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{\info
{\title Original file was misc1.tex}
{\doccomm Created using latex2rtf 2.3.18 r1266 (released May 29, 2020) on Sat May 30 17:35:19 2020
}
}
{\footer\pard\plain\f0\fs24\qc\chpgn\par}
\paperw11960\paperh16900\facingp\margl1724\margr1996\margt2249\margb963\pgnstart0\widowctrl\qj\ftnbj\f0\aftnnar
{\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \fi0 \fs20 h-Design\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 Two-Stage-Design \par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\i A}{\u8801*}{\i B}\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i A}\\s\\do5({\fs16 2}){\u8801*}{\i B}}}{\fldrslt }}
\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i A}{\u8592*}{\i B}}}{\fldrslt }}
\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i A}\\s\\do5({\fs16 2}){\u8592*}{\i B}}}{\fldrslt }}
\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i A}{\u8594*}{\i B}}}{\fldrslt }}
\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i A}\\s\\do5({\fs16 2}){\u8594*}{\i B}}}{\fldrslt }}
\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 R=({{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 1})\\,..\\,{\i R}\\s\\do5({\fs16 {\i r}}))}}{\fldrslt }}
}\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 \'d6se\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 l\'e4\'df{}t \'c4nderung \'dcbung\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 Nach Little & Rubin (1987) kann die Response-Wahrscheinlichkeit abh\'e4ngen\par
\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb210 \fi0 \fs20 {\par
{\trowd\cellx604\cellx5493\cellx8239
{\pard\intbl\ql {\~\~\~\~}\cell}
{\pard\intbl\ql {(1) von D und m\'f6glicherweise auch R,}\cell}
{\pard\intbl\ql {(weder MAR noch OAR)}\cell}
\row}
{\trowd\cellx604\cellx5493\cellx8239
{\pard\intbl\ql {}\cell}
{\pard\intbl\ql {(2) von R, aber nicht von D,}\cell}
{\pard\intbl\ql {(MAR, aber nicht OAR)}\cell}
\row}
{\trowd\cellx604\cellx5493\cellx8239
{\pard\intbl\ql {}\cell}
{\pard\intbl\ql {(3) weder von R noch von D}\cell}
{\pard\intbl\ql {(MAR und OAR)}\cell}
\row}
}\par
{\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li600\fi-300 \fs20 {\b {\b Definition 4.1:}} {}\par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb210 \li600\fi0 \fs20 Sei D eine bin\'e4re Responsevariable und seien {{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 1})}}{\fldrslt }}
} und {{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 2})}}{\fldrslt }}
} zwei beliebige (d.h. kategorielle oder stetige) unabh\'e4ngige Variablen oder auch Variablen-Vektoren. O.B.d.A. sei die Kovariable {{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 1})}}{\fldrslt }}
} f\'fcr alle Beobachtungen vollst\'e4ndig, die Kovariable {{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 2})}}{\fldrslt }}
} nicht vollst\'e4ndig vorhanden.\par
{\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li1200\fi-300 \fs20 1.\tab
Just an item \par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li1200\fi-300 \fs20 2.\tab
Just another item \par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li1200\fi-300 \fs20 3.\tab
Die Beobachtbarkeit {{\field{\*\fldinst{ EQ {\i O}\\s\\do5({\fs16 2})}}{\fldrslt }}
} von {{\field{\*\fldinst{ EQ {\i R}\\s\\do5({\fs16 2})}}{\fldrslt }}
} ist definiert als Zufallsvariable {\par
\pard\plain\s11\ql\sb120\sa120\keep\widctlpar\f0\tqc\tx4120\sl240\slmult1 \sb210 \li1200\fi0 \fs20 \tab
{\field{\*\fldinst{ EQ {\i O}\\s\\do5({\fs16 2}):= \\b \\lc\\\{ ({ \\a \\al \\co2 (1,\~\~\~{\~wenn\~{{\i R}\\s\\do5({\fs16 2})} beobachtbar ist;} ,0,\~\~\~{\~wenn\~{{\i R}\\s\\do5({\fs16 2})} nicht beobachtbar ist.} )})}}{\fldrslt }}
\par
}\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li1200\fi-300 \fs20 4.\tab
Fehlende Daten sind genau dann {\scaps0\b0\i missing at random}, wenn f\'fcr i = 0,1 gilt:\par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb210 \li1200\fi0 \fs20 {{\field{\*\fldinst{ EQ {\i P}({\i O}\\s\\do5({\fs16 2})=1|{\i D}={\i i}\\,{\i R}\\s\\do5({\fs16 1})={\i r}\\s\\do5({\fs16 1})\\,{\i R}\\s\\do5({\fs16 2})={\i r}\\s\\do5({\fs16 2})){\u8801*}{\i P}({\i O}\\s\\do5({\fs16 2})=1|{\i D}={\i i}\\,{\i R}\\s\\do5({\fs16 1})={\i r}\\s\\do5({\fs16 1}))}}{\fldrslt }}
}\par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb210 \li1200\fi0 \fs20 \par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb50 \li1200\fi-300 \fs20 5.\tab
Fehlende Daten sind genau dann {\scaps0\b0\i missing completely at random}, wenn f\'fcr i = 0,1 gilt:\par
\pard\plain\s46\ql\fi-283\li283\lin283\sb0\sa120\widctlpar\tql\tx283\f0\fs24\sl240\slmult1 \sb210 \li1200\fi0 \fs20 {{\field{\*\fldinst{ EQ {\i P}({\i O}\\s\\do5({\fs16 2})=1|{\i D}={\i i}\\,{\i R}\\s\\do5({\fs16 1})={\i r}\\s\\do5({\fs16 1})\\,{\i R}\\s\\do5({\fs16 2})={\i r}\\s\\do5({\fs16 2})){\u8801*}{\i P}({\i O}\\s\\do5({\fs16 2})=1)}}{\fldrslt }}
} \par
}}\pard\plain\s0\qj\widctlpar\f0\fs24\sl240\slmult1 \sb310 \fi0 \fs20 \par
}}
}}}