Thursday, 1 September 2011

The Shortcomings of Discriminant Analysis

Shortcomings of Discriminant Analysis:

Of the applied discriminant analysis applications that have appeared in business,finance,and economics ,most have suffered from methodological or statistical problems limiting their usefulness.These problems not limited to the areas of finance or economics only.The problems are of several types,among which difficulties include
(a)distribution of variables
(b)group dispersion
(c) interpretation of significance of individual variables
(d)reduction of dimensionality
(e)definition of groups
(f)costs of mis-classification
(g)estimation of error

One important pitfall is that standard discriminant analysis procedures assume variables to describe or characterize variables as normally distributed.However in practice deviations from normality assumptions in economics and finance is more a rule than assumption.Violation of the assumption may bias the tests of significance and standard error.Hence it is of interest to determine whether the assumption holds and what effects its relaxation may have on the tests and classification.

There are many such questions about discriminant analysis yet to be answered!!

Group: Finance 2
Author: Vrishti Garg


Graphs are visual in nature and that has been of tremendous aid in understanding plethora of unnerving statistics. Today what I learned is how to augment this visual pleasure using various softwares. Make no mistake it is not something that is done just to accentuate the beauty of a presentation. What this provides us with is information that is clearer and easier to understand. In today’s world where complexity is ever increasing these visual aids provide a solution to simplify things. One look at a graph drawn on three co-ordinates and one is able to fathom the information. Graphs are no more limited to histograms or bar charts but instead include a variety of augmentation such as pie charts, scatter plot and radar diagram. These variations help us in grasping a clear picture. And with the increasing usage of latest software GAPMINDER graphs are increasingly becoming more and more alive, swallowing loads of information which have been traditionally very cumbersome to understand. The modern day software allows one to represent graphs that show the variation in time series of data and one can actually see this differences springing to life.

A short video by Hans Rosling, developer of GAPMINDER that is available on YouTube shows 200 years of world history in four minutes. This is the amazing power that this visual aids when married with technology hold.

Another thing that struck me is their practicability ad their usage. Just by seeing such a representation a business can find out where is it lacking and what measure it needs to take to stay ahead of the competition or in the competition. Here what is needed is the understanding of the business and the environment in which it functions. Thus it becomes imperative to bring out the synergy that lies latent in combination of technology with understanding. And this is a definite way for businesses to move forward in these changing times.

Group- HR1

Author- Abhas Srivastava

Application of Discriminant Analysis in Project Management

In past few classes of Business Analytics, a common question is asked from all of us: Can a combination of variables be used to predict group membership? Ultimately, answer turns out to be positive when we are exposed to a multi-application tool called Discriminant Function Analysis.
Discriminant Analysis can be used for multiple applications in multiple fields to get multiple interpretations. This puts my focus on how it can be useful in making major termination decisions during Research and Development (R&D) projects. Most of the companies in eastern world focus on selection of R&D projects, neglecting dynamic and stochastic considerations for changing implementation process of R&D projects. They seldom make timely termination decisions for ongoing R&D projects. As a result, the successful commercialization ratio of R&D projects in eastern countries is much lower than in western countries.
Discriminant analysis at each stage can be useful in determining the variables which are best predictor of success or failure for an R&D project. The major variables which may influence project termination decisions are:
·         Degree of freedom at work
·         Degree of urgency in the project development
·         Degree of transparency of critical decisions about the project
·         Degree to which chance events influence an R&D project
·         Expected probability of commercial success
·         Expected probability of technical success etc.
To illustrate this, a study was conducted in China focusing on the reasons behind wrong timing of termination of R&D projects in various firms. Around 41 variables were grouped into six categories related to: the R&D project team, the market for the project output, the resources for the development of the project, the technology, the priority of the project, and the commercial goals.
Following this, a questionnaire was designed for project leaders to elucidate the termination decision for R&D projects at their manufacturing firms. Most of the firms surveyed were representative of their industries, and engaged in R&D and technological innovation activities. As a result, twelve variables among 41 were found to have more significant discriminating strength on the success or failure of R&D projects at three evaluation points (Initial, middle and final stage). It can be inferred that such analysis can comprehensively measure the risk that an ongoing R&D project faces.
To summarize, techniques like Discriminant Analysis facilitate integration of quantitative methods with qualitative ones, and thus is very helpful for project managers in taking termination decisions based on supported data rather than solely relying on personal operating experiences.

