8.5 Market simulation
Say we have created a small number of ice creams and we want to estimate the market share of each of those ice creams. Let’s say we have selected the following four profiles:
# use slice() to select rows
market_profiles <- profiles.all %>%
slice(c(4, 16, 23, 38)) # from profiles.all, select rows 4, 16, 23, 38 as the four profiles
market_profiles## Flavor Packaging Light Organic
## 1 Strawberry Cone Low fat Not organic
## 2 Chocolate Cone No low fat Not organic
## 3 Raspberry Homemade waffle No low fat Not organic
## 4 Raspberry Homemade waffle Low fat OrganicWe already know how to estimate which ice cream will be liked the most:
conjoint_allrespondents <- conjoint(icecream, rvar = "rating", evar = c("Flavor","Packaging","Light","Organic"))
predict(conjoint_allrespondents, market_profiles) %>%
arrange(desc(Prediction))## Conjoint Analysis
## Data : icecream
## Response variable : rating
## Explanatory variables: Flavor, Packaging, Light, Organic
## Prediction dataset : market_profiles
##
## Flavor Packaging Light Organic Prediction
## Strawberry Cone Low fat Not organic 5.124
## Raspberry Homemade waffle No low fat Not organic 5.113
## Raspberry Homemade waffle Low fat Organic 4.942
## Chocolate Cone No low fat Not organic 4.836The low fat, non-organic strawberry ice cream in a cone has the highest predicted rating across all respondents. But this doesn’t tell us what the market share of each of the four profiles will be. For this, we need to know, for each participant, which profile he or she would choose. In other words, we need to predict the ratings for each individual separately:
# same model as before, but now add by = "respondent"
conjoint_perrespondent <- conjoint(icecream, rvar = "rating", evar = c("Flavor","Packaging","Light","Organic"), by = "respondent")
predict(conjoint_perrespondent, market_profiles) %>%
arrange(respondent, desc(Prediction)) # sort by respondent and then by predicted rating## Conjoint Analysis
## Data : icecream
## Response variable : rating
## Explanatory variables: Flavor, Packaging, Light, Organic
## Prediction dataset : market_profiles
## Rows shown : 20 of 60
##
## respondent Flavor Packaging Light Organic Prediction
## Individual 1 Strawberry Cone Low fat Not organic 8.800
## Individual 1 Raspberry Homemade waffle Low fat Organic 3.700
## Individual 1 Chocolate Cone No low fat Not organic 2.800
## Individual 1 Raspberry Homemade waffle No low fat Not organic 1.300
## Individual 10 Raspberry Homemade waffle No low fat Not organic 9.950
## Individual 10 Raspberry Homemade waffle Low fat Organic 8.967
## Individual 10 Chocolate Cone No low fat Not organic 5.367
## Individual 10 Strawberry Cone Low fat Not organic 2.033
## Individual 11 Strawberry Cone Low fat Not organic 5.800
## Individual 11 Raspberry Homemade waffle Low fat Organic 5.200
## Individual 11 Chocolate Cone No low fat Not organic 3.800
## Individual 11 Raspberry Homemade waffle No low fat Not organic 2.800
## Individual 12 Raspberry Homemade waffle No low fat Not organic 9.600
## Individual 12 Raspberry Homemade waffle Low fat Organic 7.733
## Individual 12 Chocolate Cone No low fat Not organic 5.933
## Individual 12 Strawberry Cone Low fat Not organic 3.267
## Individual 13 Raspberry Homemade waffle No low fat Not organic 6.550
## Individual 13 Raspberry Homemade waffle Low fat Organic 6.200
## Individual 13 Chocolate Cone No low fat Not organic 5.300
## Individual 13 Strawberry Cone Low fat Not organic 1.300Let’s retain for each individual only his or her highest rated profile. We can do this by grouping per respondent and by adding a variable named ranking that will tell us the ranking of profiles, based on predicted rating, for every respondent:
highest_rated <- predict(conjoint_perrespondent, market_profiles) %>%
