Nonparametric Approaches
As we discussed earlier, nonparametric duration models do not make assumptions about (a)
the distribution of failure times or (b) how the independent variables change survival experiences.
The applicability of nonparametric method
Multichotomous Dependent Variables I
Last time we looked at binary dependent variables. We now move on to multichotomous dependent
variables:
1. Ordered Dependent Variables:
Presidential Approval - Approve, Indierent, Disapprove
Political Interest - ver
Introduction to Duration Models
1
What is Duration Analysis?
Duration analysis is sometimes referred to as survival analysis or event history analysis. Duration
data can be thought as being generated by what is called a failure time process. A failure tim
Maximum Likelihood Estimation (MLE)
1
Specifying a Model
Typically, we are interested in estimating parametric models of the form
yi f (, yi )
(1)
where is a vector of parameters and f is some specic functional form (probability density or
mass function).
Duration Data
1
Recording Duration Data
Given the possibility of censoring and truncation, Table 1 illustrates a good way to record duration
data.1 By recording the analysis times during which cases are observed (t0 and t1 ) and whether
Table 1: Sample Du
Binary Response Models
1
Introduction
There are many binary social outcomes that occur naturally:
A citizen votes or not
A cabinet forms or not
A pre-electoral coalition forms or not
A war is fought or not
1.1
Linear Probability Model
You might think
Discrete Time Duration Models: BTSCS
1
Introduction
As we saw before, event history data for discrete time processes generally record the dependent variable as
a series of binary outcomes denoting whether or not the event occurred at the observation point
Unobserved Heterogeneity and Frailty Models
1
Types of Duration Dependence
We have talked quite a bit about duration or time dependence so far.1 However, we have tended to talk about
it in terms of state dependence - the value of the baseline hazard depen
Competing Risks
1
Introduction
To this point, we have only looked at single-state processes i.e. we have assumed that each unit is at
risk of only one event at any one time. However, it may be the case that a unit is at risk of experiencing
multiple event
Semi-Parametric Duration Models: The Cox Model
There are basically two semi-parametric alternatives to the parametric models that we examined earlier:
(i) the piecewise-constant exponential (PCE) model and (ii) the Cox model.
1
The Piecewise-Constant Expo
The Basic Components of Duration Analysis
1
Introduction
Assume we have N units i = 1, 2 . . . N , each of which will experience some event. In general, we
think that there is some latent failure time for unit i given by Ti and some latent censoring time
Parametric Models
1
Parametric Models: The Intuition
As we saw early, a central component of duration analysis is the hazard rate. The hazard rate is the probability of experiencing an event at time ti conditional on having survived to time ti . The preci