the intercept parameters and the

common slope parameters.

Then under Ho, the MLE of θ is θ̂= (θ̂1,θ̂2,…,θ̂C−1)'with

θ̂j=(α̂j,β̂1,β̂2,…,β̂k )', and the chi-squared score statistic

g' ( θ̂)I−1 ( θ̂)g ( θ̂) has asymptotic chi-square distribution with k(C−2)

degrees of freedom. This tests the parallel lines assumptions by

testing the equality of separate slope parameters simultaneously

for all explanatory variables (SAS Institute Inc., 2008). If we

fail to reject the null hypothesis, then the test of parallelism

is recognized to be satisfied, or that the proportional odds

assumption is met.

42

If the proportional odds assumption is not met, there are several

options:

Collapse two or more levels, particularly if some of the

levels have smalln.

Do bivariate ordinal logistic analyses to see if there is

one particular independent variable that is operating

differently at different levels of the dependent variables.

Use the partial proportional odds model.

Use multinomial logistic regression

3.5 Interpretation of logistic regression

The coefficient of a continuous covariate is interpreted as the

change in the log-odds of an event of success per unit increment

in the corresponding covariate keeping other covariates constant.

In case of a categorical predictor variable, it is interpreted as

the log-odds of an event of success for a given category compared

to the reference category.

3.5.1 Why logistic regression is needed

43

One might try to use OLS regression with categorical dependent

variables. There are several reasons why this is not advisable:

The residuals are not normally distributed (as the OLS model

assumes), since they can only take on one of several values

for each combination of levels of the independent variables.

OLS might result in non-sense probabilities i.e,

probabilities greater than one or even negative.

For nominal dependent variables, the coding is completely

arbitrary, and for ordinal dependent variables it is (at

least supposedly) arbitrary up to a monotonic

transformation. Yet recoding the dependent variable will

give very different results.

3.5.2Assumptions of logistic regression

For a model to be valid, it has to satisfy certain assumptions.

According to Hosmer and Lemeshow (1989),there areassumptions one

should consider for the efficient use of logistic regression such

as:

Logistic regression assumes meaningful coding of the

variables. Logistic coefficients will be difficult to

44

interpret if not coded meaningfully. The convention for

binomial logistic regression is to code the dependent class

of greatest interest as 1 and the other class as 0.

Logistic regression does not assume a linear relationship

between the dependent and independent variables, but its

log-odds should have a linear relationship.

The dependent variable does not need to be normally

distributed, but it typically assumes a distribution from an

exponential family (e.g. binomial, Poisson, multinomial,

normal).

The groups must be mutually exclusive and exhaustive; a case

can only be in one group and every case must be a member of

one of the groups.

Larger samples are needed than for linear regression because

maximum likelihood coefficients are large sample estimates.

In other words, the estimator converges in probability to

the value being estimated.

There should not be severe co-linearity among predictor

variables.

45

3.6 Parameter estimation in ordinal logistic regression model

Fitting an ordinal regression model requires the estimation of

C−1+k parameters,i.e. the C−1 thresholds α=(α(1 ),α(2),….,α(C−1) )'and

the k components ofβ. Maximizing the log-likelihood function is

the most common procedureto obtain these estimations (e.g.

Anderson and Philips, 1981; Franses andPaap, 2001; Powers and

Xie, 2008).The standard choices for the distribution function F

are the logistic link function,F(x)=1 /(1+e−x) corresponding to the

logistic distribution function,or the probit link function,

F(x)=Φ(x), with Φ the distribution function of the standard

normal distribution.

Themaximum likelihood estimator is obtained by maximizing the

log-likelihoodfunction, i.e.

(α̂ ,β̂ )=argmax(α,β)∊❑C−1+k

l (α,β )undertheconstraintα(1)<α(2)<,….,¿α(C−1 )

, with

l (α,β )=∑i

n

∑j

C−1δijlog(F (α(j)−Xi

'β(j ))−F (α(j−1)−Xi'β(j ))), whereδij the indicator

function defined asδij={ 1,yi=j0,otherwise

(13 )

46

To explicitly take into account the ordering constraint in the

maximization, Franses and Paap (2001) recommend to re-

parameterize the log-likelihood function by replacing the vector

of thresholds α by γ = (γ(1 ),γ(2),…,γ(C−1 )¿'defined as:

α(1 )=γ(1 )

α(j )=γ(1 )+∑l=2

j(γ(l))2,forj=2,…C−1.

