1. Figure 1 Aggregate Brand-Switching (Transition) Matrix
purchased
at time t
Brand purchased at time t+1 A B C D
A B C D
200
125 50
500

2. Expected Frequencies Brand purchased at time t-1
A B C D

3. Residuals (o-e) Brand purchased at time t-1 Brand purchased at time t
A B C D

4. Standardized Residuals (o-e)/(e)
Brand
purchased
at time t-1
Brand purchased at time t A B C D
A B C D
now differential mkt shares have been factored out
...providing a purer test of loyalty and switching