Two-stage models of innovation adoption with partial observability

1. Two-stage models of innovation adoptionwith partial observability Christophe Van den Bulte Gary L. Lilien University of Pennsylvania Pennsylvania State University Georgetown University December 4, 2009

2. Structure 1. Awareness/consideration vs. evaluation • Two-stage models with partial observability • Three applications

5. Monica • A fellow sociologist asked Stanley Lieberson: Would the name Monica become more or less popular because of the scandal? Stanley Lieberson. 2000. A Matter of Taste: How Names, Fashions, and Culture Change. New Haven, CT: Yale University Press.

6. Medical Innovation • In an earlier paper, we showed that evidence of social contagion disappears after one controls for marketing effort. However, that does not mean that social contagion was not at work: “[O]ur hazard models did not distinguish between two important stages in the adoption process: awareness followed by evaluation conditional upon awareness (Rogers 1995). … Modeling the effect of marketing efforts and social contagion without distinguishing between awareness and evaluation might produce misleading results when marketing efforts are quite important in creating awareness, and social contagion is moderately—though still sizably—important in persuading actors to adopt the innovation. When both explanatory variables are forced into a single-stage model, the weaker social contagion effect may be washed out by the marketing effort, erroneously suggesting that social contagion was not at work.” Christophe Van den Bulte and Gary L. Lilien. 2001. “Medical Innovation Revisited: Social Contagion versus Marketing Effort.” American Journal of Sociology, 106 (March), 1409-35.

7. Stages in the adoption process (Rogers 1962) 1. Awareness • Interest • Evaluation • Trial • (Sustained) adoption Awareness / consideration Evaluation / adoption

8. Awareness/consideration is rarely measured • Not overt behavior  no paper trail • Not a memorable event  poor recall • Multi-wave surveys: • Expensive • Asking the question may actually make people aware Can we bridge the gap between theory and data using better models?

9. Structure 1. Awareness/consideration vs. evaluation • Two-stage models with partial observability • Three applications

10. Traditional Single-hurdle Two-stage w/ memory Two-stage w/o memory Initial state Initial state Initial state Consideration Consideration Evaluation Evaluation Evaluation Adoption Adoption Adoption Model typology

11. Standard, single-stage hazard model Hazard (in discrete time) = probability that you adopt, given that you have not adopted before Pit = Pr[Ti = ti | Ti ti] LL = Si [ ci ln { Pr[Ti = ti] } + (1 - ci) ln { Pr[Ti > ti] } ] Pit = Pr[yit =1 | yit-1 = 0] LL = SiSt [1 - dit] [ yit ln {Pit} + (1- yit) ln {1 - Pit}] Non-censoring indicator Censoring indicator

12. Notation Adoption yit = 1 if i has adopted at time t, yit = 0 otherwise Awareness/consideration ait = 1 if i is aware at time t, ait = 0 otherwise Positive evaluation = Adoption conditional on awareness eit = 1 if i evaluates product positively at time t, eit = 0 otherwise

13. Two-stage model: set-up Adoption Pr[yit = 1 | yit-1 = 0] = Pr[eit = 1, ait = 1 | yit-1 = 0] = Pr[eit = 1 | ait = 1, yit-1 = 0] Pr[ait = 1 | yit-1 = 0] Awareness Pr[ait = 1 | yit-1 = 0] = F1(a1x1it) Adoption conditional on awareness Pr[eit = 1 | ait = 1, yit-1 = 0] = F2(a2x2it)

14. Case 1: Full observability One must be in one of three states: 0: ait = 0, eit not relevant (no awareness and hence no adoption) 1: ait = 1, eit = 0 (awareness, but no positive evaluation; hence no adoption). 2: ait = 1, eit = 1 (both awareness and positive evaluation, hence adoption). Let P0it, P1it and P2itdenote the probability of being in each state, given yit-1 = 0 One can then write: LL = SiSt [1 - dit] [ (ait eit) ln P2it + ait (1- eit) ln P1it + (1- ait) ln P0it ] Practically: One can also estimate two hazard models separately, one for awareness and one for adoption given awareness F1 *F2 F1 *(1-F2) (1-F1)

15. Case 2: Partial observability, no memory The researcher does not observe ait and eit separately, but observes only their product ait* eit = yit The researcher can not estimate the same LL as before, but must contract it LL = SiSt [1 - dit] [ (ait eit) ln P2it + ait (1- eit) ln P1it + (1- ait) ln P0it ] LL = SiSt [1 - dit] [ ( yit) ln P2it + (1- yit) ln { 1 - P2it } ] LL = SiSt [1 - dit] [ yit ln { F1*F2 } + (1- yit) ln { 1 - F1*F2 } ] Limitations: 1. What prevents someone who is aware to become unaware later on? 2. Full symmetry, so only the covariates provide interpretation to stages.

