Modeling the observations

$ \newcommand{\pcyipsii}{p_{y_i|\psi_i}} \newcommand{\pcypsi}{p_{y|\psi}} \newcommand{\bpsi}{\boldsymbol{\psi}} \newcommand{\bu}{\boldsymbol{u}} \newcommand{\bx}{\boldsymbol{x}} \newcommand{\by}{\boldsymbol{y}} \newcommand{\hazard}{h} \newcommand{\std}[1]{\mbox{sd}\left(#1\right)} \newcommand{\esp}[1]{\mathbb{E}\left(#1\right)} \newcommand{\eqdef}{\mathop{=}\limits^{\mathrm{def}}} \newcommand{\prob}[1]{ \mathbb{P}\!\left(#1\right)} \newcommand{\probs}[2]{ \mathbb{P}_{#1}\!\left(#2\right)} \newcommand{\Rset}{\mbox{$\mathbb{R}$}} \newcommand{\Yr}{\mbox{$\mathcal{Y}$}} \newcommand{\teps}{\tilde{\varepsilon}} \newcommand{\like}{\cal L} \newcommand{\pypsiij}{p_{y_{ij}|\psi_{i}}} \newcommand{\ptypsiij}{p_{\transy(y_{ij})|\psi_{i}}} \newcommand{\peps}{p_{\teps}} \newcommand{\logit}{\rm logit} \newcommand{\transy}{u} \newcommand{\repy}{y^{(r)}} \newcommand{\brepy}{\boldsymbol{y}^{(r)}} $

Template:Extension \log S(t,\psi_i) &= & \hazard(t,\psi_i) \end{array}

\)

Here, $\lambda(t,\psi_i) = \hazard(t,\psi_i)$ is known as the hazard function.

In summary, defining a model for the observations means choosing a (parametric) distribution. Then, a model must be chosen for the parameters of this distribution.