14. Moderately Heterogeneous Population (2) Heterogeneous Population (1) Extremely Heterogeneous Population ( Mostly Brand Loyal (3) f (p), Distribution Actors Population P, Probability of Purchase Bernoulli Model
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17. 1-∑p (i,i) k= 1- ∑mi² ∑ p (i,i)= diagonal values of Joint Probability Table = 0.267 +0.349+0.09 = 0.706 k = 0.294/0.614 = 0.479 Example Contd. Brand Shares ( m i ) m i *(1- m i ) A 0.39 0.238 B 0.46 0.248 C 0.15 0.128
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21. Markov Models Price shift Limitations Stationarity - unrealistic a firm loosing market position will take corrective action.
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26. P i = V i (Σ k V k ) Applying Luce Model to this formulation gives the probability of purchase of i given a previous purchase of j, P i
27. ~ Previous consumption alters the unconditional brand choice probability, V i, that is, ~ P i – V i < 0, then j is a substitute for product i (the consumption of brand j lowers the probability of choosing brand i ) ~ While P i – V i > 0, then j is a compliment for product i (the consumption of brand j increases the probability of choosing brand i )