رگرسیون لجستیک

صفحه 1:
Logistic Regression 

صفحه 2:
Aims * When and Why do we Use Logistic Regression? — Binary — Multinomial Theory Behind Logistic Regression — Assessing the Model — Assessing predictors —Things that can go Wrong Interpreting Logistic Regression 

صفحه 3:
Why can’t| use linear regression?) ١ When And Why » To predict an outcome variable that is categorical from one or more categorical or continuous predictor variables. * Used because having a categorical outcome variable violates the assumption of linearity in normal regression. 

صفحه 4:
With One Predictor Outcome — We predict the probability of the outcome occurring b, and by — Can be thought of in much the same way as multiple regression — Note the normal regression equation forms part of the logistic regression equation 

صفحه 5:
With Several Predictor Outcome — We still predict the probability of the outcome occurring Differences — Note the multiple regression equation forms part of the logistic regression equation — This part of the equation expands to accommodate additional predictors 

صفحه 6:
Assessing the Model log- likelinood=¥"[y,In( Ay) ‏سا‎ y)In(1- Ay,)] i=1 —Analogous to the residual sum of squares in multiple regression —It is an indicator of how much unexplained information there is after the model has been fitted. —Large values indicate poorly fitting statistical models. 

صفحه 7:
Assessing Changes in ۱ Models * It’s possible to calculate a log- likelihood for different models and to compare these models by looking at the difference between their log- likelihoods. 72 =ALL(New- LL( Baseline (dF =kyew Kpaselirle 

صفحه 8:
Assessing Predictors: The Wald Statistic ها Similar to 25356 ‏ذأ‎ 66 Tests the null hypothesis that 6 = 0. Is biased when bis large. Better to look at Likelihood-ratio statistics. 

صفحه 9:
Assessing Predictors: The Odds Ratio or Exp(6) Indicates the change in odds resulting from a unit change in the predictor. — OR > 1: Predictor 1, Probability of outcome occurring 1 — OR < 1: Predictor 7, Probability of outcome occurring by 

صفحه 10:
< 4 ۷/0۱ کم ‎should luse? _/‏ -\\ Methods of Regression, * Forced Entry: All variables entered } ~ ۱ simultaneously. a * Hierarchical: Variables entered in blocks. — Blocks should be based on past research, or theory being tested. Good Method. * Stepwise: Variables entered on the basis of statistical criteria (i.e. relative contribution to predicting outcome). — Should be used only for exploratory analysis. 

صفحه 11:
Assumptions from Linear Reg — Linearity — Independence of Errors — Multicollinearity Unique Problems — Incomplete Information Complete Separation verdispersion 

صفحه 12:
م۴۳۵۵ 6 jorical Predictors: sdicting cancer from smoking and eating atoes. We don’t know what happens when nonsi tomatoes because we have no data in this ۲ design. ntinuous variables Il your sample contain a to include an 80. ighly anxious, Buddhist left-handed crick 

صفحه 13:
plete Separ * When the outcome variable can perfectly predicted. —E.g. predicting whether someone is a bi or your teenage son or your cat based weight. — Weight is a perfect predictor of cat/burgle unless you have a very fat cat indeed! 

صفحه 14:
Overdispersion * Overdispersion is where the variance is larger than expected from the model. » This can be caused by violating the assumption of independence. * This problem makes the standard errors too small! 

صفحه 15:
An Example >redictors of a treatment interv Participants _- 113 adults with a medical problem » Outcome: _— Cured (1) or not cured (0). Predictors: — Intervention: intervention or no treatme! = Duration: the number of days before — treatment that the patient had the pri 

صفحه 16:
Pee ees Couns co nt cond ‏سس سح‎ ‏شتسه‎ ١ ‏سسا‎ ۳ ik Rg ‏سام‎ ‏وه سا یمیت‎ hone ۵ ‏وم سود‎ foe vee ‏موق‎ ‎0 oh ۳ سا اج اسر ‎Boas‏ میس ‎Sra Bea‏ ‘ec Brecon [Bivens ‏مت سس‎ 3 ‏وس مهد‎ 

