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Statistical Analysis on the Factors Influencing Life Expectancy
- 1. Statistical Analysis on the Factors Influencing Life Expectancy Anh Do, Xuemeng Han, Hang Ngo, Jennifer Wong
- 2. Agenda ● Background & Problem ● Dataset Description ● Data Pre-Processing ● Model & Variable Selection ● Results ● Conclusion & Lessons Learned
- 3. Background & Problem Analytics question: “What factors are significant and what model is the best at predicting life expectancy at birth (LEB)?” ● Analytics goal: predictive accuracy ● Rationale: ○ Accurate prediction helps countries understand whether their investment in social and economic development is effective ○ Understanding important determinants can help countries allocate resources appropriately
- 4. Dataset Description ● Response variable: LEB (in years) ● Predictors: 22 total variables ○ Economic indicators (GDP, Total Health Expenditure as % of GDP per capita, etc) ○ Health indicators (HIV/AIDS, Vaccine coverage, Obesity, etc) ○ One categorical variable (Status: Developed or Developing country), the rest are numeric variables ● Data cleaning process: ○ Replace original Life Expectancy data with LEB due to inconsistency with official data sources (WHO) ○ Replace some predictors with missing values using more complete dataset from reliable sources (WHO and World Bank)
- 5. Data Pre-Processing ● OLS assumptions violated: Errors are heteroskedastic ● OLS assumptions violated: Multicollinearity Initial After Standardizing & Centering 1839607969.310 56.997 Variance Inflation FactorsCondition Index Condition Index: 9.450
- 6. Model & Variable Selection ● Parametric models to address heteroskedasticity and dimensionality: ○ Weighted Least Squares ○ Ridge, LASSO ○ Principal Component Regression, Partial Least Squares ● Non parametric models: ○ Regression Tree ○ Random Forest ● Two model specifications: 17 variables (full) and 14 variables (reduced) ○ There is no business restriction to keep all predictors in the model ○ Stepwise and Best Subset were run to select a reduced model ○ Both methods suggest the same set of 14 variables to be included
- 7. Results ● Regression tree was chosen as the most accurate model to predict LEB
- 8. Final model: Regression tree ● HIV_AIDS is the most important factor in predicting LEB HIV_AIDS < 0.95 79.47 47.27
- 9. Lessons Learned ● Kaggle dataset needs to be inspected carefully for data quality and validity before being analyzed ● If some data need to be replaced or dropped, it’s important to have clear rationale on the new data chosen ○ Dropped Hepatitis B data due to too many missing values ○ Replaced BMI with Obesity, and other predictors with more reliable data sources
- 10. Thank You Q & A Anh Do, Xuemeng Han, Hang Ngo, Jennifer Wong
- 11. APPENDIX
- 12. Dataset Description ● Economic indicators: ○ Status ○ GDP ○ Population ○ Total Healthcare Expenditure ○ Percentage Expenditure in Healthcare ○ Income Index ○ Years Of Schooling ● Health and Risk Factors: ○ Adult Mortality ○ Infant Deaths ○ Under Five Death ○ Polio ○ Diphtheria ○ Measles ○ HIV/AIDS ○ Thinness (5-9 years old) ○ Thinness (10-19 years old ○ Obesity ○ Alcohol Consumption
- 13. Correlation Matrix - Economic Indicators
- 14. Correlation Matrix - Health Indicators
- 15. Correlation Matrix - InfantDeaths and UnderFiveDeaths
- 16. Full Model - OLS Testing
- 17. Full Model - WLS
- 18. Full Model - Ridge & LASSO
- 19. Full Model - PCR
- 20. Full Model - PLS
- 21. Full Model - Regression Tree
- 22. Full Model- Random Forest
- 23. Full Model - Random Forest cont.
- 25. Reduced Model - WLS
- 26. Reduced Model - Ridge & LASSO
- 27. Reduced Model - PCR
- 28. Reduced Model - PLS
- 29. Reduced Model - Regression Tree
- 30. Final Results
Editor's Notes
- Anh: dataset, pre-processing Jennifer: model and variable selection, results Hang: conclusion, and challenge
- LEB is country-level statistics monitored by countries and global organizations to evaluate the quality of population health and economic development. Because of modernization and better standard of living, life expectancy worldwide has increased. So now, the increasing LEB is an important improvement on population health. According to this background and the data we collected, our predictive question is what factors are significant, and which predictive model is the best one to predict LEB. And our goal is using different methods to get the most accurate prediction of Life Expectancy, because we think this can help counties to know whether their investment is effective, and what factors are the key determinants to help them to allocate resources appropriately.
- The Life Expectancy dataset contains a total of 22 variables from the WHO’s data repository, tracking health and economic variables from 193 countries over 16 years (2000 - 2015). The response variable is LifeExpectancy, which measures average life expectancy (in age) of the population over the years. The original dataset has substantial missing data in some predictors, which are replaced by data from other sources (such as World Bank, Human Development Reports) as noted in Appendix 1. We also remove the variable HepatitisB as it has too many missing values, which will reduce the number of observations in our dataset significantly when we run parametric models. In our dataset, there is one categorical variable (Status: developed or developing country). The rest of the variables are numeric (such as $ GDP per capita, health expenditure as % of GDP per capita, % coverage of some vaccines, etc).
