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    A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem
    (Elsevier, 2023) Moges, Demmelash Mollalign; Mushi, Allen R.; Wordofa, Berhanu Guta
    This paper presents a new method for solving an intuitionistic fuzzy multi-objective linear fractional optimization (IFMOLFO) problem with crisp and intuitionistic fuzzy constraints. Here, all uncertain parameters are represented as triangular intuitionistic fuzzy numbers. We used an accuracy ranking function and variable transformation in the proposed method to convert an IFMOLFO problem into a crisp multi-objective linear optimization problem. Then, we formulated the first phase of the weighted intuitionistic fuzzy goal programming (WIFGP) model to obtain an intuitionistic fuzzy non-dominant (IFND) solution for the IFMOLFO problem. Several strategies for obtaining an IFND solution to the IFMOLFO problem have been proposed in the literature. However, in addition to constructing the phase-I WIFGP model, this study shows that the IFND solution may not be Pareto-optimal when some of the under-deviation variables are zero. As a result, the second phase of the WIFGP model is applied to address this issue. The benefits of both models are merged to provide a novel method, unlike any other method in the literature, for producing optimal solutions that satisfy both IFND and Pareto-optimal requirements. The suggested algorithm’s efficiency and reliability are demonstrated by addressing a real-life case study of an agricultural production planning problem and followed by solving a numerical example from literature.
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    Two phase heuristic algorithm for the university course timetabling problem: The case of University of Dar es Salaam
    (Tanzania Journal of Science, 2011) Mushi, Allen R.
    University course timetabling is the problem of scheduling resources such as lecturers, courses, and rooms to a number of timeslots over a planning horizon, normally a week, while satisfying a number of problem-specific constraints. Since timetabling problems differ from one institution to another, this paper investigated the case of the University of Dar Es salaam, based on the combination of Simulated Annealing (SA), and steepest descent in a two-phase approach. Solutions have been generated which greatly outperform the manually generated ones. Furthermore, the method compares well with previous work on Tabu Search but with faster execution time and higher quality on rooms allocation. It is concluded that the approach gives good results given a careful selection of parameters.
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    Solving multi-objective multilevel programming problems using two-phase intuitionistic fuzzy goal programming method
    (Elsevier, 2022) Mollalign, Demmelash; Mushi, Allen R.; Guta, Berhanu
    This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.
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    Asset liability management for Tanzania: Pension funds by stochastic programming
    (Afrika Statistika, 2018) John, Andongwisye; Larsson, Torbjörn; Singull, Martin; Mushi, Allen R.
    We present a long-termmodel of asset liability management for Tanzania pension funds. The pension system is pay-as-you-go where contributions are used to pay current benefits. The pension plan is a final salary defined benefit. Two kinds of pension benefits, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor for a long-term asset liability management is that, Tanzania pension funds face an increase of their members’ life expectancy, which will cause the retirees to contributors dependence ratio to increase. We present a stochastic programming approach which allocates assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001, with features from Tanzania pension system. In contrast to most asset liability management models for pension funds by stochastic programming, liabilities are modeled by using number of years of life expectancy for monthly benefit. Scenario trees are generated by using Monte Carlo simulation. Numerical results suggest that, in order to improve the long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target funding ratios to characterize the pension funds’ solvency situation.
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    Solving the University course timetabling problem using bat inspired algorithm
    (Tanzania Journal of Science, 2021) Limota, Ushindi; Mujuni, Egbert; Mushi, Allen R.
    Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization problem, a discrete version of BA for CPT has been proposed and tested using real-life data from the Dar es Salaam University College of Education (DUCE). The algorithm has produced promising results, as in each execution test, it generated a timetable in which all hard constraints were met and soft constraints were significantly satisfied within a few iterations.
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    Projecting Tanzania pension fund system
    (Statistics and Probability African Society, 2017) John, Andongwisye; Torbjörn, Larsson; Singull, Martin; Mushi, Allen R.
