1. EHA Frailty Models & Heterogeneous Diffusion Models
Sociology 229A, Class 10
Copyright © 2008 by Evan Schofer
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2. 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.

3. Shared Frailty Models
Shared frailty model = random intercept in an event history model
Stata: stcox var1 var2 var3, shared(clusterID)
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…

4. 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 var1 var2, frailty(gamma) shared(schoolid)
streg var1 var2, dist(e) frailty(gamma) shared(schoolid)

5. 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.

6. Heterogeneous Diffusion Models
Formula:
From Soule 1997

7. 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
David Strang and Nancy Brandon Tuma. Spatial and Temporal Heterogeneity in Diffusion. The American Journal of Sociology, Vol. 99, No. 3 (Nov., 1993), pp
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