Do dollars decide in Africa whether a child should live or not? Association of health expenditure on health outcomes in Africa Health expenditures have a statistically significant effect, although low, on infant, neonatal and under‐five mortality in Africa. Supervisor: professor Whitehead Author: Soheila Abachi 11/17/2014
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Do dollars decide in Africa whether a child should live or not? Association of health expenditure on health outcomes in Africa Health expenditures have a statistically significant effect, although low, on infant, neonatal and under‐five mortality in Africa. Supervisor: professor Whitehead Author: Soheila Abachi 11/17/2014
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Table of Contents 1. Abstract ................................................................................................................................................ 3
Health expenditures have a statistically significant effect on infant, neonatal and under‐five mortality. For African countries, our results imply that total health expenditures (as well as the government component) are certainly important contributor to health outcomes in terms of child mortality rates. Per capita government expenditure on health seemed to be more significant on models especially per capita government expenditure on health for the year 1995. Inter correlation of the two sets of variables, health expenditures and mortality rates, are strong but not between the variables. Infant, neonatal and under‐five mortalities are negatively correlated with the health expenditure in the Sub‐Saharan African countries studied. Health care expenditure seems to be only one of the many factors important in improving the health status of a member. The analysis presented in this paper finds evidence of a weak statistically significant relationship between per capita health spending, and health outcomes. Each of the health outcomes can be an indication of the other health outcome. Neonatal mortality rate itself is an indication of how high or low the infant mortality is going to be in a specific year in a country. This may be due to the infection caused death among the under five which accounts for 73% of under 5 death in Africa. In countries with high infant mortality rate, the absence of a strong statistical relationship may be due to model misspecification or may reflect the fact that at high levels of population health, the returns for the increases in health spending are small. For future studies, other variables should be included.
Abbreviations PC95TEXH 1995 Per capita total expenditure on health (PPP int. $) PC05TEXH 2005 Per capita total expenditure on health (PPP int. $) PC95GEXH 1995 Per capita government expenditure on health (PPP int. $) PC05GEXH 2005 Per capita government expenditure on health (PPP int. $) UFD00 2000 Number of under‐five deaths (thousands) UFD10 2010 Number of under‐five deaths (thousands) ID00 2000 Number of infant deaths (thousands), ID10 2010 Number of infant deaths (thousands) ND00 2000 Number of neonatal deaths (thousands) ND10 2010 Number of neonatal deaths (thousands)
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2. Introduction Life expectancy is linked to economic growth and, 10% increase in life expectancy at
birth will increase the economic growth rate by 0.35% a year, according to WHO (world health organization). There is evidence that empowering health will bring significant benefits for the economy (1). Low health status is a heavy financial burden and according to Commission on Macroeconomics and Health (2001) economic growth of wealthy and poor countries is about 50% different due to the life expectancy and health status. Economists consider child health and mortality as important indicators of the success or failure of a government policy especially when studying developing countries (2). Health definitely is linked with sustainable economic growth and development. This could be due to the fact that healthy population is more productive at work, spend more time in the workplace, stay in labor force longer, invest in their own and children’s education leading to the increased productivity and generally earn higher incomes which could potentially be the funds available for investment in the economy (3).