The parameter γ is uniquely defined bythatγ(j )>0,forj>1.The log-

likelihood function (13) can be rewritten as:

l (α,β )=∑i

n

∑j

C−1

δijlog(F(γ(1)+∑l=2

j(γ(l))2−Xi

'β(j ))−F(γ(1)+∑l=2

j−1(γ(l) )2−Xi

'β(j )))(14)

The maximum likelihood estimators of γ∧β are then given by

(γ̂ ,β̂ )=argmax(γ,β )∊❑C−1+k

l (γ,β )(15)

The advantage of the optimization problem in (15) is that no

constraints need to be put on the parameters: the resulting

estimates for the thresholds αwillbe automatically ordered.

Furthermore, equality of two thresholds implies zero values for

somej , withj>1, yielding minus infinity for the

47

objectivefunction in (14), and they can be excluded from the

solutions set.

3.6.2Odds Ratios

The odds ratio is the ratio of the odds of an event occurring in

one group to the odds of occurring in another group.In a cohort

study, odds ratio can be calculated by determining the odds of a

risk factor among individualswith the event of interest divided

by the odds of a risk factor among individuals without the event

of interest (Cornfield, 1951).In binary logistic regression, odds

ratio is the exponential of the estimated coefficientβ̂(exp (β̂)).An

odds ratio of one corresponds to an explanatory variable that

does not affect the outcome variable. For a continuous covariate,

exp (β̂) is the predicted change in odds of being malnourished

(underweight) for a unit increase in a predictor variable. In

case of categorical predictor variables, exp (β̂) is the predicted

change in odds of being malnourished for a given category of the

predictor variable with respect to the reference category.

Odds ratios and proportional odds:

48

The odds ratio of the event Yi≤j at x1 relative to the same

event at x2 is

¿=γ(j)(x1 )/[1−γ(j) (x1 ) ]γ(j)(x2 )/[1−γ(j) (x2 ) ]

=exp (α(j)−X1

'β)exp (α(j)−X2

'β)=exp [ (X2

'−X1' )β ] (16)

which is independent of j.Thus the cumulative odds ratio is

proportional to the distance between X1'∧X2

' which made McCullagh

(1980) call the cumulative logit a proportional odds model.

3. 6.3 Model Building and Variable Selection for Logistic

Regression

With several explanatory variables (predictors), there are many

potential models. Model selection for logistic regression faces

the same issues as ordinary regression. The selection process

becomes difficult when the number of explanatory variables

increases because of the increase in possible effects and

interactions. In model selection there are two competing goals:

on one hand the model should be complex enough to fit the data

well. On the other hand, it should be simple to interpret,

smoothing rather than over fitting the data (Agresti, 2002).

49

A multivariable model should contain at the outset all covariates

significant in the uni-variate analysis at the p-value 0.2 to

0.25 level and any other that are thought to be of clinical

importance. Any covariate that has the potential to be an

important confounder should also be included. Following the fit

of the multivariable model, we use the p-values from the Wald

tests of the individual coefficients to identify covariates that

might be deleted from the model. The partial likelihood ratio

test should confirm that the deleted covariate is not

significant. We should also check if the removal of a covariate

produces a ‘significant’ change in the coefficient of any of the

covariates remaining in the model. We continue until no covariate

can be deleted from the model.

3.7 Model selection for logistic regression

3.7.1Model deviance relative to its degrees of freedom

With a wide set of possible models available, as in the family of

generalizedlinear models, model selection is very important. It

often involves searchingfor the simplest reasonable model that

50

adequately describes the observeddata. Normed likelihoods and

deviances can provide ameasure of the distance of each model from

the data, of relative goodness offit. Two different types of

model selection may be distinguished:

1. A complex model containing many parameters may be under

consideration.A simpler submodel is to be selected by eliminating

some ofthe parameters (or, conversely, some parameter may be

added to a simple model).

2. Several distinct model functions, usually with different

parametersets, may be in competition.

Both situations require some means of calibrating normed

likelihoods for models of different complexity to make them

comparable (Lindsey, 1996).

3.7.2The Akaike information criterion (AIC)

The Akaike (1969) Information Criterion (AIC) is computed as:

AIC (p )=nln(SS (RES )p )+2p,

where SS(RES )p is the residual sum of squares and

pisthenumberofpredictors. Since SS(RES )pdecreases as the number

of independent variables increases, the first termin AIC51

decreases withp. However, the second term in AIC increases with

pand serves as a penalty for increasing the number of parameters

in the model. Thus, it trades off precision of fit against the

number of parameters used to obtain that fit.The AIC criterion is

widely used, although it is known that the criterion tends to

select models with larger subset sizes than the true model.

Because of this tendency to select models with larger number of

independent variables, a number of alternative criteria have been

developed. One such criterion is Schwarz (1978) Bayesian

Criterion (SBC) given by:

SBC (p)=nln (SS (RES)p)+ln (n )p.

Note that SBC uses the multiplierln(n) (instead of 2 in AIC).

