Discriminant Analysis Case Study
The following is a sample Discriminant Analysis Case Study. There are several key elements required to conduct a successful Discriminant Analysis. This type of analysis is a type of classificatory tool, in the sense that it analyzes sample data and it finds mathematical criteria to discriminate different groups within the sample. It has very powerful application in marketing and other fields.
The following descriptive statistics are obtained:
Some variables seem to depart significantly from normality, based on the large skewness coefficient, relative to their corresponding standard error. The following normal test is performed:
The variables that depart significantly from normality are:
¨ Air and sea passenger transport
For the purpose of this discriminant analysis, the grouping variable will be whether or not the country belongs to the Eurozone.
The correlation matrix shows the existence of linear association between several predictors, which suggests that the appropriate method to use is the stepwise approach. The following results are obtained with the aid of SPSS:
The assumption of homogeneity of covariance matrices is not met, p = .009
Observe that the grouping variable (Belongs to the Eurozone or not) has only two categories, so there is only one discriminant function to determine the groups. The discriminant function contributes significantly at explaining the differences between the two groups, Wilk’s Lambda = 0.574, p < .001.
The following final model is obtained:
Hence, only the variables Life expectancy at birth (years) for Women (2008) and Employment rate older workers (55-64), are required to be included in the model. The rest 9 variables are not required to explain the differences between the two groups.
The above table shows the standardized canonical discriminant coefficients. It is observed that Life expectancy at birth (years) for Women (2008) is slightly more important to the model than Employment rate older workers (55-64), because the change in one standard deviation in Life expectancy at birth (years) for Women (2008) has a relatively larger effect in the discriminant function than a change in one standard deviation in Employment rate older workers (55-64).
The above table shows the loadings of all the initial predictors on the discriminant function.
The above table shows the canonical (non-standardized) discriminant function coefficients.
The countries on the Eurozone tend to have positive values of the discriminant function, whereas the countries that are not members of the Eurozone tend to have negative values of the discriminant function. Also, the countries on the Eurozone tend to have higher life expectancy for women than those not from the Eurozone, whereas the countries that are not members of the Eurozone tend to have a higher rate of older workers (55-64) than those countries from the Eurozone.
The classification obtained for this discriminant analysis is satisfactory, considering that 87.5% of cases were correctly classified.
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