16. Case 3: Partial observability, perfect memory The trick is to keep track of the many ways in which someone can end up adopting at time t. Someone who adopts at time 1 must have become aware and evaluative at time 1 Pr(T = 1) = F1(1) F2(1) Someone who adopts at time 2 may: Have become aware at time 1, but evaluative only at time 2 Have become aware only at time 2, and immediately evaluative Pr(T = 2) = F1(1) [1 - F2(1)] F2(2) + [1- F1(1)] F1(2) F2(2) = F2(2) { F1(1) [1 - F2(1)] + [1- F1(1)] F1(2) }

17. Case 3: Partial observability, perfect memory (ct’d) In general, we can write: Pr(T = t) = F2(t) { F1(1) [1 - F2(1)] [1 - F2(2)] [1 - F2(3)] … [1 - F2(t-1)] + [1- F1(1)] F1(2) [1 - F2(2)] [1 - F2(3)] … [1 - F2(t-1)] + [1- F1(1)] [1 - F1(2)] F1(3) [1 - F2(3)] … [1 - F2(t-1)] + … + [1- F1(1)] [1 - F1(2)] [1 - F1(3)] … [1 - F1(t-1)] F1(t) } = F2(t) Sst { Pk<s [1- F1(k)] } F1(s) { Psq<t [1- F2(q)] }

18. Case 3: Partial observability, perfect memory (ct’d) Also, we can write: Pr(T > t) = Ppt [1- F1(p)] + [1 - F2(t)] [ Sst { Pk<s [1- F1(k)] } F1(s) { Psq<t [1- F2(q)] } ] Having expressions for both Pr(T = t) and Pr(T > t), we can plug them in the general formula for hazard models LL = Si [ ci ln { Pr[Ti = ti] } + (1 - ci) ln { Pr[Ti > ti] } ]

19. Estimating the models with standard software Single-stageAny BDV software 2-stage w/o memoryLimdep (“Abowd-Ferber probit”) A few lines of code in SAS or Stata 2-stage w/ memoryNot as handy to code in “canned” statistical software. But can be coded rather easily in Excel

20. Structure 1. Awareness/consideration vs. evaluation • Two-stage models with partial observability • Three applications

21. Application I: Medical Innovation Important study Good test case Strong marketing effects Weak contagion effects, but probably still effects

22. Data on tetracycline adoption Monthly, November 1953-February 1955 (first 17 mos.) 121 physicians in 4 small Midwestern cities 87% (105) had adopted by end of observation period Data collected by Coleman, Katz and Menzel; covariates focus on personal characteristics and social networks Additional archival data on marketing effort (advertising in 4 journals) Coleman, Katz and Menzel 1966; Burt 1987; Marsden and Podolny 1990; Strang and Tuma 1993; Valente 1996; Van den Bulte and Lilien 2001

23. Covariates Awareness • Number of journals (log) • Science orientation • Advertising : Mt= mt + (1-d) Mt-1 • Advisor status • Advisor status x Advertising Evaluation / Adoption • Summer (dummy) • Age and Age2 • Chief / admin / honorary • Science orientation • Social network exposure : SNEit = [ Sj wij yjt-1]g • Advisor status • Advisor status x SNE

24. Medical Innovation application: Results for models with social contagion from direct ties Single-Stage Model Two-Stage Models _____________________________________________ Zero Memory Perfect Memory Note.—Results are from complementary log-log models. The significance levels reported are for likelihood ratio tests that the parameter of interest is zero, except for tests of g, where the test is g = 1. a SNE stands for social network exposure b Nested model with g = 1 does not converge. * P < .10; ** P < .05; *** P < .01; **** P < .001

25. Medical Innovation application: Results for models with social contagion from structural equivalents Single-Stage Model Two-Stage Models _____________________________________________ Zero Memory Perfect Memory Note.—Results are from complementary log-log models. The significance levels reported are for likelihood ratio tests that the parameter of interest is zero, except for tests of g, where the test is g = 1. a SNE stands for social network exposure b Nested model with g = 1 does not converge. * P < .10; ** P < .05; *** P < .01; **** P < .001

