Product Attributes

UCSD MGT 100 Week 03

Kenneth C. Wilbur and Dan Yavorsky

Let’s reflect

Market Mapping

  • Positioning in attribute space
  • Economic theories of differentiation: Vertical, horizontal
  • Perceptual maps

Marketing strategy

  • Segmentation: How do customers differ

  • Targeting: Which segments do we seek to attract and serve

  • Positioning

        - What value proposition do we present
        - How do our product's objective attributes compare to competitors
        - Where do customers perceive us to be
        - How do we want to influence consumer perceptions          
  • Market mapping helps with Positioning

Market Maps

  • Market maps use customer data to depict competitive situations. Why?

      - Understand brand/product positions in the market
      - Track changes
      - Identify new products or features to develop
      - Understand competitor imitation/differentiation decisions
      - Evaluate results of recent tactics
      - Cross-selling, advertising, identifying complements or substitutes, bundles...

Market maps

  • We often lack ground truth data

        - Using a single map to set strategy is risky
  • Repeated mapping builds confidence
    (“Movies, not pictures”)

  • Many large brands do this regularly

Vertical Diff., AKA quality

  • Product attributes where more is better, all else constant
    • Efficacy, e.g. CPU speed or horsepower
    • Efficiency, e.g. power consumption
    • Input good quality (e.g. clothes, food)
  • Important: not everyone buys the better option (why not?)

Horizontal Diff., AKA fit or match

  • Product attributes w heterogeneous valuations
    • Physical location
    • Familiarity, e.g. what you grew up with
    • Taste, e.g. sweetness or umami
    • Brand image, e.g. Tide, Jif, Coca-Cola
    • Complements, e.g. headphones or charging cables

Hotelling (1929)

Ice cream vendors

Median voter theorem

  • Suppose you are the UCSD Chancellor

  • You want to know how much each UC Campus competes with you for California freshman applicants

  • You posit that selectivity and time-to-degree matter most

        - Students want to connect with smart students
        - Students want to graduate on time

What if there are too many product attributes to graph?

  • Enter Principal Components Analysis

        - Powerful way to summarize data 
        - Projects high-dimensional data into a lower dimensional space 
        - Designed to minimize information loss during compression
        - Pearson (1901) invented; Hotelling rediscovered (1933 & 36)

Principal Components Analysis (PCA)

  1. For \(J\) products with \(K<J\) continuous attributes,
    we have \(X\), a \(J\times K\) matrix

  2. Consider this a \(K\)-dimensional space containing \(J\) points

  3. Calculate \(X'X\), a \(K \times K\) covariance matrix of the attributes

  4. 1st \(x\) eigenvectors of the attribute covariance matrix give unit vectors to map products in \(x\)-dimensional space

       - We'll use first 1 or 2 eigenvectors for visualization


  1. How do I interpret the principal components?

       - Each principal component is a linear combination of the larger space's axes
       - Principal components are the "new axes" for the newly-compressed space
       - Principal components are always orthogonal to each other, by construction
  2. What are the main assumptions of PCA?

       - Variables are continuous and linearly related
       - Principal components that explain the most variation matter most
       - Drawbacks: information loss, reduced spatial interpretability, outlier sensitivity
  3. How do I choose the # of principal components?

       - Business criteria: 1 or 2 if you want to visualize the data
       - Business criteria: Or, value of compressed data in subsequent operations 
       - Statistical criteria: Cume variance explained, scree plot, eigenvalue > 1
  4. What are some similar tools to PCA?

       - Factor analysis, linear discriminant analysis, independent component analysis... 

How does PCA relate to K-means?

  • K-Means identifies clusters within a dataset

        - K-Means augments a dataset by identifying similarities within it
        - K-Means never discards data
  • PCA combines data dimensions to condense data with minimal information loss

        - PCA is designed to optimally reduce data dimensionality
        - PCA facilitates visual interpretation but does not identify similarities 
  • Both are unsupervised ML algos

       - Both have "tuning parameters" (e.g. # segments, # principal components)
       - They serve different purposes & can be used together
       - E.g. run PCA to first compress large data, then K-Means to group points
       - Or, K-Means to identify clusters, then PCA to visualize them in 2D space

Conceptual organization

Mapping Practicalities

  1. How to measure intangible attributes like trust?

       - Ask consumers, e.g. "How much do you trust this brand?"
       - Marketing Research exists to measure subjective attributes and perceptions
  2. What if we don’t know, or can’t measure, the most important attributes?

       - Multidimensional scaling
  3. How should we weigh attributes?

