Modelling the stability and determinants of household food insecurity: a multivariate longitudinal ordinal logistic regression approach

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.