Thus, it more heavily penalizes models with a larger number of

independent variables than does AIC. The appropriate value of the

subset size is determined by the value ofp at which SBC (p)

attains its minimum value (Rawlings et al, 1998).

3.8 Assessment of the Fitof Logistic Regression Model

After fitting the logistic regression model or once a model has

been developed through the various steps in estimating the

52

coefficients, there are several techniques involved in assessing

the appropriateness, adequacy and usefulness of the model.

First,the overall goodness of fit of the model will be tested.

Thenthe importance of each of the explanatory variables will be

assessed by carrying out statistical tests of significance of the

coefficients (Agrresti, 1996).

3.8.1Goodness of Fit of the Model

3.8.1.1Deviance and Pearson's Goodness-of-Fit Test

By goodness of fit of a model we mean how well the model

describes the response variable. Assessing goodness of fit

involves investigating how close values are predicted by the

model with that of observed values (Bewick et al., 2005). We can

compare the likelihood of the current model (Lc) with that of the

full modelor saturated model (Lf).The scaled devianceis often

defined,in generalized linearmodel (GLM) terminology,as:

D (c,f )=−2log(Lc

Lf ) (17)

where the full model is the model that has as many location

parameters as observations, that is, n linearly independent53

parameters. Thus, it reproduces the data exactly but with no

simplification,hence being of little use for interpretation. The

current model is the model that lies between the maximal and the

minimal model.The larger the deviance, the less fit is the model

to the data (Lindsey, 1996).The deviance has a chi-

squaredasymptotic null distribution with degrees of freedom equal

to the difference between the numbers ofparameters in the

saturated and unsaturated models.

In addition, Pearson's goodness-of-fit test is a very common and

useful test for several purposes. It can help determine whether a

model fits well, or a pair of categorical variables is

associated. It is computed as:

X2=∑i=1

C (Oi−Ei)2

Ei,(18)

whereOiis a count of the number of observed items in categoryi,

Ei is the expected number of items in category i, and ‘C’ is the

number of categories. Since the binomial formula forms the

foundation of this test, the expected number of items in a

category is determined by the expected value of a binomial random

54

variable. That is,Ei=npi   where n is the number of

observationsand piis the probability of obtaining an observation

in category i.  The Pearson chi-square statistics has an

asymptotic X2-distribution with (C-1) degrees of freedom when it

is used to test several proportions simultaneously.

3.8.1.2 Pseudo-R2

When analyzing data with a logistic regression, an equivalent

statistic to R-squared does not exist.  The model estimates from

a logistic regression are maximum likelihood estimates arrived at

through an iterative process.  They are not calculated to

minimize variance, so the OLS approach to goodness-of-fit does

not apply. However, to evaluate the goodness-of-fit of logistic

models, several pseudo R-squares have been developed. These are

"pseudo" R-squares because they look like R-squared in the sense

that they are on a similar scale, ranging from 0 to 1 (though

some pseudo R-squares never achieve 0 or 1) with higher values

indicating better model fit, but they cannot be interpreted as

one would interpret an OLS R-squared and different pseudo R-

squares can arrive at very different values. The most commonly

55

encountered pseudo R-squares are Cox and Snell pseudo R-square,

Nagelkerke / Cragg & Uhler's R-square, McKelvey &Zavoina, etc.

Let Lf be likelihood of the model with predictors and L0 is

likelihood of model with only intercept (null model), then the

Cox and Snell R2is given by:

R2=1−[L0Lf ]2n (19 )

The ratio of the likelihoods inEq.19 reflects the improvement of

the full model over the intercept model (the smaller the ratio,

the greater the improvement).Note that Cox & Snell's pseudo R-

squared does not attain the value one even if the full model

predicts the outcome perfectly.The NagelkerkeR2can be evaluated

as:

R2=

1−[L0

Lf ]2n

1−L0

2n

(20)

where itadjusts Cox& Snell's so that the range of possible values

extends to 1.

3.8.1.3 Likelihood-Ratio Test

56

An alternative and widely used approach to test the significance

of a number of explanatory variables is the likelihood ratio

test. This is appropriate for a variety of types of statistical

models. Agrresti (1990) argues that the likelihood ratio test is

better, particularly if the sample size is small or the number of

parameters is large. The likelihood-ratio test uses the ratio of

the maximized value of the likelihood function for the full model

(Lf) over the maximized value of the likelihood function for the

null model (L0). The likelihood-ratio test statistic is given by:

G2=−2ln[ L0Lf ]=−2 {ln L0−ln Lf} (21)

where L0 is the likelihood function of the null model and Lf is

the likelihood function of the full model evaluated at the

MLEs.This natural log transformation of the likelihood functions

yields an asymptotically chi-squared statistic with degree of

freedom equal to the difference between the numbers of parameters

estimated in the two models (Menard, 2002). It tests the null

hypothesis that all population logistic regressions coefficients

are zero except the constant one. i.e., it tests:

Ho:β1=β2=β3=…=βk=0 VsH1:βj≠0foratleastonej,j=1,2,…,k

57

3.8.2 The Wald Test

The Wald test is a member of what is known as trinity of

classical likelihood testing procedures, the other two being the

likelihood ratio (LR) and Lagrange multiplier (LM) tests. It is

an alternative test which is commonly used to test the

significance of individual logistic regression coefficients. Wald

X2(chi-square) statistics are calculated as:

Zj2= ( β̂j

se(β̂j) )2

, j=1, 2,…,k (22)

Each Wald statistic is compared with a chi-square distribution

with 1 degree of freedom. Wald statistics are easy to calculate

but their reliability is questionable, particularly for small

samples. For small sample sizes, the likelihood ratio test is

more reliable than the Wald test (Agresti, 1996).

3.8.3 Residuals diagnostics

Residuals are the vital for logistic regression diagnostics. They

can be useful for identifying potential outliers or

misspecification of models and another use for residuals is in58

checking normality. As the literature on adjustment diagnosis or

evaluationtools for ordinal models is relatively scarce, Hosmer &

Lemeshow (2000) suggest the use of binary regressions,separated

for each cut-off point, thus creatingdiagnosis statistics for the

ordinal models. Residualgraphs are normally constructed for

proportional oddsmodels using the adjustment of these models to

predicta series of binary eventsY>j,j=1,2,...,C.Therefore,

forthe indicator variableYandj, the residual score forcase i and

covariatekis given by:

Uik=Xik (p [Yij]−P̂ij)

P̂ij=1

1+exp [−(α̂(j)−Xi'β̂ )]

(23)

In residual score graphs, the meanU.k and the respective

reliability intervals are placed along the vertical axis, with

the response variable categories along the horizontal axis. If

the proportional odds assumption is valid for each covariate, the

reliability intervals foreach category of the response variable

should have a similar appearance.

59

Partial residuals are also widely used for checking ifall the

covariates of the model have linear behavior.In the context of

ordinal regression, it is necessary tocalculate binary logistic

regression models for all thecut-off points of the response

variable Y, with the partialresidual for each casei and the

covariatek being defined in the following way:

rik=X'ik β̂k+p [Yij]−P̂ij

P̂ij (1−P̂ij )(24 )

The partial residual graphs provide estimates of how each

covariatexrelates to each category of response variable (Y). So,

partial residuals are used to check the need for changes in

thecovariate (linearity) or even the validity of the proportional

odds assumption(parallelism of the curves).

60

CHAPTER FOUR

4.Results and discussion

4.1 Descriptive statistics

61

According to the results shown ontable 1, the number of severely

malnourished children is 164(37.4%) while 106(24.2%) are

moderately malnourished and 168 (38.4%) are nourished.

Table 1: Classification of nutritional status of under-fivechildren in SNNPR state

Table 2 presents the descriptive statistics of the covariates

considered in this study. As can be seen from the table, among

those who took vitamin A, 71 (32.3%)are severely malnourished

while of those who never took vitamin A, 93(42.7%) are severely

malnourished. Moreover, among those who took vitamin A, 58

(26.4%) are moderately malnourished. This figure is 48 (22.0%)

among those who never took vitamin A. Among those children who

reside in urban areas 36.3%, 24.7% and 39.0% are severely

malnourished, moderately malnourished and nourished,

respectively. And for those who reside in rural areas 38.3%,

62

N %Nutritional status

Severely malnourished (< -3 z-score)

164

37.4

Moderately malnourished( -3to -2.01 z-score)

106

24.2

Nourished(>-2.0 z score) 168

38.4

23.8% and 37.9% are severely malnourished, moderately

malnourished and nourished, respectively.

Among those children whose mothers have not received iron

tablet/syrup during pregnancy, 91 (40.8%), 57 (25.6 %), 75

(33.6%) are severely malnourished, moderately malnourished and

nourished, respectively. These figures are 73 (34.0%), 49 (22.8%)

and 93 (43.3%) for those children whose mothers have received

iron tablet/syrup, respectively. We can also observe that out of

children who fall in the first age group (0-11 months), 32

(49.2%), 20 (30.8%) and 13 (20.0%) are severely malnourished,

moderately malnourished and nourished, respectively. Moreover,

among those children who fall in the last age group, 105 (33.9%),

70 (22.6%) and 135 (43.5%) are severely malnourished, moderately

malnourished and nourished, respectively.

