Marketing Research Methods | Chen Xing

Notes on Unobserved Heterogeneity

Wed, 28 May 2025 00:00:00 +0000

In quantitative marketing, unobserved heterogeneity refers to differences in consumer response parameters that cannot be explained by observed demographics or past behavior. Modeling this form of heterogeneity is crucial for uncovering true segmentation, avoiding bias from aggregation, and capturing variation in decision rules across consumers.

I recommend to review Rossi and Allenby (2003) paper first to get a big picture.

1. Latent-Class (Finite Mixture) Models

Motivation & Intuition

Consumers naturally cluster into a finite number of segments, each with its own set of brand-choice parameters (e.g., price sensitivity, loyalty effects).
Rather than forcing all consumers into a single “average” model, a latent-class approach lets the data “discover” these segments.

Technical Details

Assume $S$ segments; for individual $h$ we observe choice history $Y_h$.
Segment membership is unobserved; let $\pi_s = \Pr(\text{segment}=s)$.
The likelihood for consumer $h$ is

$$ L_h=\sum_{s=1}^S \pi_s P\left(Y_h \mid \theta_s\right) $$

where $\theta_s$ are class-specific parameters (e.g., logit coefficients).
Parameters ${\pi_s,\theta_s}$ are estimated by maximum-likelihood via the EM algorithm.
Applications show latent classes revealing:
- Differences in brand loyalty and switching patterns (Grover & Srinivasan, 1987; Kamakura & Russell, 1989)
- Correcting spurious state-dependence by attributing inertia to heterogeneity rather than to true carryover effects .

2. Choice-Process Heterogeneity

Motivation & Intuition

Not only can parameters vary, but the decision rule itself may differ: some consumers use a simple logit, others a nested-logit (planning vs. impulse), some apply conjunctive screening rules, etc.
Capturing this heterogeneity helps explain why consumers respond differently under the same marketing stimuli.

Technical Details

Extend the latent-class framework so that each class $s$ has its own choice model form $f_s(\cdot)$ and parameters $\theta_s$.
Likelihood remains a mixture, but with varying functional forms across $s$.
Example: planners vs. non-planners found via nested-logit segments (Bucklin & Lattin, 1991); conjunctive/disjunctive screening via Bayesian mixtures (Gilbride & Allenby, 2004) .

3. Continuous (Random-Coefficients) Models

Motivation & Intuition

Rather than a few discrete segments, allow each consumer to have their own parameter vector drawn from a continuous distribution (e.g. multivariate normal).
This approach approximates an “infinite” mixture, capturing subtle, smooth variation across individuals.

Technical Details

For consumer $h$, coefficients $\beta_h$ are drawn from density $g(\beta\mid\mu,\Sigma)$.
The (aggregate) choice probability is

$$ P(i \mid X)=\int P(i \mid X, \beta) g(\beta \mid \mu, \Sigma) d \beta $$
Because this integral has no closed form, estimation uses:
- Maximum Simulated Likelihood (Train, 2003): draw $R$ samples ${\beta_h^{(r)}}$ and approximate the integral by averaging.
- Hierarchical Bayes / MCMC (Allenby & Rossi, 1999): embed ${\beta_h}$ in a Bayesian hierarchy and sample via Gibbs.
These models uncover individual-level sensitivities and allow richer counterfactual simulation .

Why It Matters

Bias Reduction: Ignoring unobserved heterogeneity can bias estimates of price elasticity, advertising effects, and promotion lift.
Targeting & Personalization: Knowing individual or segment-level parameters enables more precise targeting and budget allocation.
Behavioral Insights: Distinguishing between true state dependence and mere heterogeneity clarifies how loyalty and variety-seeking operate in the market.

Decision Checklist

Segmentation vs. Continuum?
- If you want a handful of clear segments → latent-class.
- If you need a full spectrum of individual differences → continuous.
Behavioral Rules?
- If process form itself may differ → choice-process heterogeneity.
Sample Size & Resources?
- Small/moderate sample, limited compute → latent-class.
- Large data, strong hardware, need fine granularity → random-coefficients.
Interpretability vs. Flexibility?
- Prioritize interpretability and simplicity → latent-class.
- Prioritize model realism and nuance → continuous (or hybrid latent-class + continuous).

