Aurlie Lemmens, Erasmus University Rotterdam

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Testing for Inter-Country Differences in
Diffusion Using Penalized Splines

• Aurélie Lemmens, Erasmus University Rotterdam
• Stefan Stremersch, Erasmus University Rotterdam
  Emory University
• Christophe Croux, K.U. Leuven

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Testing for Inter-Country Differences
Country 1
Country 2
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Testing for Inter-Country Differences
Country 1
Country 2
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Testing for Inter-Country Differences
Country 2
Country 1
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Testing for Inter-Country Differences
Country 2
Country 1
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Why Is It Important?

• Managerial/Marketing Relevance
• Global versus local strategy
• Expectations national benchmarks
• Innovative countries (demand)
• Public Policy Making
• Do European countries differ in innovativeness?
• Especially regarding some products,
• E.g. the digital divide

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Previous Research

• Lack of formal testing, rather indirect evidence
• E.g., Dekimpe et al. 1998, Gatignon et al. 1989,
  Helsen et al. 1993, Tellis et al. 2003,
  Stremersch and Tellis 2004, Van den Bulte and
  Stremersch 2004, Desiraju et al. 2004.
• Few exceptions (Mahajan and Muller 1994, Talukdar
  et al. 2002)
• Differences in Bass (1969) parameters, BUT
• Not able to tell whether entire processes differ
  across two specific countries
• Not able to tell from which point processes start
  to diverge/converge
• S-shaped processes only
• Sensitive to data window
• Only reliable estimates after inflection point
• Significance of difference between parameters is
  dependent upon time window.

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Methodology Penalized Splines

• Recently developed in statistics (Coull et al.
  2001, Ruppert et al. 2003, Durban et al. 2005)
• Semi-parametric approach (Van Heerde et al. 2001)
• Flexible shape (movies, non-durables, sales data)
• Overall and point-wise (at each time) test
• Early and on-going diagnostics (before inflection
  point)
• Multi-country, multi-product approach
• Control for (un)observed product effects
• Draw typical diffusion / sales curves for
  countries or regions
• Increases statistical power and avoid
  multiple-testing issues

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Penalized Splines
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Model Factor-by-Curve Interaction
sales per capita/penetration of a new product
i in a given country j belonging to region r
at time t
Treatment can be the country or the region,
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Typical Diffusion Curve in j or r
Country curves

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Random Product Deviations

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Country-Specific Curves
Country Product

• VCR in Denmark

Product deviations
Country curve
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Estimation

• The model can be written as a linear mixed model
• after rearranging the different terms
• Best linear unbiased predictor (BLUP)
• Easy to implement (e.g. PROC MIXED in SAS or lme
  in S/R)
• Can use all inference theory (e.g. hypothesis
  testing)

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Data

• High-Tech Data
• Yearly
• Personal computers (for the period 1981-1992),
  internet users (1990-2003), mobile phone users
  (1987-1999), CD players (1984-1993), digital
  cameras (1998-2004), DVD (1998-2004), microwave
  ovens (1977-1993), and VCR (1977-1990).
• 15 European countries in 3 regions
• the Nordic (Denmark, Finland, Norway and Sweden),
• the Mid-West (Austria, Belgium, Germany, Ireland,
  Netherlands, Switzerland and United Kingdom)
• the Mediterranean (France, Italy, Portugal and
  Spain).

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Data

• Pharmaceuticals
• Monthly, Kg active substance sold
• 4 Lipid modifying agents fluvastatin
  (1993-2005), cerivastatin (1997-2005),
  atorvastatin (1996-2005) and rosuvastatin
  (2003-2005)
• 5 Drugs used in erectile dysfunction alprostadil
  (1995-2005), sildenafil (1998-2005), tadalafil
  (2003-2005), vardenafil (2003-2005) and
  apomorphine (2001-2005).
• 25 European countries in 4 regions
• the Nordic (as before).
• the Mid-West (as before Luxembourg)
• the Mediterranean (as before Greece)
• the Eastern Europe (Czech Republic, Estonia,
  Hungary, Latvia, Lebanon, Lithuania, Poland,
  Slovakia)

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Research Questions

• Are there significant differences in overall
  diffusion across countries?
• When does diffusion start to converge/diverge
  across countries?
• How to obtain typical, country- or
  region-specific diffusion curves,
• for cross-national or cross-regional comparisons?
• as country or region benchmarks for future
  innovations?

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Question 1 Are there significant differences in
overall diffusion across countries?
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Testing for Inter-Country Differences
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Testing for Inter-Country Differences
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Question 2 When does diffusion start to
converge/diverge across countries?
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Example (1) the Viagra Case

• Introduction of Sildenafil (Viagra) in 1998 in
  most European countries
• On-going procedure we model diffusion in UK and
  Italy after
• 1 year (12 observations each)
• 2 years (24 observations each)
• 3 years (36 observations each)
• 4 years (48 observations each)
• 5 years (60 observations each)
• 6 years (72 observations each)
• Confidence bounds provide us information each
  year whether both countries national sales
  differ at each point in time.

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Example (1) the Viagra Case
Time (months)
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Example (1) the Viagra Case
Time (months)
Time (months)
Time (months)
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Question 3 How to obtain typical, country- or
region-specific diffusion curves?

• for cross-national or cross-regional comparisons?
• as country- or region-benchmarks for future
  innovations?

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Country-Specific Curves High-Tech
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Region-Specific Curves High-Tech
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Region-Specific Curves Lipid Mod.
Eastern Mediterranean Mid-West Nordic
Time (months)
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Using Country-Specific Curves

• As pre-launch expectation for each country (or
  region)
• Summarize the information conveyed by previous
  diffusion data of related products.
• Average market potential for a given product
  class.
• Relevant set of homogeneous products.
• As benchmark for assessing of local management
• Real-time diagnostics/management.
• Allows for sequential adaptation of the marketing
  mix.
• Guessing by analogy strategy (Bass et al.
  2001).

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Example (2) the Rosuvastatin Case

• Introduction of Rosuvastatin, a lipid modifying
  agent, in February 2003.
• At that point in time, three other products from
  the same category of drugs, are available
• Atorvastatin (Lipitor, 1996)
• Cerivastatin (Baycol, Lipobay, 1997)
• Fluvastatin (Lescol, 1993)
• Estimate country-specific curves using all data
  up to January 2003.
• Allows for early diffusion data.

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Some countries perform averagely

Time (months)

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Some outperform the local benchmark
Time (months)
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Some perform worse than expected
Time (months)
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Conclusion

• The procedure allows us to
• Test whether countries exhibit significant
  differences in overall diffusion,
• Test (in real time) when those differences in
  diffusion occur,
• Construct typical diffusion curves (i) for
  cross-national comparisons, and (ii) as local
  benchmarks for a new product.
• It works with any diffusion or sales pattern,
  S-shaped or not.
• It is very simple to implement.
• It can be easily extended to test for other
  treatment effects (e.g. product, vintage) and can
  be used in many other marketing fields.

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Thanks
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Mobile phones subscribers in UK

• - - - Srinivasan and Mason (1986)
• Penalized spline

Penetration
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Testing for Inter-Region Differences