Among those children whose fathers who have no education, 75

(45.5%), 36 (21.8%), 54 (32.7%) are severely malnourished,

moderately malnourished and nourished respectively. These figures

are 89 (32.6%), 70 (25.6%) and 114 (41.8%) for those children

63

whose fathers educational level is primary/higher, respectively.

The descriptive statistics show that among those children whose

mothers are illiterate, 44.4%, 19.4%, 36.2% are severely

malnourished, moderately malnourished and nourished, respectively

while for those with primary/higher education, 31.8% are severely

malnourished, 28.1% are moderately malnourished and 40.1% are

nourished.

According to the results, among children whose mothers were not

treated by nurse/midwife 75 (37.1%) are severely malnourished 48

(23.8%) are moderately malnourished and 79 (39.1%) are nourished.

The respective figures are 37.7%, 24.6% and 37.7% for those

children whose mothers treated by nurse/midwife.

According to the output, among those children whose mothers fall

in the age group 15-20 years at first birth, 96 (41.2%) are

severely malnourished, 54 (23.2%) are moderately malnourished and

85 (35.6%) are nourished. For the age group 31-43 years, these

figures are 33.2%, 25.4%, 41.5%, respectively. And among those

64

children whose size at birth is smaller than average, 49.3%,

18.8% and 31.9% are severely malnourished, moderately

malnourished and nourished, respectively, while these figures are

25.4%, 30.8%, 43.5% for those children whose size at birth is

larger than average.

65

Table 2: A cross-tabulation of nutritional status versus

covariatesnutritional status

TotalSeverelymalnouris

hed

Moderately

malnourished

Nourished

Type of place of residence

Rural 98 61 97 256

38.3% 23.8% 37.9% 100.0%

Urban 66 45 71 182

36.3% 24.7% 39.0% 100.0%

Mother's highest educational level

No education 87 38 71 196

44.4% 19.4% 36.2% 100.0%

Primary &higher

7731.8%

6828.1%

9740.1%

242100.0

%

Sex of child Male 9843.6%

4720.9%

8035.6%

225100.0

%

Female 6631.0%

5927.7%

8841.3%

213100.0

%

66

Prenatal: nurse/midwife

No 7537.1%

4823.8%

7939.1%

202100.0

%

Yes 8937.7%

5824.6%

8937.7%

236100.0

%

During pregnancy, given or bought irontablets/syrup

No 9140.8%

5725.6%

7533.6%

223100.0

%

Yes 7334.0%

4922.8%

9343.3%

215100.0

%

Mothers' age at 1st birth

15-20 9641.2%

5423.2%

8535.6%

233100.0

%

21-43 6833.2%

5225.4%

8541.5%

205100.0

%

Received Vitamin A

No 9342.7%

4822.0%

7735.3%

218100.0

%

Yes 7132.3%

5826.4%

9141.4%

220100.0

%

Man's highest edu.

No education

7545.5%

3621.8%

5432.7%

165100.0

%

Primary/high

8932.6%

7025.6%

11441.8%

273100.0

%Child's age in month

0-11 3249.2%

2030.8%

1320.0%

65100.0

%12-23 27

42.9%16

25.4%20

31.7%63

100.0%

67

24-59 10533.9%

7022.6%

13543.5%

310100.0

%

Child size at birth

Smaller than average

6849.3%

2618.8%

4431.9%

138%100.0

%

Average 6337.1%

4023.5%

6739.4%

170100.0

%Larger than average

3325.4%

40

30.8%

5743.8%

130100%

Birth order

1-3 7736.8%

5526.3%

7736.8%

209100.0

%

4-6 6241.3%

2818.7%

6040.0%

150100.0

%

>6 2531.6%

2329.1%

3139.2%

79100.0

%

Preceding birth interval

Below 24 yrs

10140.6%

6726.9%

8132.5%

249100.0

%

24months& above

6333.3%

3920.6%

8746.0%

189100.0

%

Fitting an ordinal logistic regression model

In this study, ordinal logistic regression analysis is used to

examine the effect of each covariate on the nutritional status of

under- five children. To select the covariates to be included in

the final model, uni-variable ordinal logistic regression models

68

are developed for each covariate. The results are given on Table

3.

Table 3: Parameter estimates of uni-variable ordinal logistic

regression

Estimate

Std.Error

Wald Df Sig. 95%ConfidenceInterval

Lower Bound

Upper Bound

[Resid.place=Rural][Resid.place=Urban]

-.0660a

.179.

.137.

10

.711.

-.418.

.285.

[Edu mother=No edu] [Edumother=Primary]

-.3520a

.178.

3.887.

10

.049.

-.701 -.002

[Child Sex =Male][Child Sex =Female]

-.3890a

.178.

4.808.

10

028.

-.738 -.041.

[Treatment by=No][Treatment by=Yes]

.0420a

.177.

.057.

10

.812.

-.305.

.390.

