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# Perceptor model

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Analysis of Urban's Perceptor Model for designing and positioning frequently purchased consumer products. The presentation talks about the model description. For analysis and explanation of the model, in depth understanding of the original article (Urban, 1975) and MDS is required.

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### Perceptor model

1. 1. Glen L. Urban
2. 2.  Motive  Develop model for designing and positioning of new frequently purchased consumer products. Model structure  Trial and repeat process that produces an estimate of long- run share for a new brand. Main idea  Model the distance from the ideal brand to brand trial and repeat purchase estimates for a new product in an existing market. Outputs  Understanding of perceptions, preference and purchase process underlying product positioning decision.  Tool for estimating the market share for alternate new brand designs.
3. 3.  Long Run Market Share Model:  m = ts …………. (1)  m= long run market share,  t= fraction of the target market that ever tries the new brand (0 ≤ t ≤1)  s= share of purchases of new brand among those who have ever tried the brand (0 ≤ s ≤1) Now, Urban further developed this ‘t’ or the ultimate trial fraction on the basis of the Trial Model
4. 4.  Ultimate Trial Model:  t = qwv ………..... (2)  q = ultimate probability of trial given awareness and availability  w = long run awareness of the new brand  v = long run availability of the new brand (volume weighted percentage of stores carrying the brand) The market share of those who have used the brand is modeled as the equilibrium of a two- state Markov process
5. 5.  Steady- state Share Process:  S = P21/ (1+ P21 – P11) ……….. (3) for those who have tried the new brand  Pij = Probability of purchase of brand j at next purchase opportunity when brand i was purchased last, 0 ≤Pij≤ 1.0,  i or j = 1 refers to new brand,  i or j = 2 refers to all other brands. This Markov formulation assumes that the frequency of purchase of the new brand is the same as existing brands.
6. 6.  Perception and Preference Mapping  Xby = ∑Aα=1fyarba …………………… (4)  xby, = coordinates of brand b on dimension y for the perceptual map of those who have not tried our brand, but who are aware of concept (b = 1, 2, . . . B, where B = new brand; y = 1,2,. . .Y)  fya = factor score coefficient for dimension y and attribute scale a (a = 1,2,. . . A)  rba = standardized average rating of brand b on scale a. Iy = coordinates of average ideal point of dimension y for map of those who have not tried our brand but are aware of the concept. This Iy would be used subsequently
7. 7.  Probability of Purchase (Trial)  q= α0 + α1dB2 ……………… (5)  q = as defined in (2)  dB = squared distance from ideal point to the new 2 brand on map for those who are aware but have not yet used the new brand  α0 , α1 = coefficients to be determined empirically
8. 8.  In case of a perceptual space having z dimensions where the new brand occupies the position Xz and ideal position is Iz, then:  dB2 = ∑zz=1hz(Xz-Iz)2 …………….. (6)  Hz = importance weights for dimension z
9. 9.  Probability of Repeat  P11 = β 0 + β1d2B …………… (7)  pll = probability of repeat purchase if new brand was purchased last. (0 ≤p11 ≤ 1.0)  d2B = distance squared from ideal point to new brand after use perceptual map for those who have used the brand)  β0 , β 1 = coefficients to be determined empirically The probability of repeat purchase if the new product is not chosen (p21)is empirically determined.
10. 10.  Sources of New Brand Share  After substituting the trial (5) and repeat (7) probabilities in (2) and (3) an estimate of the share of the new brand is obtained by (1).  It is assumed that share will come from the brands that are perceptually most similar to the new brand (i.e. nearest to it on the map) and from the brands that are most widely evoked.  A brand is defined as evoked by a consumer if it has been used, if it would be considered at the next purchase, or if it is rejected as a purchase alternative.
11. 11.  Sources of New Brand Share (contd.)  Kb = m [(eb/D2bB) / ∑B=1B-1(eb/D2bB)] ………….. (8)  kb = loss in market share of existing brand b  m = market share of new brand  eb = fraction of people who have brand b in their evoked set  D2bB = distance squared from brand b to new brand B in users map This completes the model description.
12. 12. Sunny Bose IIMT