Reference

Rossi, Peter E. and Greg M. Allenby (2003), “Bayesian Statistics and Marketing,” Marketing Science, 22 (3), 304–28.the history of marketing science

Winer, R. S., & Neslin, S. A. (2023). History Of Marketing Science, The (Second Edition). World Scientific.

Enhancing Statistical Power In Marketing Experiments — A Practical Implementation Guide

Mon, 05 May 2025 00:00:00 +0000

1. Introduction

This guide provides practical techniques for increasing the statistical power of marketing experiments without relying solely on large sample sizes. Based on Meyvis and van Osselaer’s work (2018), these methods enable researchers to detect subtle marketing effects with feasible sample sizes by increasing observed effect sizes through proper design and analysis decisions.

2. Essential Tools And Resources

Required Tools:

Statistical software (R, SPSS, Stata)
Survey platforms (Qualtrics, SurveyMonkey)
Pre-registration platforms (OSF, AsPredicted.org)
Data visualization tools

Required Planning Elements:

Clearly defined hypotheses
Detailed experimental designs
Predetermined analysis plans
Transparency protocols

3. Pre-Study Protocol

Pre-Registration Process:

Define your research question with specificity
Develop theory-based, testable hypotheses
Determine all analyses before data collection
Establish participant exclusion criteria
Justify sample size using power analysis
Document all decisions on a pre-registration platform

Key Implementation Step: Create a comprehensive pre-registration document that includes all exclusion criteria, covariates, and analysis plans before collecting any data.

4. Experimental Design Techniques

4.1 Within-Subjects Design Implementation:

Have each participant experience all experimental conditions
Counterbalance condition order systematically
Include buffer tasks between conditions to reduce carryover
Vary stimuli on multiple dimensions to reduce demand effects
Include checks for hypothesis guessing when manipulation is obvious

Application Criteria: Most effective when sample availability is limited and individual differences are substantial.

4.2 Covariate Implementation:

Identify variables with strong expected correlation to your DV (r > .2)
Measure covariates before introducing your manipulation
Use different measurement scales for covariates and DVs
Test for treatment-by-covariate interactions
Only include covariates that meet all statistical assumptions

Critical Requirements:

Manipulation must not affect the covariate
Covariate must not interact with the treatment
Measurement of covariate should not influence DV response

4.3 Manipulation Optimization:

Design direct rather than indirect manipulations
Create clean manipulations that avoid confounds
Use pre-tests to calibrate manipulation strength
Include manipulation checks in study design
Select manipulation levels where marginal effects are strongest

Implementation Note: Balance manipulation strength against potential demand effects.

5. Participant Management

5.1 Quality Control Procedures:

Implement Instructional Manipulation Checks (IMCs)
Monitor response times for unusually fast completion
Apply consistent exclusion criteria across all studies
Document all exclusions transparently
Complete all exclusions before hypothesis testing

Application Protocol: Define exclusion criteria explicitly in pre-registration and never deviate based on results.

5.2 Participant Selection Optimization:

Define relevant participant characteristics
Screen participants before the main study
Create more homogeneous participant groups
Consider targeted recruitment for higher relevance
Balance specificity against generalizability concerns

Implementation Strategy: Target participants for whom stimuli are relevant but avoid introducing selection biases.

6. Analytical Techniques

6.1 Planned Contrast Implementation:

Specify expected pattern of means before data collection
Develop contrast codes that directly test hypotheses
Use focused tests instead of omnibus tests
Test residual variance to confirm pattern specificity
Apply consistent analysis approaches across studies

Application Benefit: Increases power by testing only the specific pattern of interest.

6.2 Interaction Analysis Protocol:

Select moderators based on theoretical mechanisms
Avoid “meaningless moderation” that creates ceiling effects
Increase sample size appropriately for interaction tests (4x main effect sample)
Report simple effects to clarify interaction patterns
Interpret moderation in relation to underlying theory

Implementation Warning: Never test moderators post-hoc without theoretical justification.