صفحه 17:
سي م ۳ ۵ سا 0 Nowe Rao Ne ERG ‏دم‎ ۳ سس 

صفحه 18:
Cured? Numeric Inienention ۳ 6 Number ofDay.. Non 

صفحه 19:
2۳7 لاما يك ‎ight‏ ight ‏سس‎ ight @ Seal 6 ۵ ۵ اك 55 ۲ ۲ ۳۰۲ ۲ ۲ بح و۳ 2 و ing | Couns | 38 1 3 Signed ۳۷ لد | ‎Decale) Label‏ | ا | ‎Nine‏ ‎Cue ۳‏ .0( سه ۱ و سا مه ‎ore‏ مس و ع« پم ‎Rumate Number fap More‏ مه 

صفحه 20:
Missing 5 ‏و‎ كت ‎cued? (2, Not Cured None 1‏ امار و ‎Nene‏ ان ص وج سا مر ‎None‏ 6 سا ‎Imensition‏ ‏و مسا 8 Dursion une Cured oe عد سد مسد يا هط 17 ویو ی یمس 4 * ل مهن ۸ Fewer were Framerate om coco torrets 

صفحه 21:
ase processing Summary Taare ‏ان‎ م 50 10 و 2 متس عت ملاتا سات 00 vate Conse 9 Frequency ‎ao‏ عم ‎ ‎ ‎۳ ‎Block 0: Beginning Block ‎oration Histon = ‎con ‎ ‎ ‎ ‏مج ا سد ا 211 ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 

صفحه 22:
وتات 1 5 لف دا ‎os‏ مه اون ovina Geno _omeom 30 Ya ] ۳ nt te uation 777 7 977 5 

صفحه 23:
ل ست تنس ۳2 تفای | ی ار 1 6 |7030 ‎sasiee | -200 ree‏ ۳ 200 رم 0 00 inte moe 6 inita-2L09 Likathood. 154084 AL. Satimatin tetminate a eraton number 3 because paramolt Geiraige changed svisce E300} ‘Oru Tests of ode Caemctenss 35 تیه ‎OE‏ 836 ‎ome 02‏ ‎on‏ 9.928 مسمس ] “ies ] Soxeerel ‏هر‎ | 

صفحه 24:
Equation for Step 1 Varibles inthe Equation 17 | ‏جع‎ ar) 5 7 Sp mienenren 1 DF 14 e-©298+1.229(Intervention)) ۱ و ‎٩.۳‏ سه ای با او ام و ‎dds oF‏ ۱ روج ‎Or‏ ‎wis 1 OS% O11 oF 1.G00 MD.‏ ,| امد ع سا ما و ‎oP‏ سا مس ‎‘he ‏موه بط موه‎ thier cobra ‏مج رو‎ dope erro ( (bos ues oe eter than (1), Phi i koporknt bene okies ‏نج ما میم سس‎ varkble(s) ‏وه‎ sv do the ockds of (ia hie ae) bei cured. Ockeer fees tra (1 ‎he ‏اجه نموه‎ predotor kere, te kts of beret ered deo ‎ ‎ ‎ ‎ ‎ 

