|# Married woman aged 15-49 years<br>visited by government health<br>worker*|Government health worker is a CHW and includes - Health Assistants<br>(HA) deployed by the Directorate General of Health Services (DGHS)|
|---|---|
|Availability of contraceptives|Availability of any modern contraceptive at facilities|

**Sources:** **<mark>BHFS & DHS;</mark>** <mark>* relevant only for a few outcome indicators; # represents community health workers (CHW)</mark>

## **2.3 Analysis**

### **_<mark>Why machine learning analysis?</mark>_**

This study applied the machine learning technique using R programming language.<sup>23</sup> <mark>Machine learning was found to be useful for this comparative analysis since it allowed large demand- and supply-side data sets to be combined. Machine learning was applied over conventional analysis due to the following specific advantages that it offers: 1) it helps to identify the trends and patterns in large data sets easily, and with minimal human biases; and 2) machine-learning algorithms continuously learn from data to help addressing the potential errors in the data. This increases the efficiency of the analysis and the accuracy and quality of predicted outcomes or trends.</mark><sup>24</sup> <mark>Machine learning consists of a group of artificial intelligence techniques, in which the algorithms learn the patterns in the data without being explicitly programmed to carry out specific applications.</mark><sup>24</sup> <mark>In this study, a gradient boosting algorithm was used to predict the outcomes based on the predictors listed in Tables 3 and 4. Gradient boosting combines shallow and successive decision trees.</mark><sup>25</sup> <mark>Decision trees consist of recursively partitioning (also known as splitting) predictors. The goal of each tree in our model was to maximize the accuracy of prediction. Each decision tree learns successively and improves upon the previous (learning rate). Eventually, predictions are based on a weighted combination of these trees.</mark><sup>26</sup> <mark>The preprocessed data (variable scaling and removal of highly correlated predictors) was split into training (80%) and test segments (20%) for all outcome variables. First, the algorithm was trained on the training segment and then validated on the test segment to determine predictions. The data was 10-fold cross-validated, with the data split into 80% training and 20% test observations randomly, ten times for all algorithms. The average of the cross-validations was taken as the final result. The relative influence of the predictors with the output was estimated using mean decrease Gini impurity coefficient (MDG) in the gradient boosting algorithm.</mark><sup>25</sup> <mark>MDG is the average across all trees of the decrease in Gini impurity for a predictor.</mark><sup>25</sup> <mark>The mean decrease in Gini coefficient is a measure of how each variable contributes to the homogeneity of the nodes and leaves in the resulting hierarchy of decision trees. A higher MDG value shows that the degree of impurity arising from a variable category could be reduced farthest by one variable, and therefore suggests an important associated factor.</mark><sup>25</sup> <mark>The ranking of the top 10 predictors was plotted based on the MDG. Predictors with a higher relative importance value are more likely to affect the outcomes than with the lower values. For instance, the predictor on the top of the relative importance chart (given in the results) has a relatively higher relative importance value and the highest influence on the outcome indicator among all predictors considered. Similarly, the predictor on the bottom of the relative importance chart (given in the results) has the least relative importance value and the least influence on the outcome among all predictors considered.</mark>

# **3. Results**

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