Two‐thirds of deaths occur in just 10 countries. Child mortality in West and Central Africa is the highest. In these regions, more than 150 of every 1,000 children born die under age five in compare to 6 of every 1,000 children born in a wealthy country (North America, Western Europe and Japan) (UNICEF). Health care expenditure per person per year in high‐income countries exceeded US$ 2,000 while in Africa it averaged between US$13‐$21 in 2001 (Commission for Africa, 2004). In sub‐ Saharan Africa the expenditure should rise to US$ 38 by 2015 just to deliver basic treatment and care for the major communicable diseases (HIV/AIDS, TB and malaria), and early childhood and maternal illnesses (Commission for Macroeconomics and Health, 2001). Total spending on health has shown minimal to no impact on child mortality in some of earlier studies(4, 5). These studies have recorded empirical evidence that public spending on health is not the main cause of child mortality outcomes (6). The variation could be very well explained by other factors such as income, income inequality, female education, mother literacy, degree of ethnolinguistic fractionalization and findings show that these all play significant role in child mortality across countries (7‐9). These results mean that reduced poverty, income inequality, and increased female education would reduce child mortality as much than just increasing public spending on health. Despite public belief, study has shown that government health expenditures account for less than one‐seventh of one percent variation in under‐five mortality across countries and the conclusion was drawn that 95% of the variation in under‐5 mortality can be enlightened by factors such as a country’s per capita income, female educational level, resources at hospital, managed care and choice of region (10, 11). The same applies to low‐income countries where no significant relationship between health expenditure spending and infant mortality was found (12). Enhanced sanitation as a public health measure have proved to play a bigger role in improving child health in the past 150 years than even the most advanced personal medical care technologies (13, 14). Therefore, child mortality may be not a good measure of social and economic conditions such as public health, insurance coverage, or economic crises in all countries but certainly is considered good indicator for African countries. In 2000, the United Nations (UN) set eight targets, known as Millennium Development Goals, aiming to promote human development of which four are in direct or indirect relation to child mortality rate. The key targets to be reached by 2015 throughout the world are in the areas of poverty reduction, health improvements, education attainment, gender equality, environmental sustainability, and fostering global partnerships
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(figure 1). The fourth goal to reduce child mortality by two‐thirds requires action on the first goal, halving extreme poverty and hunger, since malnutrition caused by chronic hunger causes the death of more than 5 million children each year globally (15). 3. Methods
The dataset contains 12 continuous variables with the sample size of 45 (45 African countries) which is large and good enough for the central limit theorem (CLT) [approximately normally distributed]. It is hypothesized that child yearly death rate as an indicator of health outcome, depend upon variance in government and total health expenditure (figure 4, 5, 6). In this research, the economical consequences of health spending on child death rate will be studied and results will be reported. The questions to be answered are as below; 1. Neonatal mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 2. Neonatal mortality rate 2010 is a response of government and total health expenditure
2005 3. Infant mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 4. Infant mortality rate 2010 is a response of government and total health expenditure 2005 5. Under 5‐mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005 6. Under 5‐mortality rate 2010 is a response of government and total health expenditure
2005 7. Neonatal mortality rate 2000 is a response of government and total health expenditure
1995 8. Infant mortality rate 2000 is a response of government and total health expenditure 1995 9. Under 5‐mortality rate 2000 is a response of government and total health expenditure
1995 4. Analysis
4.1. Linear regression Performing linear regression about child mortality (response) and explanatory variables
(government and total health expenditures) would tell us if there is any relationship between the response and the explanatory variables thus there might be some collinearity or multicollinearity among the independent variables (exact collinearity should be considered because if there is any then the regression coefficient cannot be calculated). Correlations whether positive, negative, and associations whether strong or weak can be determined in this step.
4.1.1. Assumption of the linear regression To check the normality of each variable, Shapiro‐Wilk normality test was performed
and the p‐values were analyzed on both original dataset and the log10 transformed dataset (table 3). For the original data, the p‐values for all the variables are less than alpha so the null hypothesis is rejected in the favor of alternative hypothesis. To make the data of normal distribution log10 transformation was applied to the dataset. P‐values were improved but still most of the variables are of non‐normal distribution. PC95TEXH, PC05GEXH, UFD10 have p‐values above alpha so Ho is accepted and these variables are of normal distribution.
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Transforming improved the normality but not to satisfactory level thus since listwise deletion of outliers has the risk of losing some influential observation then I decided to keep all the data in the analysis. The hypothesis for Shapiro‐Wilk normality test is as follows;
Ho: data is normal Ha: data is non‐normal The null hypothesis for multiple linear regression is that all the slopes are equal to zero
and the alternative hypothesis is that at least one slope does not equal to zero. Ho: β1=β2=β3=β4=βi=0 Ha: at least one βi is different Best fit could be interpreted as “how good is the proposed model (regression
equation)”and if “it could predict the y values reasonably.” In other words how good is the fitted model for describing the relationship between x and y and so for predicting value of y for a given x within the acceptable x range. Goodness of fit could be measured by coefficient of determination (R2). General rule of thumb is that R2 greater than 60% would make a proposed model safe enough for making predictions.
