27 Preference Measurement
Reservation price = price a consumer willing to pay for a product
Estimation for reservation price:
- Survey question direct asks for consumer reservation price (but this estimation method tends to bias downward because participants don’t want people to know that they are price sensitive).
- From the coefficients of conjoint analysis.
Assumptions to get consumer utility from regression:
- Consumption utility equals sum of utilities for the product product attributes
Let \(N\) be the number of non-price attributes and each attributes has more than 1 level.
We use fractional factorial design to derive different profiles for consumers to choose with the goal of least number of profiles.
Then the utility function can be represented as
\[ U = \beta_0 + \beta_p \times P + \sum_{k=1}^N \beta_k \times A_k + \epsilon \]
where
\(U\) = consumer rating or utility
\(\beta\)’s = utility weights
\(\beta_0\) = heterogeneity in the range of the ratings scale per consumer.
\(P\) = price
\(A\) = non-price attributes (categorical variables)
Then the reservation price (at the individual level) for product \(P\) is
\[ r(P) = \frac{\Delta p}{\beta_p} (\sum_{k=1}^N \frac{\beta_k}{\Delta A_k} A_k) \]
where
\(\Delta p\) = difference in price between two levels (of the same attribute)
\(\Delta A_k\) = difference in attribute levels
and the dollar value for each unit of utility is
\[ \frac{\Delta p}{\beta_p} \]
and for each attribute \(k\), the utility a consumer can derive is
\[ (\frac{\beta_k}{\Delta A_k}) A_k \]
Hence, we can see that the reservation price for a product (i.e., total dollar value a consumer assigns on product \(P\)) is just the sum of utility across all attributes times dollar value for each unit of utility
Netzer et al. (2008)
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Problem
Companies: Product development, pricing segmentation, positioning, advertising, project selection, and investment decisions
Consumers: recommendation agents
Policy makers and health care professionals:
Academic researchers;
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Design and Data collection
Original goals: maximizing A-efficiency and D-efficiency (based on covariance matrix of the estimates of the partworths)
New: M-efficiency measure (accounts for managers’ considerations).
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New Adaptive method for data collection:
- Commercially available: Adaption conjoint analysis (ACA), Fast Polyhedral approach, Adaptive Self-explicated approach
Model Specification, Estimation, and Action
27.1 Conjoint Analysis
also known as conjoint measurements, which stems from mathematical psychology and psychometrics
Aims:
Willingness to pay: measure what individual are willing to give up to obtain certain product benefits
Distribution of willing to pay : measure how consumer differ
Advantages:
Improves ability to assess customers’ true wants and needs (especially price)
Dissect “everything is important”
Perception vs. preference
Perception (beliefs about the market) is largely homogeneous across customers
Preference (what product they buy) is heterogeneous across customers.
Conjoint analysis is a tool for preference assessment.
Attributes in conjoint:
Not too many attributes
Attributes should be actionable
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Need to choose reasonable range of attributes
within range under consideration
All levels should be feasible
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Number of attribute levels
Too many can be confusing
Halo effect of number of attributes (or the order of levels)
Number of profiles equal number of dummy variables with the assumption of independence
If you suspect that there might be interaction effect (violation of independence), you can either
use higher-level attribute
increase the number of profiles
Ranking and Rating conjoint analysis are not different Kalish and Nelson (1991)
Basics:
Use orthogonal array (in experimental design) to test combinations where independent contributions of all factors (attributes) are balanced.
