## Wednesday, 31 August 2011

### Application of Discriminant analysis in Retail store location planning

Discriminant Function Analysis is similar to Regression analysis, as they establish the equation for predicting the outcome. Here we generate dependent variable based on weighted combinations of independent values.

Y=C+a*x1+b*x2+c*x3…..+d*xn.

Here Y gives discriminant score. This is a weighted linear combination (sum) of the discriminating variables.

This part we learnt in class, let’s go one step ahead and understand where this discriminant analysis can be used and also what assumptions need to be considered before application of this concept.

The major underlying assumptions of DA are:

the observations are a random sample;

each predictor variable is normally distributed;

each of the allocations for the dependent categories in the initial classiﬁcation are correctly classiﬁed;

there must be at least two groups or categories, with each case belonging to only one group so that the groups are mutually exclusive and collectively exhaustive (all cases can be placed in a group);

Each group or category must be well deﬁned, clearly differentiated from any other group(s) and natural. Putting a median split on an attitude scale is not a natural way to form groups. Partitioning quantitative variables is only justiﬁable if there are easily identiﬁable gaps at the points of division;

for instance, three groups taking three available levels of amounts of housing loan;

the groups or categories should be deﬁned before collecting the data;

the attribute(s) used to separate the groups should discriminate quite clearly between the groups so that group or category overlap is clearly non-existent or minimal;

group sizes of the dependent should not be grossly different and should be at least ﬁve times the number of independent variables.

The aim of the statistical analysis in DA is to combine (weight) the variable scores in some way so that a single new composite variable, the discriminant score, is produced. This single new composite variable is used for predicting the future.

Example:

This Discriminant analysis is used extensively in categorization of customers and products. Suppose as an operations manager we are assigned a task of opening a new electronic chain store, we have to first do the mapping of customer and find the probability whether people will buy this product from this store or not. First step while doing such analysis is, collection of data from a sample of potential customers concerning their ratings of all the product attributes. Estimate the Discriminant Function Coefficients and also form the equation. The set of discriminant score, which we generate, will be used for decision making.

The table “Function at group centroid” gives the highest and lowest value; the mean of this value will be used as cut off point, so every customer whose discriminant score exceeds this cut off point can be a potential client of electronic store.

Author of Blog: T M Prakash – 13111

Group – Operations 2

Reference:

http://www.uk.sagepub.com/burns/website%20material/Chapter%2025%20-%20Discriminant%20Analysis.pdf