Aurlie Lemmens, Erasmus University Rotterdam

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Characterizing International Diffusion Patterns
Using Penalized Splines

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

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Do these diffusion curves differ?
Country 2
Country 1
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Do these diffusion curves differ?
Country 2
Country 1
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Research Question

• We want to characterize differences in diffusion
  across countries and regions, i.e.
• Whether countries or regions exhibit systematic
  differences in diffusion over the whole time
  span?
• When these differences occur in the diffusion
  process?

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Managerial and Public Relevance

• Managerial and Marketing Relevance
• Global versus local launch strategy (Kalish et
  al. 1995)
• Adaptation of the marketing mix (Stremersch and
  Tellis 2004)
• Typical diffusion patterns (Golder and Tellis
  2004) as national benchmark and early forecast
  (Goldenberg et al 2001)
• Public Policy Making
• Subsidy policy and incentive schemes Do European
  countries differ in innovativeness? E.g. the
  digital divide or new drugs prescriptions

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Previous Research

• Explains cross-national variation in diffusion by
  economic, socio-demographic and cultural
  characteristics (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)
• Mixed-influence modeling framework
• Compare country-specific Bass (1969) parameters
  (Talukdar et al. 2002) or derivates, e.g,
  diffusion speed (Van den Bulte 2000)
• E.g. Differences over the whole time span ?
  When?
• Product-life cycle (PLC) framework
• Differences in time-to-takeoff (Tellis et al.
  2003), growth rate, growth duration (Stremersch
  and Tellis, 2004), slowdown.
• No significance testing
• Relies on distributional assumptions
• Risk of misspecification for non S-shaped
  processes, e.g. movies and albums (Sawhney and
  Eliashberg 1996), non-durables with trial and
  repeat (Hardie et al. 1998).
• Sensitive to data window (Boswijk and Franses
  2005).

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Methodology Penalized Splines

• Recently developed in statistics (Ruppert et al.
  2003, Durban et al. 2005)
• Semi-parametric approach
• Rust (1988), Van Heerde et al. (2001)
• Curve/function as object Functional Data
  Analysis
• No distributional assumption flexible shape
  (movies, non-durables, sales data)
• Early and on-going diagnostics (before inflection
  point)
• Linear mixed-model framework 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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PC in France
Mobile Phones in UK
Fluvastatin in Greece
Vardenafil in Sweden
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The Diffusion Model
With the sales per capita/penetration of a
new product i in a given country j at time t
Fitted values
Product deviation
Country curve
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Typical Diffusion Curve in j
Country typical diffusion curves

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Random Product Deviations

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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), (RE)ML
• 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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Linear Mixed-Model Framework
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Data

• Consumer Durables
• Traditional studies
• Annual data
• Penetration or sales per capita
• Long time span (post inflection)
• S-shaped
• 15 European countries from 3 regions
• (Nordic, Mid-West and Mediterranean)

• Pharmaceutical Drugs
• New data set
• Monthly data
• Sales (with replacement) per capita
• Short time series (no inflection)
• Not S-shaped
• 25 European countries from 4 regions
• (Nordic, Mid-West, Mediterranean and Eastern
  Europe)

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Data

• Consumer Durables (penetration or cumulative
  sales per cap.)
• 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).
• Pharmaceuticals (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).

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Typical Diffusion Patterns (Durables)
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Typical Diffusion Patterns (Durables)

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Typical Diffusion Patterns (Durables)
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Typical Diffusion Patterns (Pharmac.)
Lipid lowering drugs
Erectile dysfunction drugs
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Testing for Differences in Diffusion
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Testing for Differences in Diffusion
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Summary

• Methodological insights
• Flexible and easy to estimate (LMM)
• Whether and when?
• Conceptual insights
• Diffusion differs across countries and regions
• Inter-country (region) differences are
  product-dependent
• Differences are also time-dependent

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Typical Diffusion Patterns as Managerial Tool

• As pre-launch expectation for each country (or
  region)
• Summarizes the information conveyed by previous
  diffusion data of a relevant set of homogeneous
  products.
• As benchmark for assessing of local management
• Real-time diagnostics, allows for sequential
  adaptation of the marketing mix.
• Example Introduction of Rosuvastatin in February
  2003.
• At that point in time, 3 products from the same
  category are available Atorvastatin (Lipitor,
  1996), Cerivastatin (Baycol, Lipobay, 1997),
  Fluvastatin (Lescol, 1993).

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Some countries are on target


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Some perform below par
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P-splines as Managerial Tool

• Real-time diagnostics for a new innovation (from
  the introduction date until the end)
• Managerial Question
• Do sales differ across countries at this time
  point?
• Example
• Introduction of Sildenafil (Viagra) in 1998 in
  UK and Italy.

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After 12 months
Time (months)
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After 12, 24, 36, 48, 60 months
Time (months)
Time (months)
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