[Treatduringpre -.352 .177 3.930 1 .047 -.700 -.00

69

g= No][Treatduringpreg= Yes]

0a . . 0 . . 4.

[Motherage@1st=<20][Motherage@1st=>20]

-.2950a

.178.

2.754.

10

.097.

-.643.

053.

[Vitamin A= No][Vitamin A= Yes]

-.3500a

.177.

3.884.

10

.049.

-.697.

-.002.

[edu. man= No edu][edu, man= Primary]

-.4700a

.184.

6.562.

10

.010.

-.830.

-.111.

[child age=0-11][child age=12-23][child age=24-59]

-.809-.4460a

. 259.257.

9.7343.013.

110

.002

.083.

-1.317-.949.

-.301

058.

[child size=<average][child size=average][child size=> average]

-.766-.3260a

.229

.217.

.229

.217.

110

.001

.133.

-1.216-.751.

-.317

.100.

[Birthor=1-3][Birthor= 4-6][Birthor= >6]

-.155-.1850a

.245

.257.

.403

.516.

110

.525

.472.

-.635-.690.

.324

.320.

[preceB.inter=<24yrs][prece.B.inter=>24yrs]

-.4470a

.180.

6.195.

10

.013.

-.799.

-.095.

70

As can be seen from Table 3 the covariates, sex of child,

educational level of mother and father/partner,size of child,

treatment during pregnancy,preceding birth interval and use of

Vitamin A are significant. At the modest 10-20% level of

significance, child age, mothers’ age at first birth and place of

residence are also considered in the final model. The results of

finalmodel are displayed in table 4 below. We can see that the

covariates place of residence, birth order and treatment by

nurse/midwife are not significant.

71

Table4: Parameter Estimates for final modelEstima

teStd.Error

Wald Df Sig. 95%ConfidenceInterval

LowerBound

UpperBound

Threshold

[Nutri. status = Severe] -2.198 .418 27.6

04 1 .000 -3.017

-1.378

[Nutri. status =Moderate] -1.088 .408 7.11

9 1 .000 -1.888 -.289

Location [Resid.place= Rural] -.053 .190 .077 1 .781 -.424 .319

[Resid.place= Urban] 0a . . 0 . . .

[Edu. mother=No edu.] -.417 .188 4.93

2 1 .026 -.785 -.049

[Edu.mother=Prim/high] 0a . . 0 . . .

[Child sex =Male] -.368 .186 3.896 1 .048 -.733 -.003

[Child sex=Female]

0a . . 0 . . .

72

[Treatment by=No] -.122 .189 .419 1 .518 -.492 .248[Treatment by=Yes] 0a . . 0 . . .

[Treatduringpreg=No] -.402 .187 4.64

0 1 .031 -.769 -.036

[Treatduringpreg=Yes] 0a . . 0 . . .

[Motherage@1st=15-20] -.380 .187 4.15

5 1 .042 -.746 -.015

[Motherage@1st=21-43] 0a . . 0 . . .

[Vitamin A= No] -.367 .185 3.959 1 .047 -.729 -.006

[Vitamin A= Yes] 0a . . 0 . . .

[eduman= No edu.] -.565 .195 8.397 1 .004 -.947 -.183

[eduman= Prim/high] 0a . . 0 . . .

[Childage=0-11] -1.060 .270 15.373 1 .000 -

1.590 -.530

[Childage=12-23] -.661 .271 5.957 1 .015 -

1.191 -.130

[Childage=24-59] 0a . . 0 . . .[Child size= <Average] -.788 .240 10.8

36 1 .001 -1.258 -.319

[Child size= Average] -.416 .225 3.41

0 1 .065 -.857 .027

[Childsize=>Average] 0a . . 0 . . .

[Birthorder= 1-3] -.278 .258 1.158 1 .282 -.784 .228

[Birthorder=4-6] -.251 .273 .847 1 .357 -.787 .284[Birthorder= >6] 0a . . 0 . . .[Prece.B.inter=Below 24] -.477 .188 6.43

8 1 .011 -.845 -.108

[Prece.B.inter=24&above] 0a . . 0 . . .

73

Link function: Logit.a. This parameter is set to zero because it is redundant.Test of goodness-of-fit of the final model

Before proceeding to examine the individual coefficients, we need

to conduct an overall test of the null hypothesis that the

location coefficients for all of the variables in the model are

zero. We can base this on the change in –2log-likelihood when the

variables are added to a model that contains only the intercept.

The change in the likelihood function has a chi-square

distribution even when there are cells with small observed and

predicted counts.