    A mandatory Tanzania pension fund with a final salary defined benefit is analyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the analysis is the increased life expectancy of members of the fund. The projection of the fund's future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possible reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts. Un fonds de pension obligataire en Tanzanie avec un salaire final défini est défini. Ce fonds est un système de retraite à prestations déterminées contributif et payant qui est très affecté par les changements démographiques. Deux types de prestations de retraite, une retraite de rachat (à la retraite) et une pension mensuelle (vieillesse) sont considérés. Un facteur décisif dans l'analyse est l'augmentation de l'espérance de vie des participants au fonds. La projection des futurs membres et des retraités du fonds se fait à l'aide des taux de mortalité attendus de la population active et de la longévité espérée. Les contributions futures, les avantages, la valeur de l'actif et du passif sont analysés. Nos projections montrent que le fonds ne sera pas pleinement durable à long terme, en raison de l'augmentation de l'espérance de vie de membres. Les contributions ne couvriront pas les paiements de prestations et la valeur de l'actif ne couvrira pas entièrement le passif. Une évaluation de certaines réformes possibles du fonds montre qu'ils ne peuvent garantir une viabilité à long terme. Un rendement plus élevé de la valeur de l'actif améliorera le ratio de financement, mais les contributions restent insuffisantes pour couvrir les paiements des prestations.
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    Optimization model for solid waste management at Ilala Municipal, Tanzania
    (Journal of Informatics and Virtual Education, 2011) Lyeme, Halidi A; Mujuni, Egbert; Mushi, Allen R.
    The existing solid waste management system at Ilala Municipal suffers from the lack of a real plan for collection centre locations and vehicle routes. In this study, a proposed mathematical model for municipal solid waste management process for Ilala municipality is presented. It includes the use of the concept of collection centres. Operational research methodology particularly Mixed Integer Programming is used to model the problem. The problem is solved to optimality which provides the best distribution of collection centres and their capacities. The solution shows a leastcost transportation plan with a cost saving of 38.3% per day compared to the current system.
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    Implementation of a goal programming model for solid waste management: A case study of Dar es Salaam – Tanzania
    (EDP Sciences, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
    In this research article, the multi-objective optimization model for solid waste management problem is solved by the goal programming method. The model has three objectives: total cost minimization, minimization of f inal waste disposal to the landfill, and environmental impact minimization. First, the model is solved for the higher priority goal, and then its value is never allowed to deteriorate. The model is solved for the next priority goal and so on until the problem is solved. The model was tested with real data for solid waste management system from Dar es Salaam city. The results determine the best locations for recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. Furthermore, the solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 78% and 57.5% respectively if fully implemented compared to the current system.
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    Mathematical programming formulations for the examinations timetable problem: The case of the University Of Dar es Salaam
    (African Journal of Science and Technology, 2004) Mushi, Allen R.
    Examinations Timetabling Problem (ETP) is the problem of assigning courses to be examined and candidates to time periods and examination rooms while satisfying a set of constraints. Every University has a different set of constraints and structure of examinations. Thus there is no general ETP model for all Universities around the world [1]. ETP is NP-Hard [2] and therefore no optimal algorithm is known for this problem which can solve a general problem within reasonable time. However, exact methods can be used to provide a benchmark for the heuristic methods. There is no general model for University Timetabling Problems because the problem feature differs from one University to another. In this paper we focus in the formulation of the ETP for the University of Dar as salaam. We formulate, test and compare three Integer Programming models. It is concluded that, although exact methods cannot give a solution to a real-size problem, these models give a good benchmark for testing the performance of other approaches. This paper also gives a direction for better exact models for the University of Dar es salaam’s ETP.
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    Multi-objective Optimization Model formulation for solid waste management in Dar es Salaam, Tanzania
    (Asian Journal of Mathematics and Applications, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
    Solid waste management is a challenging problem in developing nations. The health and environmental negative implications associated with solid waste management are very serious particularly in the developing nations where a large percent of waste is dumped into open areas. These implications are essentially on climate change and global warming due to environmental problems. In this paper, a multiobjective optimization model is developed to address the conflicting objectives of cost minimization, minimization of final waste disposal to the landfill, and environmental impact minimization. The model follows a mixed-integer programming formulation and tested by data from selected wards in Dar es Salaam city. The output is the best location of recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. The solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 76% and 55.2% respectively compared to the current system.
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    Irrigation water allocation optimization using Multi-Objective Evolutionary Algorithm (MOEA): A review
    (EDP Sciences, 2018) Fanuel, Ibrahim Mwita; Mushi, Allen R.; Kajunguri, Damian
    This paper analyzes more than 40 papers with a restricted area of application of Multi-Objective Genetic Algorithm, Non-Dominated Sorting Genetic Algorithm-II and Multi-Objective Differential Evolution (MODE) to solve the multi-objective problem in agricultural water management. The paper focused on different application aspects which include water allocation, irrigation planning, crop pattern and allocation of available land. The performance and results of these techniques are discussed. The review finds that there is a potential to use MODE to analyzed the multi-objective problem, the application is more significance due to its advantage of being simple and powerful technique than any Evolutionary Algorithm. The paper concludes with the hopeful new trend of research that demand effective use of MODE; inclusion of benefits derived from farm byproducts and production costs into the model.
