Development of a Risk Assessment Mathematical Model to Evaluate Invasion Risk of Invasive Alien Species Using Interval Multivariate Linear Regression

Abstract

Evaluation of risk of Invasive Alien Species (IAS) with uncertain and imprcise data is a challenging  task. In the present work, mathematical model for risk assessment is developed by using interval  multiple linear regression analysis in which mimic unceratin and imprecise data. Here both  dependent  and  independent  variables  are  interval-valued. 12 invasive attributes selected as model parameters. Proposed a new method find the solution of design matrix using interval least square method. Here obtained a dataset of 28 invasive plant species which contains single-valued observations of 12 parameters and invasion risk scores which are obtained from National Risk Assessment. Using the dataset formed four interval input datasets. New method is proposed to find the estimates for interval regression coefficient using  interval least suqare method. The interval regression coefficents are estimated using four different  interval  input  data  set. The quality of the approximated model is evaluted by average accuracy  ratio  and  the models are validated using well known six invasive  and  four non  invasive  species. The approximated model gives average accuracy ratio of 0.730852 along with data set 3 which is the highest among all data sets. Validation results show that the expected risk score of each plant  species  from  National  Risk  Assessment  is within  the  approximated  risk  interval. Comparing the quality and the validation results, it is found that the approximated model along with data set 3 gives better predictions of risks of invasive alien species if its invasion is dominated by biological traits.