Day 10 - Team G - Vivek Bakshi

Discriminant Analysis

Discriminant Function Analysis (DA) undertakes the same task as multiple linear regression 

by predicting an outcome. It is used when:

• the dependent is categorical with the predictor IV’s at interval level such as age, income, attitudes, perceptions, and years of education, although dummy variables can be used as predictors as in multiple regression. Logistic regression IV’s can be of any level of measurement.
• there are more than two DV categories, unlike logistic regression, which is limited to a dichotomous dependent variable.

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

Assumptions of discriminant analysis

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 defi ned, 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 defi ned 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.

Conjoint Analysis

Conjoint analysis requires research participants to make a series of trade-offs. Analysis of these trade-offs will reveal the relative importance of component attributes. To improve the predictive ability of this analysis, research participants should be grouped into similar segments based on objectives, values and/or other factors.

The exercise can be administered to survey respondents in a number of different ways. Traditionally it is administered as a ranking exercise and sometimes as a rating exercise (where the respondent awards each trade-off scenario a score indicating appeal).

In more recent years it has become common practice to present the trade-offs as a choice exercise (where the respondent simply chooses the most preferred alternative from a selection of competing alternatives - particularly common when simulating consumer choices) or as a constant sum allocation exercise (particularly common in pharmaceutical market research, where physicians indicate likely shares of prescribing, and each alternative in the trade-off is the description a real or hypothetical therapy).

Analysis is traditionally carried out with some form of multiple regression, but more recently the use of hierarchical Bayesian analysis has become widespread, enabling fairly robust statistical models of individual respondent decision behaviour to be developed.

When there are many attributes, experiments with Conjoint Analysis include problems of information overload that affect the validity of such experiments. The impact of these problems can be avoided or reduced by using Hierarchical Information Integration

Three steps--collecting trade-offs, estimating buyer value systems, and making choice predictions-- form the basics of conjoint analysis.  Although trade-off matrices are useful for explaining conjoint analysis as in this example, not many researchers use them nowadays.  It’s easier to collect conjoint data by having respondents rank or rate concept statements or by using PC-based interviewing software that decides what questions to ask each respondent, based on his previous answers.

By:

Vivek Bakshi