Notes

How to Build a Model? - Modelling Marketing Phenomena - What is Marketing?

What do managers do? Marketing Actions:

• Product Introductions.
• Pricing.
• Distribution Channels.
• Advertising and Other Promotion Activities.

How do consumers respond? Consumer responses:

• Choice (When, What, Where, How much, etc.)
• Loyalty and Satisfaction
• WOM (Positive vs Negative)

What is a Model? A simplified representation of a system or phenomenon, as in the sciences or economics, with any hypotheses required to describe the system or explain the phenomenon, often mathematically.

"A representation of the most important elements of a perceived real-world system".

• Real-World System
  • Real phenomenon
  • Managers' decision
  • Consumer behaviors
• Perceived
  • Model building is a subjective process
  • Different models for the same phenomenon
• Most important elements
  • Real world (e.g., consumer behavior) is too complex to model
  • Ceteris paribus, the simpler the better.
• Representation
  • Text, symbols, graphics, etc.
  • Ceteris paribus, the simpler the better

"All models are wrong. Some are useful" - George E. P. Box.

Challenges in Modelling Marketing Phenomena

• Who buy the product/service?
  • Heterogenous consumers Aggregation from individual responses
• Only one action?
  • No! (price, ad, product, etc.) Marketing mix interaction
• Only us?
  • No! Competitive reaction
• Immediate response?
  • No! Delayed response
• Only one region?
  • No! Multiple territories

Why Do We Need a Model?

• Better understanding on the relationship between actions (e.g., price promotion) and results (e.g., brand sales).
• Quicker but better decision (e.g., price promotion advertising).
• Finding new problems (e.g., price vs sales vs ads).
• Wiser & wider usage of existing data: Data tell you the answer to the question.
• Justifying more data collection.

The Model Building Process

• Why?
  • Explain or measure something?
  • Forecasting?
  • Finding Optimal Solutions?
  • Proving theory?

• What?

  • What do we want to explain? (i.e., dependent variable).
  • What provides the explanation? (i.e., explanatory or independent variables).
  • Any hypothesis?
  • What are the data?

• How?

  • How do we represent the real world? (i.e., specification)
    • Elements
    • Relationship
  • How do we find the parameter? (i.e., estimation or solution)

• Valid?

  • Consistent with theoretical expectation or well-known facts?
  • Useful?
  • Simple enough? (i.e. parsimony)
  • Accurate?
  • Robust?

Example: Sales vs Advertising

• Goal setting: to understand the relationship between the amount of advertising and sales quantity.
• Model Elements
  • Dependent Variable?
  • Independent Variables?
  • Data?
• How? Model Specification

Issues in Model Elements

• Measurement (i.e., variable operationalization)

  • How can we measure a marketing variable?
  • Aggregation: this is related with unit of analysis
    • Entity: buyer aggregation & product aggregation.
    • Temporal: weekly, monthly, quarterly, yearly.
    • Spatial: store, city, country, ...
  • Proxy for latent variables: scale development

• Measurement Scale

  • Metric variables (interval, ratio) vs. Categorical variables (nominal, ordinal)
  • Continuous (advertising spending) vs. Discrete variables (advertising frequency)

Dummy Variables "Sales are generally higher in Christmas season".

What can the subscript j mean here? Issues in Mathematical Relationship

• Linearity? Or Non-Linear Relationship?
• An error term
  • Given the assumption of regression, an error term should be random.
  • Researchers generally impose a distributional assumption on the error term (e.g., normal distribution).
• Heterogeneity

Advertising and Sales

• How would be the relationship between advertising (frequency) and sales?

• 

• Validation: the extent to which the model is valid

  • Check on assumptions
  • Face validity
  • Alternative model specification: performance vs. parsimony
    • Simpler model?
    • More sophisticated and complex model?
  • Alternative estimation methods
  • Alternative variable operationalization
  • Predictive accuracy
    • In sample
    • Out of sample (data split)

Overview of Regression Regression: Intuition

Regression: Equation & Regression: Alpha and Beta

Regression: Simple and Multiple

Regression: Terminology

Why Multiple Regression?

• We want to test the effect of multiple variables at the same time.
• E.g., sales as a function of price and advertising or other marketing actions.
• If we omit price, the effect of advertising is not clean (omitted variable bias).

Which IVs Should We Include?

• Use theory and intuition.
• Do not just include all variables in your dataset!
• You may use stepwise regression: this is more empirical approach as opposed to theoretical approach (For exploratory research!)

Regression: Model Fit and R2

• The R^2^ indicates the proportion of variance in the dependent variable that is explained by the independent variables.
• R^2^ varies between 0 and 1
  • 0: 0% of the variance is explained
  • 1: 100% of the variance is explained
• Definition of "good R^2^" heavily depends on context!

Regression: R^2^ and the Number of Variables

• If we add a variable, the R2 will always increase or stay the same.
• Hence, if we compare the following two models,

the second model will always "win" (i.e., higher R2).

Regression: Adjusted R^2^

• However, we would like to keep our model as compact as possible
  • Based on the R^2^, the model would keep on growing!
• We use the adjusted R^2^ which gives a penalty for using an additional variable.
  • Only when the better fit outweighs the "cost" of having an additional coefficient, the adjusted R^2^ will increase.

Regression: Coefficient Significance

• To assess coefficient significance, we look at the t-test and p-value.
• T-value = coefficient / standard error
• P-value < 0.05 then the coefficient is significant!

Regression: Coefficient Interpretation

• Only interpret if significant

• If price goes up with 1 unit, sales change with $\beta_{1}$units.
• If advertising goes up with 1 unit, sales change with $\beta_{2}$ units.
• Expected Signs? Positive or Negative?

Regression: Fitted Values

• We can use the regression model

• To calculate fitted values:

• We can compare the fitted values to the observed values.

Scenarios and Forecasting

• More importantly, we can use the model to run scenarios
• Given a price and advertising level, what would sales be?
• We can also predict the future, predict other brands, other respondents, etc.
• Very important in practice!

Association vs Causation

• Be careful of interpreting regression coefficients as causal relationship.
• Regression is based on association between variables.
• Then for causality?

Regression Application in Marketing - What Other Cases?

• Sales and Marketing Actions.
• Customer Satisfaction/Loyalty and its drivers.
• Consumer choice and its determinants.