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    Mathematical Model for Tanzania Population Growth
    (Tanzania Journal of Science, 2019) Mwakisisile, Andongwisye; Mushi, Allen R.
    In this paper, a mathematical model for Tanzania population growth is presented. The model is developed by using exponential and logistic population growth models. Real data from censuses conducted by Tanzania National Bureau of Statistics (NBS) are used. The Tanzania growth rate is obtained by using data of 1967 and 2012 censuses. The prediction of population for the period of 2013 to 2035 is done. Numerical results show that the population grows at the rate of 2.88%. In 2035 the population is expected to be 87,538,767 by exponential model and 85,102,504 by logistic model. The carrying capacity is 2,976,857,550, which implies that the population will still grow faster since it is far from its limiting value. Comparisons of the models with real data from the five censuses are done. Also NBS projections are compared with populations predicted by the two models. Both comparisons show that the exponential model is performing better than logistic model. Also, the projection up to 2050 gives the population of 135,244,161 by exponential model and 131,261,794 by logistic model.
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    Application of K-Means and Partitioning Around Mediods (PAM) clustering techniques on Maize and Beans yield in Tanzania
    (KY Publications, 2016) Mbukwa, Justine Nkundwe; Anjaneyulu, G.V.S.R.
    This paper contributes to the application of k-means and k-mediods multivariate statistical methods for the purpose of revealing optimal clusters and assessing the consistency of individual districts within the group. Data used were extracted from united republic of Tanzania (Ministry of Agriculture, Livestock and Fisheries(MALF) (2003/12) consisted a total of (n=36 districts) with both maize and beans yield. The R-statistical computing version (3.1.1) was used. The study findings revealed that 36 districts were grouped into six clusters using k-means algorithm. Using the k-mediods, it was revealed that only 11 districts were found to very well structured since their silhouette width (Si) is above 0.5. Nevertheless, the clusters validation was done in such a way that individual district whose silhouette width (Si) close to 1 was regarded as highly consistency clustered whereas districts with (Si) greater or equal to 0.25 were said to be somehow well clustered and otherwise. The paper concludes that few districts that are very consistent given the threshold margin should to be monitored and evaluated effectively to ascertain productivity. The study recommends that the government should pay attention on allocating the scarce resources to the consistency clusters along with policy review in favour of smallholder farmers through access and timely for all important farm inputs in future.
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    Statistical Analytic Tool for Dimensionalities in Big Data: The role of Hierarchical Cluster Analysis
    (Research India Publications, 2016) Mbukwa, Justine N.; Tabita, G Neeha; Anjaneyulu, GVSR; Rajasekharam, OV
    An interest for presenting this paper rose because of massive increase information with a very high dimensional from different sources in this era of globalization. Data are produced continuously and are unstructured (1). This paper is confined to literature review search for big data issue and challenges of several scopes in data. It brings a detailed discussion on the problem on these data and analysis done using the effective multivariate statistical tool namely clustering analysis technique as a data reduction technique. It is used as a base for discussion for existing challenge of multi-dimensionalities of data. The findings indicated that, the world is noisy due to massive flow of information continuously. Findings revealed that data emanating from face book, you tube and twitter can be used to predict the epidemic of influenza and even market trend (2 and 3). With face book data is used to predict the people`s interest. However, data from different sources have been proved to be useful in decision making efficiently and effectively for public as well as private sector. Cluster analysis technique sorts data/alike things into groups, to see if there a high natural degree association among members of the same group and low between members of different groups. Finally, this technique has proved failure to handle such heap of data with varied sources. With regards to data stored, it remains to be a challenge in terms of analysis among researchers and scientists. Therefore, it calls for advanced statistical software to cater for such an existing challenges.
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    Aretrospective evaluation of the intellectual structure of private agricultural and food standards research in global trade
    (International Trade, Politics and Development, 2023) Lwesya, Francis; Mbukwa, Justine N.