Submitted by:
Prashant Pandey - 13155
Group - Operations 1

Discriminant Analysis and Hostile Takeovers

Discriminant Analysis and Hostile Takeovers

Mergers and Acquisitions have been the flavor of the decade ever since the Acquisition of Tetley by Tata Tea. Indian organizations since then have gotten a flair for successfully outbidding and acquiring foreign companies and thus gain a global foot print. A recent activity where Reliance Industries picked up a 14.9% stake in the Oberoi Group as a white knight against ITC Ltd has led open another discussion which had been rage in the West, that of Hostile takeovers. Hostile takeovers have been a very common phenomenon since the 1980s. But statistically speaking hostile takeovers generally lead to acquisitions at very high premiums which could lead to their failures.

In order to measure the success of a hostile takeover a Discriminant Analysis can be used. Financial and investment variables which may be relevant to hostile takeovers are:

· Earnings per share as an estimate of future profits,

· P/E ratio,

· Debt/net worth as a measure of the target firm's ability to finance the proposed debt often associated with a takeover,

· The total number of shares of the common stock,

· The price of the stock,

· The percentage of institutional holdings,

· The percentage of the total number of shares sought by the bidder, which is typically related to what is needed to take control of the firm, and is related to the cost of the takeover bid,

· Cash flow per share, which affects the ability of the target firm to support additional debt, and

· Book value per share as an estimate of the value of the firm

The importance of these variables to the success of a hostile takeover is examined by employing a multiple discriminant analysis (MDA) model, with the groups being the successful and unsuccessful takeovers of the target firms

AUTHOR NAME:Rishi Sonthalia


Threat levels of Spiderman's enemies

Today's topic in BA classes was regarding the graphical representations of data through SPSS (with a much required help from MS Excel). Topic was easy, and hence participation was all-time high. And only because of some men like Ragu I'm writing this post (he started it). Because, roughly, 86% of people expected me to simply copy and paste some stuff from the net.

So here I am, representing graphically, my research results.

The research topic was "Threat levels of Spiderman's enemies". I would not go into the details of the research, since it is quite likely to gulp more than 100 pages of Arial font-size 12. But I'll try to explain the process in as easy a way as possible after the GRAPH!

By Delphi method, 
First, the six most important attributes of super villains were found out (intellect, extraordinary powers, goal/motive, psychopath, antisocial and solipsism);

Second, weights were assigned to each of the six attributes again by expert opinions (which were calculated in percents respectively, 17.241, 11.724, 20.690, 19.310, 12.414 and 18.621);

Third, Spider-man fans rated ten of top Spiderman’s enemies out of 10 for each of the six attributes. And then the scores were given on the basis of assigned weights.
The result was a much expected one (apart from a few surprises like Scorpion and Dr. Octopus for entirely different reasons).

The following data is represented in the above graph, and the threat level is calculated out of 10:

Dr. Octopus
Green goblin

(Green Goblin is the most threatening of all Spiderman’s enemies, and Lizard is least threatening.)

P.S. So, why represent graphically?

  1. Graphical representations make it easy to understand and interpret data at a glance.
  2. Such representations help to do comparisons among many things. 
  3. Moreover it makes data easy to recall.

Post P.S. If you didn’t like it, maybe you never read comics

Author: Jitesh Sharma
Group: Marketing 5

GAPMINDER....Make sense of the world with fun

Gapminder is a tool that allows the user to present a huge amount of world data visually in the form of moving, interactive graphs.Gapminder takes a stream of data dependent on time, and presents it visually, in the form of moving graphs. The strength of this tool is the data it gives access to. a staggering amount of worldwide data, from geographical disasters and national economy, to personal poverty and AIDS.

The data covered in Gapminder is worldwide. The data is displayed on a graph, with variables shown on the x-axis and y-axis with size and colour variations to depict magnitude and categories. The graph can compare multiple sets of data at one time, over a period of years which facilitates easy comparison. Sections of a graph can be zoomed in on, and the path of individual points can be followed, to emphasize specific data when needed. The Gapminder data can even be displayed over a map, so that statistical changes can be shown geographically.

Some of the projects undertaken by Gapminder are described below.

World Income Distribution is an interactive display of statistics on household income distribution for Bangladesh, Brazil, China, India, Indonesia, Japan, Nigeria, Pakistan and USA and the World as a whole in each year from 1970 to 1998.

Dollar Street is an interactive display of the world in the form of a street. The street number depicts the daily income per person in the family. All people of the world live on Dollar Street. The poorest live on the left end and the richest on the extreme right end. All other people live in between on a continuous scale of daily incomes.

Human Development Trends 2003 is a linear thematic Flash presentation is developed with United Nations Development Program (UNDP) for the release of the Human Development Report 200.

World Health Chart 2001 is a display of 50 to 100 years of health development for all countries of the World with time series for 35 indicators provided by the World Health Organization.