Do we know the most important attributes?

  • Multidimensional scaling draws perceptual maps
  1. Suppose you can measure product similarity

  2. For \(J\) products, populate the \(J\times J\) matrix of similarity scores

       - With J brands, we have J points in J dimensions. Each dimension j indicates similarity to brand j. PCA can projects J dimensions into 2D for plotting
  3. Use PCA to reduce to a lower-dimensional space

       - Pro: We don't need to predefine attributes
       - Con: Axes can be hard to interpret

Multidimensional scaling

MDS Intuition, in 2D space

      - With a ruler and map, measure distances between 20 US cities ("similarity")
      - Record distances in a 20x20 matrix: PCA into 2D should recreate the map
      - But, we don't usually know the map we are recreating, so we look for ground-truth comparisons to indicate credibility and reliability


      - Poli Sci: Which political candidate positioning, eg left to right
      - Psychologists: understand perceptions and evaluation of personality traits
      - Marketers: how consumers perceive brands or perceive product attributes

Example: Netzer et al. (2012)

How to weigh product attributes?

  • Demand modeling uses product attributes and prices to explain customer purchases

  • Heterogeneous demand modeling uses product attributes, prices and customer attributes to explain purchases

          - "Revealed preferences": Demand models explain observed choices in uncontrolled market environments
  • Related: Conjoint analysis estimates attribute weights in simulated choice environments

          - "Stated preferences": Conjoint explain hypothetical choice data in controlled experiments

Text data

  • The Challenge
  • Embeddings
  • LLMs: What are they doing
  • What does it all mean?

The Challenge

  • Suppose an English speaker knows \(n\) words, say \(n=10,000\)

  • How many unique strings of \(N\) words can they generate?

        - N=1: 10,000
        - N=2: 10,000^2=100,000,000
        - N=3: 10,000^3=1,000,000,000,000=1 Trillion
        - N=4: 10,000^4=10^16
        - N=5: 10,000^5=10^20
        - N=6: 10,000^5=10^24=1 Trillion Trillions
        - ....
  • Why do we make kids learn proper grammar?

        - Average formal written English sentence is ~15 words


  • represent words as vectors in high-dim space

        - Really, "tokens," but assume words==tokens for simplicity
  • Assume \(W\) words, \(A<W\) abstract concepts

        - Assume we have all text data from all history. Each sentence is a point in $W$-dimensional space
  • We could run PCA to reduce from \(W\) to \(A\) dimensions

        - Assume we have infinite computing resources
        - We now have every sentence represented as a point in continuous A-space

Cool things about embeddings

  • Compression stores enormous textual data in a small space, other than human memory
  • We can do math using words!

Many ways to encode embeddings

LLMs: Given a prompt,

  1. Recode prompt to maximize contextual understanding

       - E.g. 'the bank of the river is steep' vs 'the bank near the river is solvent'
       - This step is the 'attention' step you hear a lot about
       - Basically, modify every word's location depending on every other word's position in the prompt sequence
  2. Feed recoded prompt into transformer as a sequence of points in concept-space

  3. Predict the next point and add it to the sequence

  4. Repeat step 3 until no more good predictions

  5. Repeat steps 1-4 many many times, then hire humans to evaluate results, use evaluations for RLHF to refine the process

  6. Sell access to customers

        - Use the money to train a bigger LLM

Example: Concept Space

Example: Sentences as Vector Sequences

What LLMs Can and Can’t Do

  • Can generate intelligible semantic sequences

  • Can help humans save time and effort in semantic tasks

  • Can uncover previously unknown relations in training data

  • Can enable semantic analysis of product review corpuses to understand customer perceptions, evaluations and satisfaction

  • Can’t distinguish truth from frequency in training data

        - Need a conceptual model of the world for this
        - LLMs propagate popular biases in training data, unless taught otherwise
  • Can’t reliably evaluate previously-unknown relationships in training data

        - At least, not by themselves, or not yet; but maybe soon
  • Can’t discover new relationships that are not present in training data

        - At least, not by themselves, or not yet; but maybe soon
  • Can’t think, reason, imagine, feel, want, question

        - But might complement other components that do these things

What happens next?

  • Truly, no one knows yet. The tech is far ahead of science

        - LLMs are productive combinations of existing components
        - This has happened before: stats/ML theory chases applications 
        - Spellchecker and calculator are wrong long-term analogies
  • My guesses

        - "It's easy to predict everything, except for the future."
        - Simple tasks: LLMs outcompete humans 
        - Medium-complexity tasks: LLMs help low-skill humans compete 
        - Complex tasks: Skillful LLM use requires highly skilled humans
        - Law matters a LOT: Personal liability, copyright, privacy, disclosure
        - In eqm, typical quality should rise; *not* using LLMs will handicap
        - Long term: More automation, more products, more concentration of capital 
        - More word math techniques will be invented, some will be useful
  • What future new technologies might complement LLMs?