From the results, table 5, we see that the difference between

the two log-likelihoods (the chi-square test statistic) has an

observed significance level of less than 0.05. Thus, we can

reject the null hypothesis that the model without predictors is

as good as the model with the predictors, and conclude that the

model with predictors improves the model fit. In other words the

significant chi-square statistic indicates that the final model

is a significant improvement over the baseline intercept-only

model. This is an indication that the model gives better

74

predictions than if one just guessed based on the marginal

probabilities for the outcome categories.

Table 5: Results of deviance based goodness-of-fit test

Model -2 Log

Likelihood

Chi-Square Df Sig.

Intercept

Only940.808

Final 878.680 62.128 15 .000

Another method of checking the goodness-of-fit of a model is

through comparing the observed frequencies with those of the

expected frequencies obtained based on the fitted (predicted)

probabilities. We can use Pearson and Deviance chi-square tests

for this purpose. The results of the two tests are given in table

6. We can see that the null hypothesis that the model fits well

is not rejected since both test statistics are not significant.

This result supports the conclusion we reached at using the

difference in the -2log likelihood between the intercept only

model and the model with covariates.

75

Table 6: Results of Goodness-of-Fit tests

Chi-Square Df Sig.Pearson 862.328 847 .350Deviance 874.521 847 .249.

R2-statistics

There are various pseudoR2 statistics of goodness-of-fit of

logistic regression models. However, these measures are not

considered as the R2in ordinary least squares regression due to

the categorical nature of the response variable. The results are

given in Table 7. The Cox and Snell, Nagelkerke and McFadden

pseudo R2statistics are 13.2%, 15.0% and 6.6%, respectively.

Table 7:Pseudo R-Square

Cox and Snell .132Nagelkerke .150McFadden .066

Test of parallelism

One important assumption of the ordinal logistic regression model

is that the regression coefficients are the same for all

76

categories of the response variable. If we reject the assumption

of parallelism, we should consider the multinomial regression

model which estimates separate coefficients for each category.

The result of test of parallelism is shown in Table 8 below.At

the 5% level of significance there is no adequate evidence to

reject the null hypothesis that thelocation parameters are the

same across response categories. Therefore, we conclude that the

slope coefficients are the same across the response categories.

Table 8: Test of Parallel Lines

Model -2 LogLikelihood

Chi-Square Df Sig.

Null Hypothesis 878.680General 853.810 24.870 15 .052

4.2Interpretation and discussion of results

When the assumption of proportionality/parallelism holds, the

coefficients of the explanatory variables in an ordinal logistic

regression model are interpreted in terms of the logarithm of the

ratio of the odd of a particular category to the reference

77

category. Interpretation of the parameters corresponding to the

significant variables is presented below.

Mothers’ age at first birth significantly influences the

nutritional status of children. The likelihood of severe/moderate

malnutrition for children whose mothers aged 15-20 years at first

birth is about 1.46 times higher than those whose mothers’ age at

first birth was 21 or more. This figure can be as low as 1.015

and as high as 2.109 with 95 percent confidence. This result is

consistent with that of Raj (2009) in that the risk of

malnutrition is higher in young children born to mothers who get

married earlier than in those born to women who give birth at a

mature age.Therefore, as maturity of mothers increases at first

birth, the likelihood of child malnutrition decreases.

The other significant covariate is mothers’ treatment with iron

tablet/syrup during pregnancy. The estimated odds ratio

(OR=exp(0.402)=1.495) indicates that the likelihood of

severe/moderate malnutrition for children whose mothers haven’t

taken iron tablet/syrup during pregnancy is 1.495 times higher

78

than those children whose mothers received iron tablet/syrup

during pregnancy.This figure can be as low as 1.037 and as large

as 2.157. The study result indicates that the likelihood of

getting malnourished decreases for those children whose mothers

are treated by iron tablet/syrup during pregnancy. This result is

consistent with that of Das et al (2011) in that the antenatal

and/or postnatal care status of mothers significantly affects the

nutritional status of children under-five years of age. The

results also indicate that the likelihood of severe/moderate

malnutrition for children who were not given Vitamin A in the six

months prior to the survey is 1.444 times higher than those

children who were given Vitamin A. Moreover, male children are

1.445 times more likely to experience severe/moderate

malnutrition as compared to their female counterparts.Ahmed et al

(2012) also found that female children are less likely to become

moderately andseverely malnourished than their male counterparts.

At the country level in Ethiopia, all the four welfare monitoring

surveys from 1996-2004 have revealed that boys are more

vulnerable to malnutrition than girls with respect to the three

79

indices (wasting, stunting, and underweight) (Alemu et al.,

2007).

