EHA Frailty Models Heterogeneous Diffusion Models Sociology 229

EHA: Frailty & Random Effects • Two kinds of models: – Unshared Frailty •

Shared Frailty Models • Shared frailty model = random intercept in an event history

Shared Frailty Models • Shared frailty (random effects) are useful for: – 1. Clustered

Heterogeneous Diffusion Models • Strang, Tuma, and Greve – adapted continuous time EHA models

Heterogeneous Diffusion Models • Formula: » From Soule 1997

Heterogeneous Diffusion Models – Heterogeneous diffusion models are available in SAS, via a module

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EHA: Frailty & Random Effects • Two kinds of models: – Unshared Frailty • Models for “unobserved heterogeneity” • Only available for parametric models • Refers to individual-specific (unknown) characteristics that affect likelihood of failure – Shared Frailty – a “random effects” model • Useful for clustered data (non-independent cases) • Can be used with Cox & parametric models.

Shared Frailty Models • Shared frailty model = random intercept in an event history model • Stata: stcox var 1 var 2 var 3, shared(cluster. ID) • Cluster ID variable could be country id, school id, etc… • Formula: Cox model with shared frailty • Where ui is a random variable for i groups • Parametric shared frailty models are similar…

Shared Frailty Models • Shared frailty (random effects) are useful for: – 1. Clustered data • Just like prior examples – 2. Models with repeated events • Repeated events is a kind of clustering within caseid • Again, dummy variables (FEM) is a reasonable option – In stata, you’d have to enter the dummies manually • Stata: specify cluster ID and form of frailty • stcox var 1 var 2, frailty(gamma) shared(schoolid) • streg var 1 var 2, dist(e) frailty(gamma) shared(schoolid)

Heterogeneous Diffusion Models • Strang, Tuma, and Greve – adapted continuous time EHA models to incorporate network diffusion processes • Useful for studying network influences on adoption events • Models allow for specification of separate terms to assess: • Highly influential adopters (likely to produce an adoption cascade) • Highly “susceptible” adopters – influenced by previous adopters • Vectors or matrices of network distance.

Heterogeneous Diffusion Models • Formula: » From Soule 1997

Heterogeneous Diffusion Models – Heterogeneous diffusion models are available in SAS, via a module created by David Strang • No implementation in STATA so far – Some relevant cites: • Henrich R. Greve, David Strang and Nancy Brandon Tuma. Specification and Estimation of Heterogeneous Diffusion Models. Sociological Methodology, Vol. 25, (1995), pp. 377 -420. • David Strang and Nancy Brandon Tuma. Spatial and Temporal Heterogeneity in Diffusion. The American Journal of Sociology, Vol. 99, No. 3 (Nov. , 1993), pp. 614 -639 • Sarah A. Soule. The Student Divestment Movement in the United States and Tactical Diffusion: The Shantytown Protest. Social Forces, Vol. 75, No. 3 (Mar. , 1997), pp. 855 -882