صفحه 25:
Step? Variables Duration Duration by intervention 0 Overall Statistics 

صفحه 26:
7۳ .6 ‏صا‎ ‏سر‎ upon bos we a 90/60 

صفحه 27:
anaes Grophs Wes adden _Wesow ‏ع‎ ‎eat ‎Desc ‏مس‎ ‎compare teens ener Lines Mode etre ١ ١ ‏صوق‎ ‎١ ‎0 ‎9 ‎7 ‏ومع‎ 0 | ١ 1 , 0 0 Rocgrcutes ‏مهس تا‎ ‏مه سس و۳‎ ‎ur re‏ 0 یسیو بیج ‎neve er‏ عرصم ‎Po LB er‏ | الم لجسو ص - 7 لاصف ی گر ۳ ‎P orecta tw wave ۳ FEF]‏ ام ها دامس مس رد مق ‎beacg rons‏ 2 ‎F Lovee vain ke‏ ‎vrata au‏ 9( ‎seer ‎1 ‎ ‎ee ‎sony ‏هموح ‎ ‎ ‎ ‎Woy cose‏ ونیم ‎fis]‏ هس تساج ص ل را مره 7 موس ] | 7 ‏اسر سس سح ۳2[ ‎anvil ‎aston Reopens 9 ‏هه‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 

صفحه 28:
‘seu 700 Net oures ‏مت‎ ‎uo ‏مت‎ ‎owes ‎ures ‎Net owes Net cures ‏مه مد‎ ‏دان امار‎ wes مهد case Summaries? Tamera 9 Prose له 47 وود 20957 71930 42387 سس 71930 وود 0 تس وود 7 7 1 Intervention 17 NoTeatment ‏و‎ ‎0 ‎Io Tresiment Intention ‏مسر‎ ‎NoTreatment ‎NoTreatment ‎oTrearean ‎No Teaerant Iron No Treamen 15 10 Notouree ‏مت‎ ‏مرج‎ ‎cured مود cues urd Notcuree curs curs مهد Norcures 15 ممم 1010016006116 3 

صفحه 29:
Summary The overall fit of the final model is shown by log-likelihood statistic. — If the significance of the chi-square statistic is less than .05, then the model is a significant fit of the data. Check the table labelled Variables in the equation to see which variables significantly predict the outcome. Use the odds ratio, Exp(B), for interpretation. — OR > 1, then as the predictor increases, the odds of the outcome occurring increase. — OR < 1, then as the predictor increases, the odds of the outcome occurring decrease. — The confidence interval of the OR should not cross 1! Check the table /abelled Variables not in the equation to see which variables did not significantly predict the outcome. 

صفحه 30:
Reporting the Analysis TABLE 8.3 How to report logistic re ونا 0005 ‎٠6١‏ [© 9596 یت نت۱ ۱0۷۵۴ (8)58 Included Constant -0.29 (0.27) Intervention 4.23" (0.40) 1.56 3.42 7.48 

صفحه 31:
تا = ۳ 0 4 . ۳ 5 تتم اوها ‎ultinomial‏ ‎regression‏ * Logistic regression to predict membership of more t| two categories. It (basically) works in the same way as binary-logi: regression. The analysis breaks the outcome variable down into’ series of comparisons between two categories. — E.g., if you have three outcome categories (A, B and C), then the analysis will consist of two comparisons that } choose: + Compare everything against your first category (e.g. A vs. Avs. C), + Or your last category (e.g. A vs. C and B vs. C), + Ora custom category (e.g. B vs. A and B vs. C). percent parts of the analysis and output < me as we have just seen for binary ion 

صفحه 32:
| may not be Fre ۳ ‏ور‎ he, ۳۹9 chat-up lines used by 348 men and 672 a night-club were recorded. * Outcome: — Whether the chat-up line resulted in one of the following three events: + The person got no response or the recipient walked away, + The person obtained the recipient’s phone number, + The person left the night-club with the recipient. * Predictors: — The content of the chat-up lines were rated for: + Funniness (0 = not funny at all, 10 = the funniest thing have ever heard) * Sexuality (0 = no sexual content at all, 10 = very s direct) * Moral vales (0 = the chat-up line does not reflect characteristics, 10 = the chat-up line is very indice jood characteristics). ler of recipient 

صفحه 33:
‘Sten Summary Pes Mode! Fitting Criteria Effect Salection Te: Tntereert, 3 i. Mate, Entered | Funny, Bani ger Furs ner?! 

