Estimated Marginal Probabilities
Estimates the marginal probability P(T=t|x) based on estimated hazard rates. The hazard rates may or may not depend on covariates. The covariates have to be equal across all estimated hazard rates. Therefore the given hazard rates should only vary over time.
estMargProb(haz)
haz |
Numeric vector of estimated hazard rates. |
The argument *haz* must be given for the all intervals [a_0, a_1), [a_1, a_2), ..., [a_q-1, a_q), [a_q, Inf).
Named vector of estimated marginal probabilities.
It is assumed that all time points up to the last interval [a_q, Inf) are available. If not already present, these can be added manually.
Thomas Welchowski welchow@imbie.meb.uni-bonn.de
Gerhard Tutz and Matthias Schmid, (2016), Modeling discrete time-to-event data, Springer series in statistics, Doi: 10.1007/978-3-319-28158-2
# Example unemployment data library(Ecdat) data(UnempDur) # Select subsample subUnempDur <- UnempDur [1:100, ] # Convert to long format UnempLong <- dataLong (dataSet=subUnempDur, timeColumn="spell", censColumn="censor1") head(UnempLong) # Estimate binomial model with logit link Fit <- glm(formula=y ~ timeInt + age + logwage, data=UnempLong, family=binomial()) # Estimate discrete survival function given age, logwage of first person hazard <- predict(Fit, newdata=subset(UnempLong, obj==1), type="response") # Estimate marginal probabilities given age, logwage of first person MarginalProbCondX <- estMargProb (c(hazard, 1)) MarginalProbCondX sum(MarginalProbCondX)==1 # TRUE: Marginal probabilities must sum to 1!
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