26. Results Fit across three models Evidence of contagion • Effect’s significance across models • Non-linearity effect differs between cohesion and equivalence Other • Advertising decay rate across models • Very large effect of chief / admin / honorary position • Effects may vary across stages • Science orientation • Advisor status

27. Application II: a new drug Some key differences w/ previous study Higher risk and ambiguity Life-threatening condition if left untreated More complex treatment plans More detailed data Data on self-reported vs. sociometric leadership Data on prescription volume after adoption Data on sales calls, by month-physician

28. Data on new drug adoption Monthly, 2005-2007 (first 17 mos.) 193 physicians in 3 large cities Only prescribers of existing drugs for same medical condition 35% (68) had adopted by end of observation period Network data Sociometric survey Discussion and patient referral ties Response rate 45%, 32%, and 25%  We cannot properly identify positional equivalence Prescription data for both respondents and non-respondents  We can properly identify contagion through direct contacts Sales call data Number of details for focal drug, by physician and by month Data from Iyengar, Van den Bulte and Valente, MSI Report 08-120.

29. Covariates Awareness • Sociometric in-degree • Self-reported opinion leadership • Primary practice with university/teaching hospital • Not a specialist (but primary care) • Patient volume (# patients seen with medical condition) • Tendency to refer patients before initiating treatment • City dummies • Detailing : Mit= mit + (1-d) Mit-1 Evaluation / Adoption • Sociometric in-degree • Self-reported opinion leadership • Primary practice with university/teaching hospital • Patient volume (# patients seen with medical condition) • Tendency to refer patients before initiating treatment • Detailing : Mit= mit + (1-d) Mit-1 • Social network exposure : SNEit = [ Sj wij qjt-1]

30. Application to new drug: Results for models with social contagion from direct ties Single-Stage Model Two-Stage Models _____________________________________________ Zero Memory Perfect Memory Note.—Results are from probit models. The significance levels reported for single-stage and zero-memory models are from Wald tests that the parameter of interest is zero. a SNE stands for social network exposure * P < .10; ** P < .05; *** P < .01

31. Results Fit across three models Evidence of marketing effort • Important in both stages • In this application, decay rate does not increase across models Measures of opinion leadership • Sociometric leadership: only in awareness/consideration • Self-reported leadership: only in evaluation Other effects may vary across stages as well • University/teaching hospital

32. Application III: ATM adoption Data set analyzed several times in economics Good test case Efficiency effects have been documented Legitimation effects unknown (though expected) Measures of both local and global density Hannan and McDowell 1984a, 1984b, 1987; Saloner and Shepard 1995; Sinha and Chandrashekaran 1992

33. Data on ATM adoption Annual, 1971-79 (first nine years of ATM use in U.S.A.) 3683 banks in operation for the entire nine-year period 392 different local banking markets 20% (739) of banks had adopted by end of 1979 Data collected by Federal Reserve; covariates focus on market structure, bank size, profitability and type.

34. Covariates Consideration • Global density (prior adoptions across U.S.) • Demand deposits as % total assets • Market share Efficiency (incl. rivalry) • Local density (prior adoptions within market) • Demand deposits as % total assets • Market share • Off-premise ATMs legally allowed • Urban bank • Average market wage rate • Price / year dummies • Number of banks in market • CR3 concentration ratio • 1-year growth in assets • Return on assets • Total assets • Ownership by bank holding company Rival precedence Economic value Comp. Intensity Ability to pay

35. ATM application: Results Single-Stage Models ___________________________________ Fixed base rate Flexible base rate Two-Stage Models __________________________________ Zero Memory Perfect Memory Note.—Results are from probit models. The significance levels reported are for likelihood ratio tests that the parameter of interest is zero. * P < .05; ** P < .01; *** P < .001

36. Results Fit across three models Evidence of legitimacy effect • Effect of global density across models Other • Some efficiency effects that are marginally significant in single-stage model disappear in two-stage models • Effects may vary across stages • Market share

37. Conclusion Using models to bridge gap in richness between theory and data Areas of use • Mass media effects vs. network effects • Legitimation processes in neo-institutional theory • Deviance (deviant behavior vs. detection) • Discrimination (selective application vs. discrimination) • Life course research (e.g., sexual intercourse vs. pregnancy) No free lunch • Need for data on time of separate transitions is substituted by need for good covariates and theory