- The Breusch-Pagan test of 302.85 was significant, highlighting heteroskedasticity problem. The Condition Index (CI) and Variance Inflation Factors (VIF) suggested the presence of multicollinearity. Centering and standardizing the data reduced the multicollinearity problem significantly, but did not entirely fix it. The CI decreased from 1.8 billion to 57. The main “culprits” for multicollinearity were InfantDeaths and UnderFiveDeaths (both VIFs were close to 300). InfantDeaths was removed from the dataset since UnderFiveDeaths had a higher correlation with LifeExpectancy (Appendix 6). The CI fell to 9.45 and no VIFs exceeded 10.
- To address heteroskedasticity, a WLS model was run. For the dimensionality issues, Ridge, LASSO, PCR, and PLS were all included as potential analytics methods. Since our analytic goal is predictive accuracy, trees were also performed and evaluated along with the other models. In terms of the variables, there was no business restriction to keep all of them in the model. When we ran a stepwise method for variable selection, the optimal number of variables was 14. Both the stepwise and best subset methods gave as the same 14 variables to be included in the reduced model.
- To perform cross-validation, we did a 60-40 split for the training and test subsamples. All the RMSE for the models were about the same around 0.39. The tree methods were the lowest with 0.389783, and actually we got the exact same results for the full and reduced tree. We suspect this is because the reduced model only had three fewer variables than the full model and these predictors were likely not important anyway when performing the tree splitting algorithm.
- Since our analytics goal is prediction accuracy, the regression tree, which has the lowest RMSE, was chosen. The tree model first partitions the data based on number of deaths per 1,000 live births (0-4 years) due to HIV_AIDS. Countries with this rate lower than 0.95 generally have higher life expectancies compared to countries with higher rates, especially if the rate is higher than 5.05. A random forest model was also generated to analyze variable importance and confirmed that HIV_AIDS was the most important variable that contributed to the reduction of MSE when predicting LifeExpectancy (Appendix 9).
- First challenge: Kaggle dataset needs to be inspected carefully for data quality and validity before being analyzed. Author quoted WHO data, but we don’t know if the author collected data properly. Once we checked, we realized there were significant missing values in some predictors. If we used this original dataset, a lot of valuable observations would be excluded from parametric models such as OLS, WLS. There were also major inputting errors in some variables. Second challenge: If some data needs to be replaced or dropped, it’s important to have clear rationale on the new data chosen. 1st example: Dropped Hepatitis B variable because there was systematic missing values. Some developed countries did not administer Hepatitis B vaccines until recently (2017, 2018), therefore didn’t collect data on this vaccine coverage from earlier periods. 2nd example: Replaced original BMI data due to inputting errors. A person with BMI of over 30 is considered obese, while this data contains a significant number of country average BMI of 80 and above. BMI over the years in some countries also fluctuates by 10 times, which was unreasonable. We decided to replace this variable with data from a more reliable source (directly from WHO), with data on percentage of population with BMI of over 30 kg/m2. We included this variable because we think that obesity is a relevant factor in predicting LEB.
- The Life Expectancy dataset contains a total of 22 variables from the WHO’s data repository, tracking health and economic variables from 193 countries over 16 years (2000 - 2015). The response variable is LifeExpectancy, which measures average life expectancy (in age) of the population over the years. The original dataset has substantial missing data in some predictors, which are replaced by data from other sources (such as World Bank, Human Development Reports) as noted in Appendix 1. We also remove the variable HepatitisB as it has too many missing values, which will reduce the number of observations in our dataset significantly when we run parametric models. In our dataset, there is one categorical variable (Status: developed or developing country). The rest of the variables are numeric (such as $ GDP per capita, health expenditure as % of GDP per capita, % coverage of some vaccines, etc).
- The Life Expectancy dataset contains a total of 22 variables from the WHO’s data repository, tracking health and economic variables from 193 countries over 16 years (2000 - 2015). The response variable is LifeExpectancy, which measures average life expectancy (in age) of the population over the years. The original dataset has substantial missing data in some predictors, which are replaced by data from other sources (such as World Bank, Human Development Reports) as noted in Appendix 1. We also remove the variable HepatitisB as it has too many missing values, which will reduce the number of observations in our dataset significantly when we run parametric models. In our dataset, there is one categorical variable (Status: developed or developing country). The rest of the variables are numeric (such as $ GDP per capita, health expenditure as % of GDP per capita, % coverage of some vaccines, etc).
- The Life Expectancy dataset contains a total of 22 variables from the WHO’s data repository, tracking health and economic variables from 193 countries over 16 years (2000 - 2015). The response variable is LifeExpectancy, which measures average life expectancy (in age) of the population over the years. The original dataset has substantial missing data in some predictors, which are replaced by data from other sources (such as World Bank, Human Development Reports) as noted in Appendix 1. We also remove the variable HepatitisB as it has too many missing values, which will reduce the number of observations in our dataset significantly when we run parametric models. In our dataset, there is one categorical variable (Status: developed or developing country). The rest of the variables are numeric (such as $ GDP per capita, health expenditure as % of GDP per capita, % coverage of some vaccines, etc).
- The Life Expectancy dataset contains a total of 22 variables from the WHO’s data repository, tracking health and economic variables from 193 countries over 16 years (2000 - 2015). The response variable is LifeExpectancy, which measures average life expectancy (in age) of the population over the years. The original dataset has substantial missing data in some predictors, which are replaced by data from other sources (such as World Bank, Human Development Reports) as noted in Appendix 1. We also remove the variable HepatitisB as it has too many missing values, which will reduce the number of observations in our dataset significantly when we run parametric models. In our dataset, there is one categorical variable (Status: developed or developing country). The rest of the variables are numeric (such as $ GDP per capita, health expenditure as % of GDP per capita, % coverage of some vaccines, etc).