# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 3 Results  
For the evaluation of MIGHT, we used the \"scramap\" (Statistical Comparison of Multiple Algorithms in Multiple Problems) [50] package for the R programming language. The idea is that, when given a matrix with results of different algorithms for different problems, the package uses statistical tests and corrections to assess the differences between algorithms, which is the main idea behind MIGHT, except that we are not dealing with algorithm performances. We evaluated our methodology using eight different experiments on four different datasets. For each dataset, to create the rules for borrowing, the methodology uses both MIGHTv1 and MIGHTv2. After creating the rules for each country, its missing value can be either an average or a median of the values of the countries that are eligible for borrowing. We also calculate the missing value as an average or a median from the value from all of the countries that are involved in the borrowing process. This means not only the countries that are eligible and are results from our methodology. We have done this for each country on each test instance from the dataset, and, in both scenarios, we calculate the absolute error between the borrowed value and the true analytical value. For a better understanding of how the methodology works, we present an example dataset and present the evaluation process in detail. The selected dataset contains nutrient values collected for Potassium (K) in foods belonging to the food group \"Fruits\". The data collection process is as follows:  
1. Method type is chosen as \"A\" (Analytical result/s) or \"AG\" (Analytical, generic). 2. Food group is \"Fruits\". 3. In this example, the food group includes only raw foods, so the separate foods, i.e., fruits, are chosen aiming towards as much data as possible. 4. The nutrient is Potassium (K), since it is common nutrient in fruit [51]. At the first stage, we collected data for 18 foods: apple, banana, blueberry, cantaloupe, cherry, grape, grapefruit, lemon, mango, melon, orange, peach, pear, pineapple, plum, raspberry, strawberry, and tomato. 5. To choose the countries, a binary matrix is constructed. The rows are all the fruits that we have data for, and the columns are the identification numbers of the national FCDBs. Although this step is meant for choosing countries, we are also recursively choosing foods, because there is no point in keeping foods that have missing data for many countries. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Country** & **Country\({}_{1}\)** & **Country\({}_{2}\)** &... & **Country\({}_{m}\)** \\ \hline Country\({}_{1}\) & / & \(n-a\) &... & \(n-a\) \\ Country\({}_{2}\) & \(n-b\) & / &... & \(n-a\) \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ Country\({}_{m}\) & \(n-b\) & \(n-b\) &... & / \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Matrix formed from summing the rules from all the models, where \(m\) is the number of countries, \(n\) is the number of models, \(a,b\in\mathbb{N}\), and \(0\leq a,b\leq n\). For MIGHTv1 \(a=b\), for MIGHTv2 \(a\
eq b\). After collecting the Potassium (K) data for the group \"Fruits\", we check that all the data are in the same measure unit (grams, milligrams, etc. ), and if needed conversions are made. In this example, the dataset consists of data for 16 fruits extracted from 9 national FCDBs, i.e., \(n=16\) and \(m=9\). The next step is to apply our methodology to the data. First, we check the restrictions for the number of problems and datasets (\(n\geq r\) and \(m\geq 3\)). Since \(m=9\), the condition for the number of datasets \(m\geq 3\) is satisfied. The number \(r\) depends on the statistical test used, so in order to find \(r\) we first need to know what kind of statistical test to apply. Before testing the null hypothesis, the three conditions for choosing the appropriate test must be checked:  
1. Independence: In our case, events are the processes used to obtain/measure the values of Potassium (K) in a fruit.