7. Avoiding Methodological Pitfalls

Common Malpractice Warning Signs:

Analyzing data before collection is complete
Testing multiple exclusion criteria selectively
Adding covariates post-hoc based on results
Optional stopping when results become significant

Prevention Protocol:

Establish all analytical decisions before data collection
Apply criteria consistently across all studies
Report all analyses conducted, significant or not
Maintain a detailed research log for all decisions
Conduct confirmatory replications for important findings

8. Power Enhancement Techniques Summary

Measurement Optimization:

Implement multi-item scales rather than single items
Verify reliability (α > .8) before deployment
Select measures with appropriate sensitivity

Error Variance Reduction:

Standardize experimental environment
Create consistent procedural instructions
Implement computerized timing when possible

Stimuli Optimization:

Select stimuli with sufficient room for movement (avoid floor/ceiling)
Match stimuli appropriately to participant demographics
Conduct pilot tests to assess malleability

Data Quality Control:

Remove problematic data points using predetermined criteria
Apply appropriate transformations for skewed distributions
Document all data processing steps transparently

9. Replication Protocol

Implementation Steps:

Reproduce original study with minimal modifications
Apply identical exclusion criteria and analyses
Compare effect sizes between original and replication
If confirmed, extend with additional conditions
If unsuccessful, systematically examine methodological differences

Strategic Application: Use replications to validate effects and build cumulative knowledge.

10. Effect Size Reference Guide

Effect Size Type	Small	Medium	Large
Cohen’s d	0.2	0.5	0.8
η²	.01	.06	.15
R²	.01	.09	.25

Sample Size Required for 80% Power (Two-tailed, $ \alpha = .05$)

Effect Size (d)	Between-Subjects	Within-Subjects (r=.5)
0.2 (Small)	394 per group	199 total
0.5 (Medium)	64 per group	33 total
0.8 (Large)	26 per group	14 total

Conclusion

Effective marketing experiments require both scientific rigor and practical feasibility. By implementing these techniques systematically, researchers can increase statistical power without relying solely on massive samples. Remember that the goal is not simply statistical significance but accurately measuring marketing phenomena with precision and integrity.

Reference

Meyvis, T., & Van Osselaer, S. M. J. (2018). Increasing the Power of Your Study by Increasing the Effect Size. Journal of Consumer Research, 44(5), 1157–1173. https://doi.org/10.1093/jcr/ucx110

Text Mining with R Notes

Thu, 25 Jan 2024 00:00:00 +0000

Textbook

Text Mining with R

Tutorial

juliasilge.github.io/tidytext/
Sentiment Analysis: Introduction to the Syuzhet Package

Definitions

A token is a meaningful unit of text, most often a word, that we are interested in using for further analysis, and tokenization is the process of splitting text into tokens.

Key functions

unnest_tokens(): do tokenization and get one-word-per-row format.
anti_join(get_stopwords()): We can remove stop words (accessible in a tidy form with the function get_stopwords()) with an anti_join.

R code

# Loading necessary libraries
library(sentimentr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(magrittr)

# Example text
mytext <- c("The phone has scratches.", "The phone has no scratches.")

# Converting text into sentences
mytext <- get_sentences(mytext)

# Performing sentiment analysis
sentiment(mytext)

##    element_id sentence_id word_count  sentiment
## 1:          1           1          4 -0.3000000
## 2:          2           1          5  0.2683282

library(syuzhet)

## 
## Attaching package: 'syuzhet'

## The following object is masked from 'package:sentimentr':
## 
##     get_sentences

# Example sentences
sentences <- c("The phone has scratches.", "The phone has no scratches.")

# Get sentiment scores
sentiment_scores <- get_nrc_sentiment(sentences)

# View scores
sentiment_scores

##   anger anticipation disgust fear joy sadness surprise trust negative positive
## 1     0            0       0    0   0       0        0     0        0        0
## 2     0            0       0    0   0       0        0     0        0        0

# not work well

Learning Resource: Social Network Analysis

Fri, 24 Nov 2023 00:00:00 +0000

Check out igraph R-package 📦!

