Abstract:
Multivariate longitudinal ordinal data are collected for studying the dependence between
multivariate ordinal outcomes, the changes over time and associated determinant factors. This
emanates from the interdependence of the three dimensions of household food security statuses,
the stability of these dimensions over time and the additional contribution of covariates on the
dependence structure.
It is generally known that the random effect models have a lack of population-averaged
interpretation for non-normally distributed outcomes in analysing ordinal data. In this thesis, we
propose an alternative model for analysing multivariate longitudinal ordinal data with application
to the household food insecurity by developing a pair copula construction (PCC) and cumulative
logit marginal distributions-based model using the full maximum likelihood estimation (MLE)
method. The simplified log-likelihood function of the D-vine pair copula multivariate discrete
random variables was obtained with its parameters estimated.
Data were collected from 646 households living in selected rural Woredas of South Wollo Zone
of the Amhara Regional State, Ethiopia from June 2014 to June 2015 three times at six months
interval. Multistage cluster sampling was employed to select representative Woredas and
households. The household food security status was determined using both the quartile score and
composite index. Three distinct pair copula models with cumulative logit version were employed
for multivariate, longitudinal and multivariate longitudinal ordinal data applicable for household
food security.
The first model was employed to assess the dependence between food security dimensions and
their corresponding determinant factors simultaneously. The copula parameter of this model
indicated that household food security dimensions have significant and positive pairwise dependence. The marginal parameters showed that smaller land size, shortage of rainfall,
cultivating once a year, and the presence of disease were positively associated with chronic to
mild food insecurity in all dimensions. Moreover, cold agro-ecology and market price increase
were associated with household food insecurity at availability and accessibility dimensions.
The second model was used to assess the stability of household food security over time and the
determinant factors. The copula parameter revealed that individual household food security status is not stable over time. Moreover, the marginal parameter indicated that presence of crop
disease, market price increase and medium agro-ecology were the significant recurrent factors
for households to have chronic to mild food insecurity throughout the study period. One-time
cultivation per year was the temporal significant factor for household food insecurity.
The third model was developed for measuring the dependence between the three dimensions,
namely, their stability over time, the effects of the covariates both on the dependence structure,
and stability over time simultaneously. The copula parameter of the population-average
cumulative logit model revealed that food security dimensions were positively dependent to each
other and the individual household food security status is not stable over time.
The marginal parameter of this model provided that lower agro-ecology, shortage of rainfall,
presence of cultivation disease, increased market price, use of pesticides, cultivating smaller
types of cereal crops, and cultivating once per year were positively affects the household food in security in availability dimension. On the other hand, lower agro-ecology, increased market
price, herbing small amount of livestock, hot agro-ecology and small farmland size positively
affect the household food insecurity in the accessibility dimension. Furthermore, households
headed by wife, divorced/widowed marital status of the household head, shortage of rainfall, and
small farmland size positively affect the household food in-security in utilisation dimension.
This model provided a population-average interpretation with acceptable computational
challenges in multivariate longitudinal ordinal data analysis. The study suggests that food
security situation analysis is a multidimensional so that over-sighting the three dimensions over
time simultaneously provides detail household food security situation than the single dimension.
The pair copula population-average cumulative logit model addressed all the food security dimensions simultaneously, and the model found computationally effective. Therefore, we
suggest this model to apply for other application areas for not extremely large number of
outcomes and covariates.
