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3. Model and Data 
The aim of this study is to explore determinants of changes 
between the discrete states "unmarried", "first marriage" 
and "(first)divorce". A continous-time-discrete-state semi¬ 
Markov-process seems to be an appropriate model because 
events may happen at any point in time and the risk of 
change is allowed to be duration-dependent. Marriages are 
not only dissolved by divorce but also by the "competing 
risk" of death of one of the spouses (Figure 1). 
socio-economic 
covariates x 
rst 
2t.divorce 
r t, X) 
unmarried 
—irst 
7 
marriage 
widowed 
Figure 1 A Model for the change of family states 
Observed duration times until the dissolution of a marriage 
by death are treated as censored data. As usual in event¬ 
history analysis (Tuma and Hannan, 1984; Diekmann and Mit- 
ter, 1984b) a hazardrate or "risk"-equation incorporating 
the socio-economic covariates is estimated by methods of 
Maximum-Likelihood or Partial-Likelihood. The hazardrate r., 
(t, x) can be interpreted as the "risk" or "instantaneous' 
likelihood of a first marriage, while the rate r,, (t, x) is 
the risk of divorce (Figure 1). Formally the rate is defined 
as: 
ft) 
(1)r. (t,g) s lim ProbltiatTtrt. 
At-0 
At 
G,(t),