Morten Frydenberg Wednesday, 12 May 2004

Transcription

1 " $% " * +, " --. / ",, 2 ", $, % $ 4 %78 % / "92:8/- 788;<= obese >?5"= "8= < "A57 57 "χ 2 = -value=. 5 OR =, OR = = = + OR B " B Linear ang Logistic Regression: Note.

2 = + OR 2 women - % β β = + woman = β, % = β + β. C β = β = OR β β = + woman OR β = OR vs % logor ORD? < 2 " % = = =.5 = = 2 logit logit = 7 robability logit= 8 β β $ logit logit = + woman β β = + woman E = + ex β β woman = + + ex β + β woman 9 / 2,, logit β β char sex[omit] xi: logit obese i.sex = = + woman i.sex _Isex_ naturally coded; _Isex_ omitted Iteration : log lielihood = Iteration : log lielihood = Logit estimates Number of obs = 49 LR chi2 =.5 Prob > chi2 =. Log lielihood = Pseudo R2 = _Isex_ _cons Linear ang Logistic Regression: Note. 2

3 logit ˆ β = OR β β = = + woman 75= OR _Isex_ _cons OR = ex =. 75= ;.59. OR= OR= " ;ex.8= ;47. 75= :.8;.425. logit β β = = + woman, xi: logit obese i.sex,or i.sex _Isex_ naturally coded; _Isex_ omitted Iteration : log lielihood = Iteration : log lielihood = Logit estimates Number of obs = 49 LR chi2 =.5 Prob > chi2 =. Log lielihood = Pseudo R2 = 9 obese Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Isex_ % D 2 2 F logit β β = = + age,age β "age;8 age;5 = = β + β age logit 45 5 = = β + β age logit 45 β 5 β % exβ % % % D *,, gene age45=age-45 logit obese age45 = = β + β age logit 45 Iteration : log lielihood = Iteration : log lielihood = Logit estimates Number of obs = 49 LR chi2 = 4 Prob > chi2 =. Log lielihood = Pseudo R2 = age _cons = = β + β age logit 45 β ;.895 +,.7 5;.5 +, 7.4;.7 age? < Linear ang Logistic Regression: Note.

4 logit = = β + β age 45 β.48 47; ;.459 % 2 +", ; =.7 ;2 2,, logit obese obese Odds Ratio Std. Err. z P> z [95% Conf. Interval] age log = age ex 45 revalence = + ex + 45 revalence age age - = β + β age 45, 4 / egen agegr7=cutage, at,5,4,45,5,55,,2 label table agegr7,cmin age max age count obese sum obeserow agegr7 minage maxage Nobese sumobese Total 4, , ds α od = + α agei i= agei i i - = α + αi agei i= α ; α i % i ; char agegr7[omit] xi: logit obese i.agegr _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _cons Linear ang Logistic Regression: Note. 4

5 - = α + β agei 5 i= xi: logit obese i.agegr7,or -- obese Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ ; , D - ds α od = + α agei * /H " testarm _Iagegr*. / _Iagegr7_ = 2 _Iagegr7_2 = _Iagegr7_ = 4 _Iagegr7_4 = 5 _Iagegr7_5 = _Iagegr7_ = chi2 = 55 Prob > chi2 =. I i= i char agegr7[omit] J 57 xi: logit obese i.agegr7,or -- obese Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ _Iagegr7_ , $+..; ", D? ˆ α ˆ α4.5 αˆ log < revalence log - - model model revalence 5 model model * / / = β + β woman + β age Linear ang Logistic Regression: Note. 5

6 * = β + β woman + β age 45 2 β 5 β % β 2 % % β 2 K age % % age * 45 = β + β woman + β age 2,, xi:logit obese i.sex age45 i.sex _Isex_ naturally coded; _Isex_ omitted Iteration : log lielihood = Iteration : log lielihood = Logit estimates Number of obs = 49 LR chi22 = 55.8 Prob > chi2 =. Log lielihood = Pseudo R2 = _Isex_ age _cons sex age $58= 5 * 45 = β + β woman + β age 2 xi:logit obese i.sex age45, or obese Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Isex_ age % L.; L.4 ; ;.5 D log * = β + β woman + β age 45 - men women revalence men women * -, = α + α age = γ + γ age L " = β + β woman + β age + β woman age α = β α = β 2 γ = β + β γ = β + β 2 β = γ α β = γ α 5 * = β + β woman + β2 age 45 + β woman age 45 xi: logit obese i.sex*age _Isex_ age _IsexXage4~ _cons > obese Odds Ratio Std. Err z P> z [95% Conf. Interval] _Isex_ age _IsexXage4~ Linear ang Logistic Regression: Note.

7 * = β + β woman + β age 45 + β woman age 45 log men men women ? revalence.. women * tab cancer age - age cases controls [95% Conf. Interval] >= ; + tab cancer age, or - age Odds Ratio chi2 P>chi2 [95% Conf. Interval] >= < * tab cancer age - age cases controls [95% Conf. Interval] >= * +; + tab cancer age, or base -- age Odds Ratio chi2 P>chi2 [95% Conf. Interval] >= * char age [omit] xi:logit cancer i.smoer i.age,or i.smoer _Ismoer_- naturally coded; _Ismoer_ omitted i.age _Iage_- naturally coded; _Iage_ omitted Iteration : log lielihood = Iteration : log lielihood = Iteration 2: log lielihood = Iteration : log lielihood = Iteration 4: log lielihood = Iteration 5: log lielihood = Iteration : log lielihood = Logit estimates Number of obs = 977 LR chi2 = 5 Prob > chi2 =. Log lielihood = Pseudo R2 = -- cancer Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Ismoer_ _Iage_ _Iage_ _Iage_ _Iage_ _Iage_ * char age [omit] xi:logit cancer i.smoer i.age,or i.smoer _Ismoer_- naturally coded; _Ismoer_ omitted i.age _Iage_- naturally coded; _Iage_ omitted Iteration : log lielihood = Iteration : log lielihood = Iteration 2: log lielihood = Iteration : log lielihood = Iteration 4: log lielihood = Iteration 5: log lielihood = Logit estimates Number of obs = 977 LR chi2 = 5 Prob > chi2 =. Log lielihood = Pseudo R2 = -- cancer Odds Ratio Std. Err. z P> z [95% Conf. Interval] _Ismoer_ _Iage_ _Iage_ _Iage_ _Iage_ _Iage_ % D Linear ang Logistic Regression: Note. 7

8 % 4, 2,, / LR chi2 = 5 Prob > chi2 =. / % %/ % / B B % 4 2,, xi:logit cancer i.smoer i.age estimates store model xi:logit cancer i.smoer estimates store model2 lrtest model model2 lielihood-ratio test LR chi25 = 2.82 Assumtion: model2 nested in model Prob > chi2 =. /D = + β x = β " $ " " β " " x x2 x = OR OR OR 2 5 β 2 x x % x 2 x 2 M x x = β x, % " = + β x = = + β x = β 2 x x % x 2 x 2 M x x x x2 OR = OR OR OR 2? x exβ + β x = = Pr[ Y = ] = + exβ + β x = Y =/ x %x 2 Mx - / N + %% / / $ 5. %" = + β x = β < Linear ang Logistic Regression: Note. 8

9 % % * % % * H 7 Linear ang Logistic Regression: Note. 9