4.2. Principal component analysis Textbooks state that “principal component analysis is performed on a matrix of Pearson
correlation coefficients therefore data should satisfy the assumptions for this statistic”. To extract the important variables out of the 12 variables in the original dataset and
reduce the dimensionality principal component analysis is to be performed. Components are orthogonal to each other (uncorrelated). PCA is more sensible when data are highly correlated (correlation coefficients bigger than 0.3 and smaller than ‐0.3) and even though normality of the dataset is not essential but would be preferred. If all the variables on the same scale, only then the predictions and interpretation would be rational and this could be achieved by standardizing the data and performing transformation.
4.2.1. Assumption of principal component analysis Linearity is preferred and so the relationship between all observed variables should be
linear. Normal distribution of each observed variable is also desirable but not necessary. For the latter reason variables that demonstrate skewness may be transformed to better approximate the normality. One could also assume the normality of the dataset if the sample size is greater than 25 because the Pearson correlation coefficient is robust against violations of the normality assumption. According to Dr. Whitehead if dataset does not contain any zero values then it can be analyzed by principal component analysis. In addition, normality is preferred not essential, and independence is not required.
The dataset contains no missing values but some unusually large or small values are present which maybe outliers contributing to the non‐normal distribution of the dataset. I kept all the units in because these values maybe influential not outliers.
Variables are relatively correlated for example; per capita health expenditure, government and total, are positively related meaning that increase in one would lead in increasing the other (table 2).
Normality of the original dataset was tested but the data were non‐linear therefore, two forms of transformation were performed, square root and log10. Square root transforming of all the variables did not much help the linearity and normality whereas log10 transforming of
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all the variables induced the normality to some degree keeping its original characteristics (Figure 9, 10).
4.3. Redundancy analysis Redundancy analysis is done to show that there is a linear dependence of the child
mortality variables, Y on the health expenditure variables, X. In redundancy analysis linear regression is applied to represent response variable (child mortality) as linear function of explanatory variable (health expenditure) and then to use PCA in order to visualize the result. Among those components of Y which can be linearly explained with X (multivariate linear regression) one could take those components which represent most of the variance. 5. Results
5.1. General linear model Several multiple linear models were tested with the null hypothesis that the slopes are
all equal to zero. All the tested models have p‐values smaller than alpha (0.5) leading to the rejection of null hypothesis in favor of alternative hypothesis meaning that at least one β is different from zero. There is significant relationship between the independent and the response variable and so changes in x would affect the changes in y.
All the possible models were tested. The answers for biological questions are as follows; Biological question 1: Neonatal mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 2: Neonatal mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 3: Infant mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 4: Infant mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 5: Under 5‐mortality rate 2010 has association with the government and total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 6: Under 5‐mortality rate 2010 has association with the government and total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 2005 government health expenditure (table 4). Biological question 7: Neonatal mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4). Biological question 8: Infant mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4).
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Biological question 9: Under 5‐mortality rate 2000 has association with the government and total health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is more dependent on the 1995 government health expenditure (table 4).
Testing the dependence of child mortality rate of 2010, neonatal, infant, and under five, the conclusion can be made that all these variables are more dependent on the government expenditure 1995 and 2005. Another interpretation of the models could be that government expenditure of year 1995 had big influence on the child mortality rates of 2010 (table 4).
Also testing for the dependence of child mortality rate of 2000, neonatal, infant, and under five, the conclusion can be made that all these variables are more dependent on the government expenditure of 1995 (table 4).
The overall interpretation could be that child mortality rates are more dependent on the government expenditure rather than on the total health expenditure (table 4).
Quality of fit of the abovementioned models were assessed one by one (figure 13‐19, 34, 35).
To evaluate the quality of fit a model, few assumptions shall be met; • Normality of error terms by Normal Q‐Q plot • Constant variance by plotting residuals vs. fitted values • Independence of error terms by auto‐correlation analysis (time series) • Presence of influential observations by Cook’s D
For example, the quality of fit of the model 6 was evaluated. The plots show no evident pattern to the residuals vs. fitted values plot and give almost an impression of horizontal band confirming that constant variance assumption is met. The Normal Q‐Q plot passes the pen test and so the normality assumption is met. The residuals vs. leverage plot checks out the absence of influential observations as observation 30 (country; Mauritania) that was previously introduced as influential is out of the Cook’s distance range. Therefore, we conclude that all assumptions are met and none is violated. It is interesting to know that Mauritania is classified as low‐income country by World Bank but has relatively high per capita total and government expenditure with significantly low child death rates.