    Purpose The aim of this article was to present a retrospective assessment of the intellectual structure of private agricultural and food standards research in global trade. This study was motivated by the increasing role of standards and certifications in governing global agricultural and food trade. Design/methodology/approach The current investigation was carried out with bibliometric methods using VOSviewer software. Techniques such as citation, co-citation, keyword co-occurrence, keyword evolution and co-authorship analyses were performed to tackle the research questions. Articles were extracted from Scopus database for the period 1998–2022 (30th August 2022) with selected keywords (“Private food standard*” OR “food standard*” OR “agri-food standard*” AND “agri*” OR “agro*” OR “farm*” OR “food*” AND “international trade” OR “global trade” OR “international business”) along certain filters (subject – Economics and Business management: language – English: Document – article and review articles and source – journals). Findings The results show that the intellectual structure of private agricultural and food standards research in global trade has evolved around five clusters, namely: (1) the political economy of food standards, (2) food standards and their challenges in global trade, (3) food standards and integration into value chains, (4) food standards and market access and (5) food standards and exports from developing countries. However, the authors found the research gaps in each of the thematic clusters. Research limitations/implications The main limitation of this study is that the authors focused their attention on certain aspects of bibliometric review, such as the intellectual structure of the field, the citation analysis and the collaboration network. Future research could attempt to explore new field development through bibliographic coupling and deepening of conceptual structure using content analysis by incorporating the research methods used in the respective studies. Practical implications The emerging research areas in private agricultural and food standards in global trade are related to topics on food quality, sustainable development, genetically modified organisms, World Trade Organization, tariff structure, trade agreements, food industry and European Union. However, there is less research and little collaboration between Africa and developed countries. For example, Africa's total publications were (15), while the US had (46), China (15), Belgium (23), Germany (27), Italy (32) and the UK (24). Originality/value There are limited studies that have conducted a retrospective evaluation of the intellectual structure of private agricultural and food standards research in the global trade using bibliometric analysis. The present investigation is novel in identifying the thematic research clusters, emerging issues and future research directions. This is more important to developing countries as their agricultural produce face challenges to access markets of the developed world.
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    Effect of Statistics on Collaboration for Enhancing Institutional Sustainability: A Case of Mzumbe University-Tanzania
    (Springer Nature Switzerland, 2024) Mbukwa, Justine N.; Mbegalo, Tukae; Lwaho, Joseph
    The article discusses the effects of statistics on collaboration and its potential in spearheading sustainable industrial development. In this regard, three days’ workshop were conducted by Mzumbe University Laboratory for Interdisciplinary Analysis (MULISA) in collaboration with the Ifakara health institute. These activities are statistical literacy, scientific writing and winning the research grants. The objective was to create a smooth environment for the sustainability of the statistical laboratory through knowledge. The participants in the workshop were students and lecturers at Mzumbe University, and researchers and interns from Ifakara Research Institute (IHI). The majority of the participants in all three days of workshop were males. The results revealed that the workshop has increased the research and publication activities among MULISA collaborators after the workshop compared to before the workshop. This noted benefit derived from the sharing the skills and collaboration during the workshop. Therefore, the collaborative workshops and training are the engineering tool for sustainability because it allows sharing of new knowledge. The collaboration in writing enhances thoughts, ideas, and knowledge transferability to the next generation.
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    Climate change, food security, and diarrhoea prevalence nexus in Tanzania
    (humanities and social sciences communications, 2024) Kitole, Felician Andrew; Mbukwa, Justine N.; Tibamanya, Felister Y.; Sesabo, Jennifer Kasanda
    The impact of climate change on food security and public health has hindered poverty reduction efforts in developing nations, including Tanzania, resulting in the impoverishment of millions and compromising both health and food production. To unravel these complex interactions, rigorous scientific research is indispensable. Leveraging three waves of the Agriculture Sample Census (2002/03, 2007/08, 2019/20), this study meticulously examines the interplay between climate change, food security, and diarrhoea prevalence in Tanzania. Employing Instrumental Variable Probit and Control Function Approach models to address endogeneity and heterogeneity, temperature anomalies serve as instrumental variables. The findings reveal a substantial impact of climate change on both food security (−0.331142, p < 0.01) and diarrhoea incidence (0.214602, p < 0.01). These results signify that climate change places significant stress on food security, rendering households more susceptible to insecurities, and heightens health concerns through increased diarrhoea prevalence. This underscores the urgency of prioritizing public health and well-being through an agricultural lens in climate change mitigation. A comprehensive strategy is imperative, entailing a synergy of sustainable agricultural practices, robust public health interventions, and targeted policies to fortify the adaptive capacity of communities. Special emphasis should be placed on cultivating climate-resilient agricultural systems, ensuring food security, and implementing health programs tailored to address the unique challenges posed by climate-induced factors. Moreover, community engagement and awareness initiatives play a pivotal role in fostering a collective understanding and commitment to sustainable practices, contributing to the overall resilience of societies amidst the challenges of climate change.