group_by(respondent) %>%
mutate(ranking = rank(Prediction))
# have a look
highest_rated %>%
arrange(respondent, ranking)## # A tibble: 60 x 7
## # Groups: respondent [15]
## respondent Flavor Packaging Light Organic Prediction ranking
## <chr> <fct> <fct> <fct> <fct> <dbl> <dbl>
## 1 Individual 1 Raspberry Homemade waf~ No low ~ Not organ~ 1.3 1
## 2 Individual 1 Chocolate Cone No low ~ Not organ~ 2.80 2
## 3 Individual 1 Raspberry Homemade waf~ Low fat Organic 3.7 3
## 4 Individual 1 Strawberry Cone Low fat Not organ~ 8.8 4
## 5 Individual 10 Strawberry Cone Low fat Not organ~ 2.03 1
## 6 Individual 10 Chocolate Cone No low ~ Not organ~ 5.37 2
## 7 Individual 10 Raspberry Homemade waf~ Low fat Organic 8.97 3
## 8 Individual 10 Raspberry Homemade waf~ No low ~ Not organ~ 9.95 4
## 9 Individual 11 Raspberry Homemade waf~ No low ~ Not organ~ 2.8 1
## 10 Individual 11 Chocolate Cone No low ~ Not organ~ 3.80 2
## # ... with 50 more rows# we need to retain only the highest ranked ice cream
highest_rated <- highest_rated %>%
arrange(respondent, ranking) %>%
filter(ranking == 4)
highest_rated## # A tibble: 15 x 7
## # Groups: respondent [15]
## respondent Flavor Packaging Light Organic Prediction ranking
## <chr> <fct> <fct> <fct> <fct> <dbl> <dbl>
## 1 Individual 1 Strawberry Cone Low fat Not organ~ 8.8 4
## 2 Individual 10 Raspberry Homemade waf~ No low ~ Not organ~ 9.95 4
## 3 Individual 11 Strawberry Cone Low fat Not organ~ 5.80 4
## 4 Individual 12 Raspberry Homemade waf~ No low ~ Not organ~ 9.60 4
## 5 Individual 13 Raspberry Homemade waf~ No low ~ Not organ~ 6.55 4
## 6 Individual 14 Raspberry Homemade waf~ No low ~ Not organ~ 9.8 4
## 7 Individual 15 Strawberry Cone Low fat Not organ~ 8.53 4
## 8 Individual 2 Strawberry Cone Low fat Not organ~ 9.63 4
## 9 Individual 3 Chocolate Cone No low ~ Not organ~ 5.57 4
## 10 Individual 4 Raspberry Homemade waf~ Low fat Organic 4.2 4
## 11 Individual 5 Strawberry Cone Low fat Not organ~ 4.93 4
## 12 Individual 6 Raspberry Homemade waf~ Low fat Organic 9.40 4
## 13 Individual 7 Strawberry Cone Low fat Not organ~ 9.17 4
## 14 Individual 8 Chocolate Cone No low ~ Not organ~ 4.93 4
## 15 Individual 9 Strawberry Cone Low fat Not organ~ 7.87 4We can now estimate the market share:
market_share <- highest_rated %>%
group_by(Flavor, Packaging, Light, Organic) %>%
summarize(count = n()) %>%
arrange(desc(count))## `summarise()` regrouping output by 'Flavor', 'Packaging', 'Light' (override with `.groups` argument)## # A tibble: 4 x 5
## # Groups: Flavor, Packaging, Light [4]
## Flavor Packaging Light Organic count
## <fct> <fct> <fct> <fct> <int>
## 1 Strawberry Cone Low fat Not organic 7
## 2 Raspberry Homemade waffle No low fat Not organic 4
## 3 Chocolate Cone No low fat Not organic 2
## 4 Raspberry Homemade waffle Low fat Organic 2We see that the strawberry, cone, low fat, not organic ice cream is favored by 7 out of 15 respondents, the raspberry, homemade waffle, no low fat, not organic ice cream is favored by 4 out of 15 respondents, and so on.