## Thursday, 1 September 2011

### Use of Discriminant Analysis (Wilk’s Lambda and Eigen Values) in Irrigation

Discriminant analysis is a statistical method that is used by researchers to help them understand the relationship between a "dependent variable" and one or more "independent variables." A dependent variable is the variable that a researcher is trying to explain or predict from the values of the independent variables. Discriminant analysis is similar to regression analysis and analysis of variance (ANOVA). The principal difference between discriminant analysis and the other two methods is with regard to the nature of the dependent variable.

In the most simple case one has two groups and p predictor variables. A linear discriminant equation, , is constructed such that the two groups differ as much as possible on D. That is, the weights are chosen so that were you to compute a discriminant score ( Di ) for each subject and then do an ANOVA on D, the ratio of the between groups sum of squares to the within groups sum of squares is as large as possible. The value of this ratio is the eigenvalue. In statistics, Wilks's lambda is used in multivariate analysis of variance (MANOVA analysis) to compare group means on a combination of dependent variables. Both the values tell that whether the groups have been well differentiated and formed or not. Wilk’s Lambda value is in between 0 to 1. Lower wilk’s lambda value and higher eigen value signifies that the groups have been well differentiated.

The Discriminant analysis has a wide variety of usage in various industries for different purposes. One such example is of the agriculture sector, where this analysis was used to find the effluent quality indicators for use in irrigation.

Fresh water shortage is growing water starved regions with increasing population. Besides, over extraction of underground water depletes water table and makes good quality aquifer vulnerable to contaminate by unfavourable substances. Release of effluents from domestic, industry etc. affects quality of natural resources. Reuse of wastewater can meet plant requirements but contaminate natural resources and produce degraded crops. Through discriminant analysis the usability variety of industrial effluents by their chemical properties was found for irrigation.

The data about various effluents was collected and regression scores were calculated. This helped in identifying the most discriminating factors. Cases were classified within group covariance matrix with ‘usablity of effluent for irrigation’ as grouping variable. On the basis of level of significance i.e. Wilk’s lambda, discriminant function was selected.

This method helped in identifying the significant properties of a variety of effluents. Identification of significant properties helped to assess and control chemical quality of a particular effluent during use for irrigation crops.

POsted by: Mohit Gupta
Operations_Group 2