        - Argument about Sentient AI comes down to this
        - Robots? World models? Causal reasoning engines? Volition? 

  • How have you seen LLMs affect the world over the past year?

Conjoint Analysis

  • Generate consumer choice data, analyze it to

    • Use a supervised choice model to map the market
    • choose locations in attribute space
    • predict sales and profits

Choosing Product Attributes

  • Until now, we studied existing product attributes

    • What about choosing new product attribute levels?
    • Or what about introducing new attributes?
  • Enter conjoint analysis:
    Survey and model to estimate attribute utilities

  • Probably the most popular quant marketing framework

      - Autos, phones, hardware, durables
      - Travel, hospitality, entertainment
      - Professional services, transportation
      - Consumer package goods
  • Combines well with cost data to select optimal attributes

How to do conjoint analysis

  1. Identify \(K\) product attributes and levels/values \(x_k\)

  2. Hire consumers to make choices

  3. Sample from product space, record consumer choices

  4. Specify model, i.e. \(U_j=\sum_{k}x_{jk}\beta_k-\alpha p_j+\epsilon_j\)
    and \(P_j=\frac{\sum_{k}x_{jk}\beta_k-\alpha_k p_j}{\sum_l\sum_{k}x_{lk}\beta_k-\alpha p_l}\)

       - Beware: p is price , P is choice probability or market share
  5. Calibrate choice model to estimate attribute utilities

  6. Combine estimated model with cost data to choose product locations and predict outcomes

Trucks Example

Phones/Service Plans Example

Case study: UberPOOL

  • In 2013, Uber hypothesized

    - some riders would wait and walk for lower price
    - some riders would trade pre-trip predictability for lower price
    - shared ridership could ↓ average price and ↑ quantity
    - more efficient use of drivers, cars, roads, fuel

Business case was clear! But …

  • Shared rides were new for Uber

          - Rider/driver matching algo could reflect various tradeoffs            
          - POOL reduces routing and timing predictability 
  • Uber had little experience with price-sensitive segments

          - What price tradeoffs would incentivize new behaviors?
          - How much would POOL expand Uber usage vs cannibalize other services?
  • Coordination costs were unknown

          - "I will never take POOL when I need to be somewhere at a specific time"
          - Would riders wait at designated pickup points?
          - How would comunicating costs upfront affect rider behavior?
  • So, Uber used market research to design UberPOOL


  1. 23 in-home diverse interviews in Chicago and DC

       - Interviewed {prospective, new, exp.} riders to (1) map rider's regular travel, (2) explore decision factors and criteria, (3) a ride-along for context
       - Findings identified 6 attributes for testing
  2. Online Maximum Differentiation Survey

       - Selected participants based on city, Uber experience & product; N=3k, 22min

Maxdiff results

Conjoint Design

Conjoint Sample Question

Conjoint Model

Conjoint Findings

Product Redesign

Business Results

More Products

Conjoint: Limitations, Workarounds

  • We may fail to consider most important attributes or levels

      - But we can consult with experts beforehand and ask participants during
  • Additive utility model may miss interactions or other nonlinearities

      - But this is testable & can be specified in the utility model
  • Exploring a large attribute space gets expensive

      - But we can prioritize attributes and use efficient, adaptive sampling algorithms
  • Assumes accurate hypothetical choices based on attributes

      - But we can train consumers how to mimic more organic choices 
  • Participants may not represent the market

      - But we can measure & debias some dimensions of selection 
  • Choice setting may not represent typical purchase contexts

      - But we can model the retail channel and vary # of competing products
  • Participant fatigue or inattention

      - But we can incentivize them and check for preference reversals
  • Consumer preferences evolve

      - But we can repeat our conjoints regularly to gauge durability

Class script

  • Let’s use PCA to draw some product maps.

Wrapping up


  • Let’s take a look


  • Market maps use customer data to depict competitive situations

  • PCA projects high dimensional data into lower dimensional space w minimal information loss

  • Embeddings represent words as points in concept-space, enabling word-math

  • Conjoint analysis uses survey choice data to

        - map markets
        - estimate product attribute utilities
        - help design products as bundles of attributes
        - predict how location choice leads to revenues, profits

Going further