# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 2 Materials and Methods
### Related Work
#### 2.2.1 Traditional Approaches for Borrowing FCD  
Although food composition data may appear to be simply a collection of foods with the nutrients listed alongside them, to ensure that the values reported are used correctly, there are actually a number of considerations that users should take into account:  
* variability of the composition of a food item;
* misunderstanding of nutrient definitions;
* use of an incorrect conversion factor; and
* use of a nutrient interchangeably with its sub-types. When using FCD on its own, the limitations that should be considered include the inherent variability in the composition of a food item, the number of food items and range of nutrients covered \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Food** & **NO** & **FR** & **IT** & **UK** & **CH** & **SE** & **ES** & **BE** & **DK** & **USA** & **CA** & **SI** & **NL** & **CZ** & **AU** & **PT** \\ \hline Apple & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ Banana & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\ Blueberry & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ Cherry & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ \(i\) & : & : & : & : & : & : & : & : & : & : & : & : & : & : & : & : \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Binary matrix for selecting which national FCDBs to include. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Food/FCDB** & **County\({}_{1}\)** & **County\({}_{2}\)** & **County\({}_{3}\)** &... & **County\({}_{m}\)** \\ \hline Food\({}_{1}\) & \(Value_{11}\) & \(Value_{12}\) & \(Value_{13}\) &... & \(Value_{1}m\) \\ Food\({}_{2}\) & \(Value_{21}\) & \(Value_{22}\) & \(Value_{23}\) &... & \(Value_{2}m\) \\ Food\({}_{3}\) & \(Value_{31}\) & \(Value_{32}\) & \(Value_{33}\) &... & \(Value_{3}m\) \\ : & : & : & : & : & : & : & : \\ Food\({}_{n}\) & \(Value_{n1}\) & \(Value_{n2}\) & \(Value_{n3}\) &... & \(Value_{nm}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Generalized for values from one nutrient in several foods from several FCDBs. by a database. Errors that may be associated with using a FCDB include: an understanding of nutrient definitions such as available carbohydrate (excluding fiber) versus total carbohydrates (including fiber) and calculation errors for fatty acid values. This commonly includes the use of an incorrect conversion factor, e.g., the use of fatty acids per 100 g of total fatty acids instead of per 100 g of the food item, or calculation of vitamin A intake without considering the pro-vitamin A compounds (alphacarotene, beta-carotene, and betacrylptoxanthin). Similarly, interchangeable use of vitamin E and alpha-tocopherol is another common error (vitamin E actually includes alpha-, beta-, delta- and gamma-tocopherols and tocotrienols). Nowadays, many countries have their own national FCDBs that are readily available online [20]. When using the food composition data of another country, there are few things that we must be observant of:  
* differing cultivators, soils, climates and agricultural practices;
* differing food production and processing practices;
* variation in the composition of recipe ingredients with the same name; and
* variation in food products available. Each of these factors can have significant impact on the micro-nutrient composition of food items. FCD may differ between countries as a result of different things such as varied definitions of nutrients, analytical methods (e.g., fiber), nutrient calculations (e.g., energy), the reference quantity of foods contained in the database (per 100 g vs. per serving) and the nutrient values that are available for the foods. The treatment of missing values may vary between countries despite efforts to adjust the practices. When selecting another FCDB to borrow values from, the following must be taken into account [17; 18]:  
1. The FCDB should contain up-to-date FCD. 2.