Summary of Concepts

See my notes in “Analyzing Social Media Networks with NodeXL: Insights from A Connected World” (Hansen et al. 2019), Chapter 3 Sections 3.1-3.5 (pages 31-42).

Node: Represents an entity (e.g., individual, organization) within the network.
Edge: Connects two nodes, symbolizing a relationship or interaction.
Graph: The entire structure comprising nodes and edges.
Degree: Number of connections for a node, with in-degree and out-degree in directed networks.
Path: Sequence of edges linking two nodes.
Centrality: Quantifies the importance of nodes.
- Degree Centrality: Frequency of a node in the network.
- Betweenness Centrality: Frequency of a node appearing on shortest paths between other nodes.
- Closeness Centrality: Proximity of a node to all other nodes.
- Eigenvector Centrality: Influence level of a node.
Diameter: Longest shortest path within the network.
Community: Nodes more densely connected to each other than to the rest of the network.
Homophily: Tendency to connect with similar others.
Structural Holes: Gaps offering strategic advantages in information flow.
Social Capital: Benefits and resources accessible through social networks.
Small-world Network: Characterized by short path lengths and high clustering.
Scale-free Network: Features a power-law degree distribution with few highly connected nodes.
Network Density: Proportion of actual connections to potential connections.
Modularity: Strength of a network’s division into modules or communities.

Summary Table

The following summary table is from (Kane et al. 2014).

Understanding the Role of Random Graphs in Network Analysis

Contextual Analysis of Network Metrics:
- Random graphs help in evaluating the significance of network metrics by providing a comparison point.
- This approach determines if observed network patterns are typical or atypical under certain conditions.
Assessing Significance and Likelihood:
- By comparing real network characteristics to those of random graphs, it’s possible to assess the likelihood of these characteristics occurring by chance.
- Significant differences in metrics like clustering suggest underlying social processes, not just random formation.
Baseline for Comparison (Null Model):
- A random graph acts as a baseline, representing a network where connections are formed randomly.
- Comparing real networks to this baseline identifies non-random, significant features of the network.

Randomization tests enable you to identify:

Whether features of your original network are particularly unusual.

Simplicity in Modeling:
- The simplest random graph mirrors the original graph in terms of number of nodes and density, facilitating easier statistical analysis.
Methodological Rigor:
- Utilizing random graphs adds rigor and depth to network analysis.
- It aids in discerning meaningful social network patterns from those that might arise randomly.

This summary encapsulates the importance of using random graphs in social network analysis, particularly for understanding the significance and context of various network properties and metrics.

Datacamp course notes: key functions in `igraph`

Chapter 1: Basic Network Analysis

Creating and Visualizing Graphs

Create Graph: graph.edgelist(as.matrix(df), directed = FALSE)
Vertices and Edges: V(g), E(g)
Graph Order and Size: gorder(g), gsize(g)
Plot Graph: plot(g)

Attributes

Add Vertex Attributes: set_vertex_attr(g, "attribute", value)
Get Vertex Attributes: vertex_attr(g)
Add Edge Attributes: set_edge_attr(g, "attribute", value)
Get Edge Attributes: edge_attr(g)

Subsetting and Coloring

Subsetting Networks: E(g)[[.inc('vertex')]], E(g)[[condition]]
Coloring Vertices: V(g)$color <- ifelse(condition, "color1", "color2")

Layouts

Graph Layouts: plot(g, layout = layout.fruchterman.reingold(g))

Chapter 2: Advanced Network Analysis Techniques

Directionality and Degrees

Check Directionality: is.directed(g)
Degree Analysis: degree(g, mode = c("out"))

Neighbors

Identify Neighbors: neighbors(g, "vertex", mode = c("mode"))
Common Neighbors: intersection(x, y)

Paths

Longest Paths: farthest_vertices(g), get_diameter(g)
Ego Networks: ego(g, N, 'vertex', mode=c('mode'))

Importance Measures

Betweenness: betweenness(g, directed = TRUE, normalized = TRUE)
Other Measures: degree, eigenvector centrality, closeness centrality, pagerank centrality

Chapter 3: Network Metrics and Random Graphs

Centrality and Density

Eigenvector Centrality: eigen_centrality(g)$vector
Network Density: edge_density(g)