Children whose age is less than 11 months are 2.89 times more

likely to be severely/moderately malnourished as compared to

those in the age group 24-59 months. This figure can be as low as

1.7 and as high as 4.9. In other words, the odds of

severe/moderate malnutrition are higher forchildren of age less

than 11 months as compared to those children of age 24 to 59

months, holding all other covariates constant. Moreover, Children

whose age falls between 12 and 23 months are 1.94 times more

likely to be severely/moderately malnourished as compared to

those in the age group 24-59 months. This result agrees with that

of Pryer (2003) in that theage of a child is significantly

associated with status of malnutrition.However, the result is

inconsistent with the finding of Afeworket al (2005) in which age

and malnutrition are positively associated.

From the results we can also see that the size of children at

birth is significant. The odds of severe /moderate malnutrition

80

for children whose size was smaller than average at birth are 2.2

times higher as compared to those children whose size was larger

than average. However, there is no significant difference in the

likelihood of severe/moderate malnutrition between children of

average and larger than average sizes at birth. Our result

matches that of Rayhan et al (2006) in that children born with

smaller than average size had higher risk of being malnourished

as compared to those with larger size at birth. Thus, result

shows that as the size of children at birth increases, the

likelihood of getting malnourished decreases.

Preceding birth interval is a significant predictor of child

malnutrition. The odds of severe/moderate malnutrition for

children with preceding birth interval below 24 months is 1.611

times higher than those with preceding birth interval 24 years

and above, keeping all other covariates fixed. This figure can be

as low as 1.115 and as high as 2.328. This result is consistent

with the findings of Sommerfelt et al. (2008) in that higher

birth spacing is likely to improve child nutrition since the

mother gets enough time for proper childcare and feeding. The

81

finding of ACC/SCN (2008) also indicates that closely spaced

pregnancies are often associated with the mother having little

time to regain lost fat and nutrient stores.So, the less the

birth spacing, the higher the risk of child malnutrition.

The other significant predictor is mothers’ educational status.

The estimated odds ratio (OR=exp(0.417) = 1.52) indicates that

the likelihood of severe/moderate malnutrition for children whose

mothers are illiterate is 1.52 times larger than those children

whose mothers’ educational level is primary/higher, keeping all

other covariates constant. This figure can fall between 1.050 and

2.192, inclusive. Moreover, children whose father/partner is

illiterate are 1.76times more likely to experience

severe/moderate malnutrition as compared to those children whose

father’s/partner’s educational level is primary/higher. Our

result is consistent with that of Caldwell (1979) who found that

infant and child mortality are highly associated with mothers’

education that increases the awareness of how to care for their

children beforeand after birth and enables them to change feeding

and child care practices by shaping and modifying the traditional

familial relationships. The study also revealed that education

82

plays an important role to improve knowledge of medical and

health care. Particularly mothers’ education enhances more

effective health care practices that increase their productivity

and influence infant and child mortality.

CHAPTER FIVE

5. Conclusions and Recommendation

5.1Conclusion

The study shows that various socio-demographic and health service

covariates are significant determinants of malnutrition.

Accordingly, the findings of the study show that size of child at

birth, use of vitamin A during six months prior to the survey,

prenatal treatment by iron tablet/syrup, education level of

mother/father/partner, mothers’ age at first birth, preceding83

birth interval, sex and age of a child have statistically

significant effect on the outcome of nutritional status of

children under-five years of age.

For instance, as the size of a child at birth rises, the

likelihood of getting malnourished falls. Those children who are

privileged to use vitamin A have more chance of escaping from the

problem of malnutrition. Moreover, prenatal treatment of mothers

by iron tablet/syrup is very important to reduce the problem of

malnutrition in children of under-five years of age.

5.2 Recommendation

84

The results obtained using ordinal logistic regressions indicate

certain directions to come up with recommendations that can help

to tackle the problem of malnutrition of children under-five

years of age in the SNNPR region. Some of the recommendations

are:

Children from mothers who were treated by iron tablet/syrup

during pregnancy were at less risk of malnutrition. Thus,

treatment of mothers during pregnancy should be given due

attention.

Children from mothers of age 10-20 years at first birth are

at higher risk of malnutrition. Thus, educating women about

the adverse effect of early marriage (conception) is of

paramount importance.

Shorter birth intervals are associated with a higher

likelihood of child malnutrition. Thus, the advantage of

adequate birth spacing should be communicated to the

society.

Children of earlier age (less than 11 months) are more

vulnerable to malnutrition. Thus, special attention should

be given for children in this age group.85

Access to education for mothers/fathers/partners should be

given due emphasis.

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Annex

89

90

I, the undersigned, declare that the thesis is my original work

and has not been presented for a degree in any other university

and that all sources of material used for the thesis have been

dully acknowledged.

Name: Desalegne Mesa

Signature_____________________________

Date_________________________________

This thesis has been submitted for examination with my approval

as a university advisor.

Name: Dr. Emmanuel G/Yohannes

Signature_____________________________

Date_________________________________

91