Then rank all the reduced combinations in order
Uses:
New product development
Package design
Pricing and brand alternatives
Descriptions of new products or services
Alternative service design
Also organizations as consumers
Outcome variable can be:
Preference
Likelihood to purchase
best value for the money
Convenience of use
Suitability for a specific job
Psychological images (e.g., ruggedness, distinctiveness, conservativeness)
Can be used in conjunction with
factor analysis: firm-level decision variables (attribute/factor), dimension reduction technique
perceptual mapping: multidimensional scaling
cluster analysis: customer-level variables, segmentation technique
Suggested packages (in order of preference):
AlgDesignconjointfaisalconjointmlogitconf.designprefmod
27.1.1 Full-Profile
##
## Call:
## lm(formula = frml)
##
## Residuals:
## 1 2 3 4 5 6 7 8 9 10
## 1.1345 -1.4897 0.3103 -0.2655 0.3103 0.1931 1.5931 -1.4310 -1.4310 1.1207
## 11 12 13
## 0.3690 1.1931 -1.6069
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.3937 0.5439 6.240 0.00155 **
## factor(x$price)1 -1.5172 0.7944 -1.910 0.11440
## factor(x$price)2 -1.1414 0.6889 -1.657 0.15844
## factor(x$variety)1 -0.4747 0.6889 -0.689 0.52141
## factor(x$variety)2 -0.6747 0.6889 -0.979 0.37234
## factor(x$kind)1 0.6586 0.6889 0.956 0.38293
## factor(x$kind)2 -1.5172 0.7944 -1.910 0.11440
## factor(x$aroma)1 0.6293 0.5093 1.236 0.27150
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.78 on 5 degrees of freedom
## Multiple R-squared: 0.8184, Adjusted R-squared: 0.5642
## F-statistic: 3.22 on 7 and 5 DF, p-value: 0.108227.1.4 Hybrid
- Combination of Full-Profile and Adaptive
27.1.8 Application
library(conjoint)
Experiment = expand.grid(weight = c("a","b"),
Price = c("Low","High"),
Warranty = c("2","3"),
Battery = c("10","20"))
partial_design = caFactorialDesign(Experiment,type = "orthogonal",seed = 123)
partial_profile = caEncodedDesign(partial_design)
levels <- c("a","b","Low","High","2","3","10","20")
lev.df <- data.frame(levels)
data = c("")Example by Martin Muller
# Declaration of features and feature values
feature_names <- c("LENGTH", "ILLUSTRATION", "CLAPS")
feature_values <- list()
feature_values[[1]] <- c("2min", "7min", "20min")
feature_values[[2]] <- c("several images", "one image", "no image")
feature_values[[3]] <- c("+500 claps", "less than 500 claps")
# All concept generation
articles <- expand.grid(LENGTH = feature_values[[1]],
ILLUSTRATION = feature_values[[2]],
CLAPS = feature_values[[3]])
library (conjoint)
maxNumberOfArticles = 8
# Selection of relevant concepts
selectedArticles <- caFactorialDesign(data = articles,
type = 'fractional',
cards = maxNumberOfArticles)
# Checking if selected concepts are relevant for study
corrSelectedArticles <- caEncodedDesign(selectedArticles)
#print(cor(corr_design_mails))
print(cor(corrSelectedArticles))## LENGTH ILLUSTRATION CLAPS
## LENGTH 1.0000000 0 0.1240347
## ILLUSTRATION 0.0000000 1 0.0000000
## CLAPS 0.1240347 0 1.0000000
# List of rates of each article allowing to compare them
ranking = c(7 / 7, 3 / 7, 3 / 7, 5 / 7, 2 / 7, 6 / 7, 3 / 7, 0 / 7)
# Performing conjoint analysis
Conjoint(ranking, selectedArticles, unlist(feature_values))##
## Call:
## lm(formula = frml)
##
## Residuals:
## 1 2 3 4 5 6 7 8
## -0,03401 -0,02041 0,07483 0,10884 -0,12925 0,05442 -0,07483 0,02041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0,44898 0,05651 7,945 0,0155 *
## factor(x$LENGTH)1 0,25850 0,07534 3,431 0,0755 .
## factor(x$LENGTH)2 0,06803 0,07534 0,903 0,4619
## factor(x$ILLUSTRATION)1 0,30612 0,07534 4,063 0,0556 .
## factor(x$ILLUSTRATION)2 -0,18367 0,08835 -2,079 0,1732
## factor(x$CLAPS)1 0,02041 0,05651 0,361 0,7526
## ---
## Signif. codes: 0 '***' 0,001 '**' 0,01 '*' 0,05 '.' 0,1 ' ' 1
##
## Residual standard error: 0,1495 on 2 degrees of freedom
## Multiple R-squared: 0,9389, Adjusted R-squared: 0,7863
## F-statistic: 6,151 on 5 and 2 DF, p-value: 0,1457## [1] "Part worths (utilities) of levels (model parameters for whole sample):"
## levnms utls
## 1 intercept 0,449
## 2 2min 0,2585
## 3 7min 0,068
## 4 20min -0,3265
## 5 several images 0,3061
## 6 one image -0,1837
## 7 no image -0,1224
## 8 +500 claps 0,0204
## 9 less than 500 claps -0,0204
## [1] "Average importance of factors (attributes):"
## [1] 52,44 43,90 3,66
## [1] Sum of average importance: 100
## [1] "Chart of average factors importance"