While conducting some research, there are a few questions that the researcher has to deal with. They might wonder if the groups are different? What are the variables, based on which, the groups different? If such questions have occurred in your head, then the discriminant analysis will help you to answer those.
If you are a student of statistics or associated with any other related profession, you might need to gather enough information on discriminant analysis. Read this blog to learn about it in details.
Definition of Discrimination Analysis
Discriminant analysis can be defined as the statistical method which helps researchers understand how several or one independent variable is connected. Dependent variable can be considered as the variable which is predicted from the independent variables’ values.
The technique of discriminant analysis lets the researcher examine the research data when the dependent variable is categorical by nature. By the term, ‘categorical’, it is meant that the dependent variable has several categories.
The discriminant analysis is similar to the analysis of variance (ANOVA) and the regression analysis.
Purpose and Objective of Discrimination Analysis
The main purpose of Discriminant analysis is to form discriminant functions. These functions are independent variables’ combination that will perfectly discriminate between the dependent variable’s categories. The researcher gets to assess if the groups have considerable differences as per the independent variables. Other than this, the classification’s accuracy is also evaluated by the discriminant analysis.
A researcher can usually predict to which category or group a subject belongs. For example, if a recruiting manager wishes to know if the candidates will be high performers or low performers, a researcher can utilise the discriminant analysis. In short, the objectives of discriminant analysis can be summed up as follows:
- Figuring out whether there are major differences among the groups, as per the independent variables.
- Determining which independent variable adds to most of the differences in between groups
- Forming discriminant functions
- Assessing how accurate the classification is
Types of Discrimination Analysis
There are various types of discrimination analysis,
- Linear discriminant analysis- This analysis is conducted to perform dimensionality reduction while conserving the data on class discrimination. This type can be seen as a general form of Fisher’s linear discriminant. Usually, in machine learning, pattern recognition, and statistics, the linear discriminant analysis is used to identify a linear combination of features. These features divide or characterise two or more than two objects or events. The combination which is acquired as the result can be implemented as a linear classifier, and also for dimensionality reduction.
- Multiple discriminant analysis- Multiple discriminant analysis is utilised to reduce a multivariate signal to create a low dimensional signal that can be classified. Researchers cannot do direct classification using multiple discriminant analysis. This technique only helps in the production of compressed signals which are open for classification.
This method is extremely simple and requires very little mathematical implications. Through multiple discriminant analysis, an analyst can consider different stocks and highlight data pints, an important factor for a specific type of analysis. When accurately applied, this technique assists in factoring variables like price, in accordance with the values with which historical volatility and consistency are calculated.
- Quadratic discriminant analysis- In this technique, an observation is categorised into the group which has the smallest squared distance. However, the squared distance cannot be reduced to a linear function. Quadratic distance is not symmetric, unlike linear distance. Quadratic distance is called the generalised squared distance. When the determinant of the sample group covariance matrix is less than one, the generalised squared distance can be negative.
- Canonical discriminant analysis- This is a dimension reduction method which is linked with Principal component analysis and Canonical correlation. When different interval variables and a classification variable are provided, the canonical analysis produces canonical variables. These variables are utilised to summarise variation between class similar to total variation’s summarisation which is carried out by principal components.
- Gaussian discriminant analysis- When data can be brought closer with a normal distribution, the Gaussian discrimination analysis is used. While doing this particular analysis, standard deviations and two variables are important.
Steps Involved in Conducting Discrimination Analysis
To conduct a discriminant analysis, you need to go through various steps. These steps are as follows:
- Formulation- At first, the problem is formulated after figuring out the objectives, the independent variables and the criterion variable. There must be two or more collectively exhaustive and mutually exclusive categories in the criterion variable. If the dependent variable is ratio scaled or interval, it needs to be changed into categories. Also, you can place the dependent variable’s distribution and create an equal-sized group. On the basis of a theoretical model or any earlier research, the predictor variables must be selected.
Next, the sample needs to be divided into two parts. One part, which is known as the analysis sample or estimation, is utilised for assessing the discriminant function. The remaining part, known as the validation sample or holdout, is kept for validating the function.
- Estimation of the discriminant function coefficients- As you identify the analysis sample, you can assess the discriminant function coefficients. There are two broad approaches for doing this, the direct method and the stepwise method. In the direct method, the discriminant function is estimated so that all of the predictors are simultaneously included. The stepwise method involves entering the predictor variables sequentially on the basis of their discrimination ability between groups.
- Determination of significance- If the estimated discriminant functions are not statistically significant, there will be no meaning of interpreting the analysis. The null hypothesis should be statistically tested. In SPSS, this test is done on the basis of Wilk’s l. An approximate F statistic, in SAS, is calculated on the basis of an approximation to the likelihood ratio distribution. If significant discrimination is indicated by a rejection of the null hypothesis, you can continue to interpret the results.
- Interpretation of the results- The discriminant coefficients are interpreted in a similar way like the multiple regression analysis. The coefficient value for a specific predictor depends on other predictors. An assessment of the standardised discriminant function coefficients, certain plots, and the structure correlations aid the interpretation of the results. The coefficient signs may be random, but they point out which variable values produce large and small function values and link them with specific groups.
- Evaluation of the validity of the discriminant analysis- As mentioned above, using the validation sample, the classification matrix is developed. The discriminant weights are multiplied by the predictor variables’ value in the holdout sample to produce discriminant scores for the holdout sample cases. After this, these cases are then allocated to groups on the basis of their discriminant scores. Following this, the percentage of correctly classified cases or the hit ratio is determined.
What are the Situations Where we Use Discrimination Analysis
Situations in which the discriminant analysis can be used are as follows:
- This technique may be used to know if heavy, medium and light soft drink users are different as per their frozen food consumption.
- In any business, the discriminant analysis may be used to understand the attributes or characteristics of the consumers who possess store loyalty and those who do not.
- In Psychology, this method may be used to distinguish between grocery buyers as price sensitive and non-price sensitive according to their psychological characteristics or attributes.
Assumptions of Discrimination Analysis
The major assumptions of discrimination analysis are given below:
- A random sample is selected as the observations
- All the assignments for the dependent categories are correctly classified in the initial classification
- The predictor variables are distributed normally
- Each category or group should be well defined and differentiated clearly from other groups
- The dependent variables’ group sizes must not be grossly different, and it should be five times the independent variables’ numbers at least
- Minimum two categories or groups must be there. The cases should belong to only one group so that all the groups are collectively exhaustive and mutually exclusive
- The categories or groups must be defined prior to gathering the data
- The characteristics utilised to differentiate the groups must clearly discriminate amidst the groups so that the categories don’t overlap
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So, this is all the basic information you need to know about the discriminant analysis. This information will help you carry out any academic or professional task.
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