Bonferonni outlier test was done for the models that initially have adjusted r‐squared values of above 90%. According to this test observation 4 and 30 are outliers (table 8).
Reduced models for all the tested models were the best models as they were simple and had lower AIC compare to the full models (table 4).
5.2. Principal component analysis 5.2.1. PCA on all the variables PCA on correlation matrix (Log10 transformed data) revealed two principal components
with Eigen values more than or equal to 1 (pc1: 2.97, pc2: 1.57). These two principal components cumulatively account for 94.4% of the variance in the dataset (table 6).
Loadings for the correlation matrix (Log10 transformed data) analysis are summarized (table 6) and as noted loadings for child death rates are positively loaded on first component. The per capita health expenditure load negatively on the second component therefore 2nd component could explain the variance on the expenditure (table 6). On the first component, decrease in the health expenditure causes increase in the child mortality rate. Below is the formula for the 1st principal component:
Scree plot can be performed to decide which components to keep for the Varimax rotation analysis. Looking at the plots for PCA on correlation would reveal that only two components are important, as drop is obvious after these two components. For further analysis, only first two components were maintained. This would plot the eigenvalue associated with a principal component versus the number of the component to expose the relative magnitude of eigenvalues (Figure 20).
Looking at the biplot, one can say that death rates whether infant, neonatal or under 5 are highly correlated for 2000 and 2010. Moreover per capita government and total health expenditure are also highly correlated (Figure 21). Both health expenditure and mortality rates load high on the first component and so most of the variance on the 1st component in explained by the two set of variables but in different direction. Their importance on the component are more or less the same because the size of arrows are almost equal.
Examining the scores plot of correlation matrix analysis, prediction can be made that countries relatively spending big on the health and have very low mortality rates have negative scores (Algeria) on the 1st and 2nd component and countries with very low spending and high mortality have positive scores on the 1st component (Nigeria). Seychelles that spend high and have almost to none mortality rate have high negative scores on the 1st and relatively high negative score on the 2nd component (Figure 22).
Varimax plot makes the interpretation easy as it reveals the relationship of each original variable to the factor. This rotation maximizes the high correlations while minimizing the low correlations. Varimax plot for correlation matrix shows that the countries with relatively big health expenditure have negative scores on both the components and in converse countries with low to minimal health expenditure have positive scores on both the components (Figure 23).
5.2.2. PCA on 2 sets of variables Principal component analysis was done on the independent and dependent variable as
two set. Since the measurements are on the same scale, therefore analysis were done with the covariance matrix.
PCA of the child mortality rates revealed all the principal components with Eigen values more than or equal to 1. These two principal components cumulatively account for 99.9% of the variance in the dataset. Below is the formula for the 1st principal component:
1st pc for child mortality rates (covariance matrix) = ‐0.63(UFD00) ‐0.54(UFD10) ‐0.39(ID00) ‐0.30(ID10) ‐0.17(ND00) ‐0.170(ND10)
PCA of the health expenditure revealed all the principal components with Eigen values more than or equal to 1. These two principal components cumulatively account for 97.1% of the variance in the dataset. Scree plots for both set of PCA confirms the importance of the first 2 components (figure 26‐27). Below is the formula for the 1st principal component:
1st pc for health expenditures (covariance matrix) = ‐0.45(PC95TEXH) ‐0.69(PC05TEXH) ‐0.305(PC95GEXH) ‐0.467(PC05GEXH)
Looking at the biplot for the PCA of mortality rates, one can say that death rates of 2000 are highly correlated so are the 2010 death rates. Based on the size of arrows, importance of
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the under five death rate is more significant the neonatal and the infant. Biplot of health expenditures shows that health expenditures of 1995 are correlated and so are the 2005 expenditure thus importance of total expenditure of 2005 is more significant than the others (1995 government expenditure has the least importance) (figure 28‐29).
