13. Robustness of Imputation Methods with Backpropagation Algorithm in Nonlinear Multiple Regression

Missing observations constitute one of the most important issues in data analysis in applied research studies. The magnitude and their structure impact parameters estimation in the modeling with important consequences for decision-making. This chapter aims to evaluate the efficiency of imputation methods combined with the backpropagation algorithm in a nonlinear regression context. The evaluation is conducted through a simulation study including sample sizes (50, 100, 200, 300, and 400) with different missing data rates (10, 20, 30 40, and 50%) and three missingness mechanisms (MCAR, MAR, and MNAR). Four imputation methods (Last Observation Carried Forward, Random Forest, Amelia, and MICE) were used to impute datasets before making prediction with backpropagation algorithm. 3-MLP model was used by varying the activation functions (Logistic-Linear, Logistic-Exponential, TanH-Linear, and TanH-Exponentiel), the number of nodes in the hidden layer (3–15), and the learning rate (20–70%). Analysis of the performance criteria (\(R^2, r\), and RMSE) of the network revealed good performances when it is trained with TanH-Linear functions, 11 nodes in the hidden layer, and a learning rate of 50%. MICE and Random Forest were the most appropriate for data imputation. These methods can support up to 50% of missing rate with an optimal sample size of 200.