Missing Value Mechanisms

Abstract

We now assume that we have missing values in the second covariate. The observability of X₂ is indicated by a random variable

$$O_{2}:\begin{cases} & \text{1 if}\;\;X_{2} \;\;\textup <Emphasis Type="ItalicSmallcaps"> obervable</Emphasis> \\ & \text{0 if}\;\;X_{2} \;\;\textup<Emphasis Type="ItalicSmallcaps"> unobservable</Emphasis> \end{cases}\;\;\;\;2\dagger)$$

and instead of X₂ we observe the random variable

$$Z_{2}:=\begin{cases} X_{2} \;\;\textup{if}\;\;O_{2}=1\\ K+1 \;\;\textup{if}\;\;O_{2}=0 \end{cases}$$

with an additional category for missing values. Instead of K + 1 we also use the symbol “?” for this category in the sequel.