8.4 Many respondents

8.4.1 Estimate part-worths and importance weights

Now, let’s carry out the conjoint analysis on the full dataset to get an idea of which ice creams the 15 respondents, on average, liked the most and how important each attribute is:

conjoint_allrespondents <- conjoint(icecream, rvar = "rating", evar = c("Flavor","Packaging","Light","Organic")) # same as before, but different dataset.

summary(conjoint_allrespondents) 
## Conjoint analysis
## Data                 : icecream 
## Response variable    : rating 
## Explanatory variables: Flavor, Packaging, Light, Organic 
## 
## Conjoint part-worths:
##    Attributes          Levels     PW
##  Flavor       Chocolate        0.000
##  Flavor       Mango            1.522
##  Flavor       Raspberry        0.522
##  Flavor       Strawberry       0.767
##  Flavor       Vanilla          1.389
##  Packaging    Cone             0.000
##  Packaging    Homemade waffle -0.244
##  Packaging    Pint            -0.100
##  Light        Low fat          0.000
##  Light        No low fat       0.478
##  Organic      Not organic      0.000
##  Organic      Organic          0.307
##  Base utility ~                4.358
## 
## Conjoint importance weights:
##  Attributes    IW
##   Flavor    0.597
##   Packaging 0.096
##   Light     0.187
##   Organic   0.120
## 
## Conjoint regression results:
## 
##                            coefficient
##  (Intercept)                     4.358
##  Flavor|Mango                    1.522
##  Flavor|Raspberry                0.522
##  Flavor|Strawberry               0.767
##  Flavor|Vanilla                  1.389
##  Packaging|Homemade waffle      -0.244
##  Packaging|Pint                 -0.100
##  Light|No low fat                0.478
##  Organic|Organic                 0.307

Flavor is by far the most important attribute. Let’s plot these results:

plot(conjoint_allrespondents)

From this, we predict that, on average, people would most like an organic, non low fat, mango ice cream in a cone.

The importance weights tell us how strongly each attribute determines the average rating of an ice cream. Flavor is the most important attribute and packaging is the least important attribute. This respondent’s rating is determined for 59.7 percent by flavor and for 9.6 percent by packaging.

8.4.2 Profiles: predicted utilities

Let’s predict the ratings of all possible ice creams:

predict(conjoint_allrespondents, profiles.all) %>% # check previous sections for profiles.all
  arrange(desc(Prediction)) # show the ice creams with the highest predicted rating on top
##        Flavor       Packaging      Light     Organic Prediction
## 1       Mango            Cone No low fat     Organic   6.664444
## 2       Mango            Pint No low fat     Organic   6.564444
## 3     Vanilla            Cone No low fat     Organic   6.531111
## 4     Vanilla            Pint No low fat     Organic   6.431111
## 5       Mango Homemade waffle No low fat     Organic   6.420000
## 6       Mango            Cone No low fat Not organic   6.357778
## 7     Vanilla Homemade waffle No low fat     Organic   6.286667
## 8       Mango            Pint No low fat Not organic   6.257778
## 9     Vanilla            Cone No low fat Not organic   6.224444
## 10      Mango            Cone    Low fat     Organic   6.186667
## 11    Vanilla            Pint No low fat Not organic   6.124444
## 12      Mango Homemade waffle No low fat Not organic   6.113333
## 13      Mango            Pint    Low fat     Organic   6.086667
## 14    Vanilla            Cone    Low fat     Organic   6.053333
## 15    Vanilla Homemade waffle No low fat Not organic   5.980000
## 16    Vanilla            Pint    Low fat     Organic   5.953333
## 17      Mango Homemade waffle    Low fat     Organic   5.942222
## 18 Strawberry            Cone No low fat     Organic   5.908889
## 19      Mango            Cone    Low fat Not organic   5.880000
## 20    Vanilla Homemade waffle    Low fat     Organic   5.808889
## 21 Strawberry            Pint No low fat     Organic   5.808889
## 22      Mango            Pint    Low fat Not organic   5.780000
## 23    Vanilla            Cone    Low fat Not organic   5.746667
## 24  Raspberry            Cone No low fat     Organic   5.664444
## 25 Strawberry Homemade waffle No low fat     Organic   5.664444
## 26    Vanilla            Pint    Low fat Not organic   5.646667
## 27      Mango Homemade waffle    Low fat Not organic   5.635556
## 28 Strawberry            Cone No low fat Not organic   5.602222
## 29  Raspberry            Pint No low fat     Organic   5.564444
## 30    Vanilla Homemade waffle    Low fat Not organic   5.502222
## 31 Strawberry            Pint No low fat Not organic   5.502222
## 32 Strawberry            Cone    Low fat     Organic   5.431111
## 33  Raspberry Homemade waffle No low fat     Organic   5.420000
## 34  Raspberry            Cone No low fat Not organic   5.357778
## 35 Strawberry Homemade waffle No low fat Not organic   5.357778
## 36 Strawberry            Pint    Low fat     Organic   5.331111
## 37  Raspberry            Pint No low fat Not organic   5.257778
## 38  Raspberry            Cone    Low fat     Organic   5.186667
## 39 Strawberry Homemade waffle    Low fat     Organic   5.186667
## 40  Chocolate            Cone No low fat     Organic   5.142222
## 41 Strawberry            Cone    Low fat Not organic   5.124444
## 42  Raspberry Homemade waffle No low fat Not organic   5.113333
## 43  Raspberry            Pint    Low fat     Organic   5.086667
## 44  Chocolate            Pint No low fat     Organic   5.042222
## 45 Strawberry            Pint    Low fat Not organic   5.024444
## 46  Raspberry Homemade waffle    Low fat     Organic   4.942222
## 47  Chocolate Homemade waffle No low fat     Organic   4.897778
## 48  Raspberry            Cone    Low fat Not organic   4.880000
## 49 Strawberry Homemade waffle    Low fat Not organic   4.880000
## 50  Chocolate            Cone No low fat Not organic   4.835556
## 51  Raspberry            Pint    Low fat Not organic   4.780000
## 52  Chocolate            Pint No low fat Not organic   4.735556
## 53  Chocolate            Cone    Low fat     Organic   4.664444
## 54  Raspberry Homemade waffle    Low fat Not organic   4.635556
## 55  Chocolate Homemade waffle No low fat Not organic   4.591111
## 56  Chocolate            Pint    Low fat     Organic   4.564444
## 57  Chocolate Homemade waffle    Low fat     Organic   4.420000
## 58  Chocolate            Cone    Low fat Not organic   4.357778
## 59  Chocolate            Pint    Low fat Not organic   4.257778
## 60  Chocolate Homemade waffle    Low fat Not organic   4.113333

Same conclusions as before: we predict that, on average, people would most like an organic, non low fat, mango ice cream in a cone.