Wednesday, November 18, 2009

discriminant analysis

Text in Blue is the explanation not the part of the article



Article No. 1

Title:
DISCRIMINANT ANALYSIS

Section:
Discriminant Analysis

Category:


Meta description:
Discriminant Analysis is a technique of classification of objects and persons into groups, whose common characteristics the object or thing possesses. It can also help in assigning objects or people to existing groups. This is done based on the information available with regard to the characteristics or features of the object or person. . In other words, this is a regression based statistical technique used to ascertain which classification or group a sample of data belongs to, based on its distinct features.

Meta data:
Discriminant Analysis,

Intro text:
Discriminant Analysis is a technique of classification of objects and persons into groups, whose common characteristics the object or thing possesses. It can also help in assigning objects or people to existing groups. This is done based on the information available with regard to the characteristics or features of the object or person. In other words, this is a regression based statistical technique used to ascertain which classification or group a sample of data belongs to, based on its distinct features.

Main text:
Discriminant Analysis, as we have seen earlier, is a statistical technique to organize and optimize, the description of distinctive features of objects belonging to different groups or classes, and the assignment of objects or persons of unknown classes to existing groups. Consider the example of credit card customers. Here we may wish to distinguish between the good and the bad credit card customers. This differentiation is based on two variables, their credit history and payment status of existing credit card debt. An attempt, to study the correlation results of the good and bad customers with the other variables, namely credit history and status of credit card debt, and the interrelation of the two variables, is made. Descriptive discrimination focuses on finding a few dimensions combining the originally measured variables and those that separate the classes or collections as much as possible.

PROCEDURE OF DISCRIMINANT ANALYSIS:

Select a random sample from a group or class or objects or people. This sample is called as “training” or “learning” sample. Subject this training sample to discriminant analysis, to obtain a set of discriminant functions. The classification will be carried out based on these functions. These functions are then used by SPSS or SAS, so that, they would not be known to us. The information regarding the characteristics of this sample is stored in the dataset created by the program. The same procedure also allows a true validation of the classification functions using a file containing objects of known membership to be classified using only the information available on the classification functions and the variables developed with the “training” sample.

EXAMPLES OF DISCRIMINANT ANALYSIS:

Hereunder is an example of the application of this procedure in the construction industry. During a construction project, when a slab is cast at site, using mechanical means, it is a general practice to take concrete cubes and send them to the laboratory for strength testing. Based on the strength gain at various intervals, it is decided when to dismantle the shuttering. The benchmark for concrete to attain adequate strengths at regular intervals is as under:

3 days strength---------------------------------33%

7 days strength---------------------------------63%

21 days strength--------------------------------83%

28 days strength--------------------------------100%

An attempt is made to classify the cubes based on their strength gain. Here the discriminant function is the strength and the training sample is the sample of concrete taken at the time of casting of the slab. The slab is de-shuttered, only if the strength of cubes crosses the above value. Due to commercial considerations and shortage of time, slab is de-shuttered, as quickly as possible, thus shortening the slab cycle. Here two groups come to the fore, namely the group where adequate strength is got (group 1) after the designated time interval, post slab casting, and the other where the samples are not meeting the above strength requirements (group 2).

A graduate admissions committee may divide a set of alumni into two groups, namely those who have finished the program in five years and those that did not. Discriminant function analysis can be applied to ascertain successful completion of the graduate program based on the GRE scores and the undergraduate grade point average. Examination of the prediction model may provide insights into how each predictor individually and in combination, predicted completion or non-completion of a graduate program.

The Simplest case would be the prediction of dichotomous group membership based on a single variable. Consider a modification of the above example. The pass percentage, of a graduate course is to be decided depending upon the scores of candidates based only on the GRE verbal scores. Here there is only one variable, namely the GRE verbal score, and therefore it may be difficult to know how different variables interact with each other in prediction.

CONCLUSION:
We can thus say that discriminant analysis is a potent method of allocating an object or person to a group or community, based on certain known parameters, and also a way to classify freak samples in existing groups.

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