Looking at score plot of PCA of the mortality rates, all the variables load negatively on the pc1, some high and some low (figure 32). Score plot of PCA of the expenditures shows that all the variables have loaded negatively and relatively high on pc1 (figure 33).
Varimax plot for PCA of mortality rates shows that the countries with high mortality rates load highly negative on both the components such as Nigeria (figure 30).
Varimax plot for PCA of expenditures shows that the countries with both high government and high total health expenditures load negatively high on the first and positively high on the 2nd component such as Seychelles. In converse, countries with high total and relatively lower government health expenditures load highly negative on the first and positively but relatively lower on the 2nd component such as south Africa (figure 31).
5.3. Redundancy analysis For the variable UFD00, a one unit increase in under 5 death leads to a 1.33 decrease (‐
1.33) in the first canonical variate of set 2 when all of the other variables are held constant. Table 7 presents the standardized canonical coefficients for the first two dimensions
across both sets of variables. For the expenditure variables, the first canonical dimension is most strongly influenced by PC05TEXH (0.25) and for the second dimension (1.00).
For the mortality variables, the first dimension was most strongly influenced by UFD00 ‐1.33 and ID00 1.41 and the second dimension the ND00 ‐1.64 was the dominant variable (figure 24‐25). 6. Discussion
The overall picture is that health expenditure has impact on the child mortality rate and the results are relatively statistically significant. This may be because HIV prevalence has been high in the sub‐Saharan Africa in the two past decades (figure 3). This is in accordance to UN report 2000 saying that “trend in HIV infection will have a profound impact on future rates of infant, child and maternal mortality, life expectancy and economic growth.”
Although all the multiple linear regression models tested were accepted in the favor of the alternative hypothesis that there is relationship between mortality rates and health expenditure however the factors of the models usually were not statistically significant except the health mortality rates e.g. dependence of infant mortality rate on neonatal and under 5 mortality rates with low p‐values and high t values (table 5). Negative loadings of the health expenditure leads to positive relatively high loading of the health outcome, represented as child mortality. One could say that health expenditure has some impact even though low on the mortality rates but other variables have to be included in the analysis to decide its significance. Variables that can be included in the study could be the female education, income, access to vaccines, HIV prevalence, number of trained health professionals, hunger, sanitation, etc.
The results of this analysis are confirmatory to the other similar studies that have found little to no impact of the health expenditure on the health outcomes. 7. Acknowledgments
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I would like to acknowledge the use of data from WHO organization. Data were selected individually and then they were combined in one dataset. 8. References 1. Acemoglu, D.; Johnson, S. Disease and development: the effect of life expectancy on economic growth; National Bureau of Economic Research: 2006. 2. Sen, A., Mortality as an indicator of economic success and failure. The Economic Journal 1998, 108, 1‐25. 3. Bloom, D.; Canning, D., The health and poverty of nations: from theory to practice. Journal of Human Development 2003, 4, 47‐71. 4. Sandiford, P.; Cassel, J.; Montenegro, M.; Sanchez, G., The impact of women's literacy on child health and its interaction with access to health services. Population studies 1995, 49, 5‐17. 5. Rutherford, M. E.; Mulholland, K.; Hill, P. C., How access to health care relates to under‐five mortality in sub‐Saharan Africa: systematic review. Tropical Medicine & International Health 2010, 15, 508‐519. 6. Gupta, S.; Verhoeven, M.; Tiongson, E., Does higher government spending buy better results in education and health care? International Monetary Fund: 1999. 7. Black, R. E.; Morris, S. S.; Bryce, J., Where and why are 10 million children dying every year? The Lancet 2003, 361, 2226‐2234. 8. Lawn, J. E.; Cousens, S.; Zupan, J., 4 million neonatal deaths: when? Where? Why? The Lancet 2005, 365, 891‐900. 9. Kiros, G.‐E.; Hogan, D. P., War, famine and excess child mortality in Africa: the role of parental education. International Journal of Epidemiology 2001, 30, 447‐455. 10. Filmer, D.; Pritchett, L., The impact of public spending on health: does money matter? Social science & medicine 1999, 49, 1309‐1323. 11. Filmer, D.; Pritchett, L., Child mortality and public spending on health: how much does money matter? World Bank Publications: 1997; Vol. 1864. 12. Burnside, C.; Dollar, D., Aid, the incentive regime, and poverty reduction. World Bank, Development Research Group, Macroeconomics and Growth: 1998. 13. Preston, S. H., Mortality trends. Annual Review of Sociology 1977, 163‐178. 14. U.N., Common Database. 2005. 15. Human Development Report 2003.