Posted by

Swati Agarwal


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

Wilks' lambda

Wilks' lambda is a test statistic used in multivariate analysis of variance (MANOVA) to test whether there are differences between the means of identified groups of subjects on a combination of dependent variables. Thus, they are considering eight dependent variables and comparing the mean of this combination for two groups. Wilks' lambda performs, in the multivariate setting, with a combination of dependent variables, the same role as the F-test performs in one-way analysis of variance. Wilks' lambda is a direct measure of the proportion of variance in the combination of dependent variables that is unaccounted for by the independent variable (the grouping variable or factor). If a large proportion of the variance is accounted for by the independent variable then it suggests that there is an effect from the grouping variable and that the groups (in this case the graduates and diplomats) have different mean values. Wilks' lambda statistic can be transformed (mathematically adjusted) to a statistic which has approximately an F distribution. This makes it easier to calculate the P-value.

Author: Prashansa Wankhede

Finance Group 5


The objective of discriminant analysis in such scenarios is to understand the group differences and to predict the likelihood that an entity that will distinguish adopters and non-adopters of ecommerce based on their perception of the complexity involved in using ecommerce.

Discriminant analysis involves deriving a variate; in this case the variate is a linear combination of nine independent variables –

v Perceived complexity

v Perceived benefits

v Organizational competence

v Perceived compatibility

v Supporting industries e-readiness

v Top management support

v Market e-readiness

v IT capability

Government e-readiness that was used to discriminate between adopters and non-adopters of ecommerce. Discrimination is achieved by setting the variate’s weight for each variable to maximize the between-group variance relative to the within group variance.

The two groups (adopters/non-adopters) of this research are independent in the sense that they are separate samples containing different sets of individual subjects.

The group variable is adoption of ecommerce. The independent variable is Management support. It discriminates between adopters and non-adopters of ecommerce. Moreover, the adopters of ecommerce had greater support from management.

All the items within this variable were significant discriminators. The mean value for adopters was significantly larger than the mean value for non-adopters. This is consistent with assertion that top management support is crucial in the acquisition and diffusion of innovation.

A number of conclusions can be drawn from these results. Firstly, banks with a strong support and commitment to ecommerce from top management are more likely to adopt ecommerce. Secondly, banks that have the requisite IT and business resources (infrastructure and skills) for ecommerce adoption stand a better chance at adopting ecommerce. Thirdly, banks that have sound IT infrastructure in place are in a better position to adopt ecommerce.

Posted by

Neha Sharma


Of Bubbles and Radars! And a shot of Practical Applications!

Business Analytics
Ok! , now it’s time for my second blog... Since in today’s class we were not given any assignment, the overall atmosphere was very light at the end of the class J and the reason for no assignment was that we didn’t learn much in today’s class, so I have decided to blog about Radar and Bubble Graphs today.
Radar graphs are used when one wants to look at several different factors related to one item. They have multiple axis along which data can be plotted. Radar chart is also known as web chart, spider chart, star chart, star plot, cobweb chart, irregular polygon, polar chart, or kiviat diagram. Now those are lot of names for one chart!!! Radar charts are used for control of quality improvement to display the performance metrics of any ongoing program. They are widely being used in sports to chart a player’s strengths and weaknesses. For example, you could use a radar chart to compile data about a wide receiver on a professional football team. On one axis, you could plot the percentage of passes caught. Another axis would show his yards per completion; another, his completions per 100 plays; another, blocks made; and a final axis might show his interceptions. If a team did this for all their wide receivers, they could easily spot the best player as well as each player's strengths and weaknesses. Radar charts are helpful for small-to-moderate-sized multivariate data sets. One of the weaknesses is that the effectiveness of radar graphs is limited to data sets with less than a few hundred points. After that, they tend to be overwhelming.
Before I start writing about bubble graphs I think everyone should check out this link: Very interesting representation of data by Mr. Hans Rosling using the bubble graph.
Bubble graphs are a sub type of Plot graphs. A third data value, called the bubble data value, is added to each data item. It is used to determine the size of the bubble. A bubble graph can be used for three dimensional data or time data items. The circles in a bubble chart represent different data values, with the area of a circle corresponding to the value. Bubble chart uses area to represent numbers and hence it is suitable for positive values. If there are negative values they will be shown in different colours. A bubble chart can be used in project management to compare the risks and rewards associated among projects. In a chart each project can be represented by a bubble, the axis can represent the net present value and probability of success and the size of the bubble can represent the overall cost of the project.
Submitted By: Gargi Koyande (13077): Marketing 2.