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Log line ære modeller for kontingenstabeller

Log line ære modeller for kontingenstabeller. Kontingenstabeller Test for uafhængighed af inddelingskriterier Sammenligning med logistisk regression Odds and odds ratios Goodness -of-fit/BIC Log lineære modeller. Kontingenstabel. Contingency: mulighed/tilf ælde

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Log line ære modeller for kontingenstabeller

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  1. Log lineære modeller for kontingenstabeller • Kontingenstabeller • Test for uafhængighed af inddelingskriterier • Sammenligning med logistisk regression • Odds and odds ratios • Goodness-of-fit/BIC • Log lineære modeller

  2. Kontingenstabel • Contingency: mulighed/tilfælde • Kontingenstabel: antal observationer i klasser givet ved krydstabellering af et antal variable. • Tovejs tabel (Powers and Xie side 89):

  3. Notation f_ij: observeret antal i ij’te celle f_i+: observeret antal i i’te række F_ij: forventet antal i ij’te celle (ukendt parameter) F_i+ = F_i1+F_i2: forventet antal i i’te række (ukendt parameter)

  4. Test for uafhængighed

  5. Relation til logistisk regression

  6. Ex. X^2 for ens binomialfordelinger: (873-762.5)^2/(2063*0.37*0.63)+(533-643.5)/(1741*0.37*0.63)=55.48

  7. Generel to-vejstabel Ækvivalens med logistisk regressionsmodel kun hvis I=2 eller J=2)

  8. Eksempel X^2=94.4 (15-6=9 frihedsgrader)

  9. Odds ratios 2 gange 2 undertabel: Estimeret odds ratio for næsten altid versus nogen gange: Less than HS: (99/240)/(141/240)=99/141=0.70 HS: 129/258=0.50 Odds ratio=0.5/0.7=0.71 dvs mindre odds for imod når HS. NB: odds ratio=1 hvis uafhængighed !

  10. Modeller for kontingenstabeller

  11. Ex: likelihood ratio uafh. model vs. mættet model.

  12. Bayesian information criterion • Skelne mellem signifikante effekter og relevante effekter ! alle effekter er signifikante når antal observationer er stort nok. • BIC=G^2- antal frihedsgrader * log antal obs. • Lille værdi af BIC betyder bedre model. • Straffer modeller med mange parametre (=lille antal frihedsgrader) og straffer mere hvis mange observationer.

  13. Log lineære modeller

  14. Fortolkning via odds/odds ratios

  15. Eksempel: kørekort vs. antal biler

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