Assignment 2d, Soheila Abachi
Figure 1:
Figure 2:
: adapted fro
: adapted fro
om UN
om world baank
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Figure 3: adapted from UNAIDS
Figure 4: bar graph of the health expenditures (total and government) for the year 2005 and health outcomes (Infant, neonatal, under 5mortality rates) for the year 2010
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PC05TEXH PC05GEXH UFD10 ID10 ND10
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UFD00 UFD10 ID00 ID10 ND10 ND00
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Figure 5: bar graph of health outcomes (Infant, neonatal, under 5mortality rates) for the years 2000 and 2010
Figure 6: bar graph of the health expenditures (total and government) for the year 1995 and health outcomes (Infant, neonatal, under 5mortality rates) for the year 2000
Figure 7: box plot of original dataset
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PC95TEXH PC95GEXH UFD00 ID00 ND00
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Figure 8: scatter plot matrix for original dataset
Figure 9: box plot of log10 transformed dataset
ID00
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Figure 10: scatter plot matrix for log10 transformed dataset
Figure 11: box plot of square root transformed dataset
Original data Log10 transformed data PC95TEXH 2.221e‐09 0.437PC05TEXH 6.416e‐09 0.01336PC12TEXH 3.201e‐09 0.03242PC95GEXH 4.121e‐11 0.08201PC05GEXH 8.008e‐10 0.1731PC12GEXH 9.39e‐10 0.01635UFD00 6.136e‐11 0.03946UFD10 1.899e‐11 0.06938ID00 6.361e‐11 0.0312ID10 1.363e‐11 0.01937ND00 5.93e‐11 0.005314ND10 2.557e‐11 0.01495Original data set including all variables 2.24e‐13
-1000 -500 0
-600
-200
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Scores plot pca Mort Rate
1st principal component
2nd
prin
cipa
l com
pone
nt
AlgeriaAngola BeninBotsw aBurkina FasoBurundiCabo VeCameroonCentral African RChadComoroCongoCôte d'IvoireDemocratic Republic of the CongoEquatorial GEritrea
Ethiopia
GabonGambiaGhanaGuineaGuinea-BisKenyaLesothLiberiaMadagascarMalaw iMaliMauritanMauritiuMozambiqueNamibiNigerNigeriaRw anda
Sao Tome andSenegalSeychelSierra LeonSouth AfricaSw azilaTogoUgandaUnited Republic of TanzanZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
Table 5: summary of the selected models coefficients and p‐values
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Table 6: summary of loading on the first 2 components of PCA PCA on correlation matrix Comp 1 Comp 2 PC95TEXH ‐0.278 ‐0.263PC05TEXH ‐0.276 ‐0.343PC12TEXH ‐0.268 ‐0.337 PC95GEXH ‐0.294 ‐0.228PC05GEXH ‐0.279 ‐0.310 PC12GEXH ‐0.276 ‐0.302 UFD00 0.303 ‐0.261 UFD10 0.301 ‐0.272ID00 0.300 ‐0.280 ID10 0.299 ‐0.281ND00 0.302 ‐0.270 ND10 0.285 ‐0.296
Table 7: standardized canonical coefficients of the canonical correlation analysis 1 2 First set of variable PC05TEXH 0.25 1.00 PC05GEXH 0.09 ‐0.84 Second set of Variable UFD00 ‐1.33 ‐0.06 UFD10 0.34 0.34 ID00 1. 0.53 ID10 ‐0.16 0.36 type2log.ND00 ‐0.56 ‐1.64 type2log.ND10 0.17 0.47 Table 8: Summary of Bonferonni outlier test on the selected models