Path Length and Random Graphs

Average Path Length: mean_distance(g, directed = FALSE)
Random Graphs: erdos.renyi.game(n, p.or.m, type)

Transitivity

Transitivity: triangles(g), transitivity(g)
Local Transitivity: transitivity(g, vids = 'vertex', type = "local")

Cliques

Identifying Cliques: largest_cliques(g), max_cliques(g)

Chapter 4: Community Detection and Visualization

Assortativity and Reciprocity

Assortativity: assortativity(g, values), assortativity.degree(g, directed = FALSE)
Reciprocity: reciprocity(g)

Community Detection

Fast-Greedy Detection: fastgreedy.community(g)
Edge-Betweenness Detection: edge.betweenness.community(g)
Community Analysis: length(x), sizes(x), membership(x), plot(x, g)

Visualization

Visualization Packages: igraph, visNetwork, statnet, networkD3, ggnet, sigma, ggnetwork, rgexf, ggraph, threejs
Threejs Visualization: library(threejs), graphjs(g)
Adding Attributes: set_vertex_attr(g, "label", value = V(g)$name), set_vertex_attr(g, "color", value = "color")
Coloring Communities: x = edge.betweenness.community(g), i <- membership(x), set_vertex_attr(g, "color", value = c("color1", "color2", "color3")[i]), graphjs(g)

Useful resource

datacamp “Network Analysis in R”.
YouTube tutorial Social Network Analysis: A Beginner’s Lab in R provided by Duke University Network Analysis Center.
Textbook: “Statistical Analysis of Network Data with R” by Eric D. Kolaczyk (Kolaczyk and Csárdi 2014).

Use index to check definitions and concepts of network and R coding.

Please check out R package: igraph. If you need to know how to compute a particular attribute of the network, the reference page is a good starting point.
There are many packages available to make network plots. One very useful one is threejs which allows you to make interactive network visualizations. This package also integrates seamlessly with igraph.

Reference

Hansen, Derek, Ben Shneiderman, Marc A. Smith, and Itai Himelboim. 2019. Analyzing Social Media Networks with NodeXL. Morgan Kaufmann.

Kane, Gerald C., and Maryam Alavi, Giuseppe (Joe) Labianca, Stephen P. Borgatti, and and and. 2014. “What’s Different about Social Media Networks? A Framework and Research Agenda.” MIS Quarterly. https://doi.org/10.25300/misq/2014/38.1.13.

Kolaczyk, Eric D., and Gábor Csárdi. 2014. Statistical Analysis of Network Data with r. Springer.

Marketing Research Methods | Chen Xing

Notes on Unobserved Heterogeneity

1. Latent-Class (Finite Mixture) Models

2. Choice-Process Heterogeneity

3. Continuous (Random-Coefficients) Models

Why It Matters

Decision Checklist

Reference

Enhancing Statistical Power In Marketing Experiments — A Practical Implementation Guide

1. Introduction

2. Essential Tools And Resources

Required Tools:

Required Planning Elements:

3. Pre-Study Protocol

Pre-Registration Process:

4. Experimental Design Techniques

4.1 Within-Subjects Design Implementation:

4.2 Covariate Implementation:

4.3 Manipulation Optimization:

5. Participant Management

5.1 Quality Control Procedures:

5.2 Participant Selection Optimization:

6. Analytical Techniques

6.1 Planned Contrast Implementation:

6.2 Interaction Analysis Protocol:

7. Avoiding Methodological Pitfalls

Common Malpractice Warning Signs:

Prevention Protocol:

8. Power Enhancement Techniques Summary

Measurement Optimization:

Error Variance Reduction:

Stimuli Optimization:

Data Quality Control:

9. Replication Protocol

Implementation Steps:

10. Effect Size Reference Guide

Conclusion

Reference

Text Mining with R Notes

Textbook

Tutorial

Definitions

Key functions

R code

Learning Resource: Social Network Analysis

Summary of Concepts

Summary Table

Understanding the Role of Random Graphs in Network Analysis

Datacamp course notes: key functions in igraph

Useful resource

Reference

Datacamp course notes: key functions in `igraph`