Discriminant Analysis Dr. Satyendra Singh Professor and Director University of Winnipeg, Canada

What is a Discriminant Analysis? It forms linear combination of the independent or predictor variables to serve as a basis for classifying cases into one of the groups DV: Market Orientation of firms (7-pt Scale) o Low and High (Must be on nominal Scale) IV: Culture o Market, Adhocracy, Clan, Hierarchical (Constant sum = 100) 1

Data Integrity Run as usual checks: mean, median, outlier… Ensure all variables have complete information Careful when deleting cases with missing information. Instead check for pattern o eg. educated people gave complete info How many cases do we need? 20 cases per IV as a thumb rule SPSS produces case summary for eligible cases 2

Mean Summary for Eligible Cases 3

Analyze IV (group)mean Differences Wilks’ Lambda: λ = 0 (gr. mean is unequal) o We want lower λ and p<.05 for the group to be unequal for discriminant analysis o Adhocracy and market culture are most different for low and high market oriented firms 4

Run the test 5

Canonical Discriminant Function 19 Canonical discriminant coefficients are in unstandardized unit We can compute group centroid mean (discriminant score) = const. + b. mkt + C adh+… SPSS gives this value so we know how far the groups are from each other, ie how powerful the function is in discriminating between the groups. 6

Loading or Structure Matrix Correlations Important for us Correlation >.3 Can be used for ranking with caution Same unit is better By default, SPSS assumes that all groups have equal prior probabilities So for 2 gr.5 and for 3 gr.33 so on 7 Centroid Distance =.23 – (-.20) =.43

Group 1 Distribution 8

Group 2 Distribution 9

All-groups Distribution 10

Interpretation: Means and Structure Matrix Adhocracy culture contributes most to making firms market oriented, followed by market, hierarchical and clan culture. 11

Classification Results For example, if beer 12

Predictive Power of the Model… Maximum Chance Criterion: o it calculates the percentage of correctly classified cases if all the cases were placed in one group with the greatest possibility of occurrence o Because high market oriented group (ie. largest group) occurs 53.7% (ie 50/93) of time, it could be correct if all cases were assigned to this group. o C max = 53.7% 13

Predictive Power of the Model… Proportional Chance Criterion: o it compares the model with the priori chance of classifying cases correctly without the discriminant function o Because we’ve unequal group (low = 43, High = 50, Total = 93), we use the formula o Proportion Chance Criterion (C prop)= p*p + (1-p) * (1-p) o proportion of cases in gr 1 (p) o Proportion of cases in gr 2 (1-p) o C prop = (43/93) * (43/93) + (1-(43/93)) * (1-(43/93)) =.5017 = 50.17% 14

Predictive Power Comparison Our discriminant model has the highest discriminatory power because So we accept the model. 15

Questions?