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    Some Aspects of Correlation of Physical Capital and Infrastructures on Household Food Security: Evidence from Rural Tanzania
    (Journal of Economics and Sustainable Development, 2014) Mbukwa, Justine N.
    To achieve the first Millennium Development Goals is still a challenge. The problem of poverty in the context of hunger still persists in Tanzania. Household’s members have not sustainable access to enough and quality of food. The major objective of this study is to ascertain whether exists some aspects of correlation between physical capital and infrastructures on the households` food security. This study was carried out in rural part of Tanzania, in Mvomero district covering three villages selected randomly (a total sample 0f 382 households). Data analysis was done using SPSS version 15.0. Chi-square test was adopted for plausible analysis assesses the extent to which some correlation exists between food security status of the households against independent variables (physical capital and infrastructures of the households). 2 χ = 6.963; − p value Based on the data analyzed empirically, it is remarkable by evidence that variables such as pesticides ( = ( 2 χ = 13.343; − p value = food security in the study area. 0.008 ), tractors ( 2 χ = 0.000 10.024; − p value = 0.002 ) and electricity ) were found to be statistically significant correlated with household’s In view of these findings, there is a need to pay attention supporting rural farmers’ to be able to access farm inputs because of existing some correlation with the household food security status. Finally, this study recommends further study to be carried by incorporating advanced statistical model such cluster analysis, principal components and factor analysis which deals with large data for plausible and interpretable findings.
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    Bayesian multilevel modelling of the association between socio-economic status and stunting among under-five-year children in Tanzania
    (Journal of Health, Population and Nutrition, 2023) Musheiguza, Edwin; Mbegalo, Tukae; Mbukwa, Justine N.
    Background: Stunting is associated with socioeconomic status (SES) which is multidimensional. This study aimed to compare different SES indices in predicting stunting. Methods: This was the secondary data analysis using Tanzania Demographics and Health Surveys (TDHS). The study used 7492, 6668, and 8790 under-five-year children from TDHS 2004/5, 2010, and 2015/16, respectively. The Household Wealth Index (HWI); Water and Sanitation, Assets, Maternal education and Income (WAMI); Wealth Assets, Education, and Occupation (WEO); and the Multidimensional Poverty Index (MPI) indices were compared. The summated scores, principal component analysis (PCA), and random forest (RF) approaches were used to construct indices. The Bayesian and maximum likelihood multilevel generalized linear mixed models (MGLMM) were constructed to determine the association between each SES index and stunting. Results: The study revealed that 42.3%, 38.4%, and 32.4% of the studied under-five-year children were stunted in 2004/5, 2010, and 2015/16, respectively. Compared to other indicators of SES, the MPI had a better prediction of stunting for the TDHS 2004/5 and 2015/16, while the WAMI had a better prediction in 2010. For each score increase in WAMI, the odds of stunting were 64% [BPOR = 0.36; 95% CCI 0.3, 0.4] lower in 2010, while for each score increase in MPI there was 1 [BPOR = 1.1; 95% CCI 1.1, 1.2] times higher odds of stunting in 2015/16. Conclusion: The MPI and WAMI under PCA were the best measures of SES that predict stunting. Because MPI was the best predictor of stunting for two surveys (TDHS 2004/5 and 2015/16), studies dealing with stunting should use MPI as a proxy measure of SES. Use of BE-MGLMM in modelling stunting is encouraged. Strengthened availability of items forming MPI is inevitable for child growth potentials. Further studies should investigate the determinants of stunting using Bayesian spatial models to take into account spatial heterogeneity.
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    Spatial Distribution and Pattern Analysis of Women Sexual Violence in Tanzania
    (Springer, Cham, 2023) Mbukwa, Justine N.; Mbegalo, Tukae; Levira, Francis
    In sub-Saharan Africa, sexual violence is very common among married women. This has a negative effect on health and wellbeing. This problem has not been well documented geographically, particularly in Tanzania. The main objective of this chapter was to describe the geographical distribution of women sexual violence in Tanzania. We used data from the Tanzanian demographic and health survey (2015/2016), comprising a random sample of 10,333 women aged 15–49 years. The study used ArcMap software version 10.8, for understanding the spatial pattern of sexual violence and Chi-square to find out the drivers of high women sexual prevalence rate across the regions. Findings show sexual violence was more prevalent in the Lake and Central zones. Wealth index, marital status, partner’s education, drinking habit and occupation were the main drivers.