صفحه 34:
0 |] a Fitting ۳ Likslinood Ratio Tests مه | م اظة ‘Cox and Snell Nagelkerke McFadden, 

صفحه 35:
-2Log ‏ماع‎ ‎od of 1062" 100 077324 | 2 107" 100 889.540 | 8 102" 100 906810 | 8 84.4511 56 2 967, 960.454 967.987 972.671 967.987 989.941 967.582 Intercent Good_Mate 901.324 299.002 913.540 sex 899.002 Gender* Funny | 0 Gender*sex__} 908.454 The chi-square statistic is the difference in -2 log-likelihood between the final |The reduced model is formed by omitting an effect from the final model. The null hypothesis is that all parameters of that effect are 0 a. This reduced model is equivalent to the final model because omitting the effect does not increase the degrees of freedom, model and a reduced mod 

صفحه 36:
Output Parameter Estimates 25 Contuares nenal Ee uocans of that Up Lino p__| swe | waa | ot ‏وه‎ upper ‏مرسمه‎ ‎GetPrene Number nieroant 1 788 ero | ۳ ۱ ۶ ood Mate 12 ose | e022 +f oo] aaa soz 4208 Fury 130 no] 1.902 ‏مق‎ 976 saa Isencoroy 1 588 rag | 4274 1| ‏د ]وهم‎ nso ‏ل‎ ‎Isencer=t] 0 0 See a6 ‏مه | مه‎ 1| on] tae 4407 1570 ‏هرمع‎ | 452 0 | 4 | oon] 166 sae 2159 Iencer=t]* Funny o 0 ‏ات‎ * 34 8 soe | ‏مهد‎ 1| oo | ‏ست‎ ora 880 Isencor1] 50% ۳ 0 50 ۳2 ۳ — ifercept 1286 841 | 1 1 0 Boad_Mate 130 ose | 2028 1} azo] tase ost vat Funes | 318 i | nasa vf oon] 1398 4078 4758 Ieencer=0 soz6 | 120 | arose 1| ooo] ‏ممم‎ oo oo Ioencer=t] o 0 sex 47 ta] 1.889 + | oo | 1518 1196 1928 ‏دعر‎ | 4472 1399| 77 + ooo | a2a0 2.188 ara 0۵۵۵۱ ۳ a Isencorg} sox 7 tea | asns + {ons | ‏م‎ ast 856 ‏“ات امقر‎ 0 03 77۳ ‏عاماماعة معد و‎ 65 This parameters Sette E10 because t's ecunsant 

صفحه 37:
Interpretation Good _Mate: Whether the chat-up line showed signs of good moral fibre significantly predicted whether you got a phone number or no response/walked away, b = 0.13, Wald x2(1) = 6.02, p < .05. Funny: Whether the chat-up line was funny did not significantly edict whether you got a phone number or no response, 6 = 0.14, ald x2(1) = 1.60, p > .05 Gender: The gender of the person being chatted up significantly predicted whether they gave out their phone number or gave no response, b = —1.65, Wald x2(1) = 4.27, p< .05. Sex: The sexual content of the chat-up line significantly predicted whether you got a phone number, or no response/walked away, ۵ = 0.28, Wald x2(1) = 9.59, p< .01. FunnyxGender: The success of funny chat-up lines depended on whether they were delivered toa man or a woman because in interaction these variables predicted whether or not you got a phone number, b = 0.49, Wald x*(1) = 12.37, p< .001. Sexx Gender: The success of chat-up lines with sexual content depended on whether they were delivered to a man or a woman because in interaction these variables predicted whether or not you got a phone number, b = —0.35, Wald y2(1) = 10.82, p < .01. 

صفحه 38:
Interpretation Good Mate: Whether the chat-up line showed signs of good moral fibre did not ponincently predict whether you went home with the date or got a slap in the face, b = 0.13, Wald ۶)1( = 2.42, p> 5, Funny: Whether the crate line was funny significa predicted whether you went home with the date or no response, 6 = 0.32, Wald (1) = 6.46, p< .05. Gender: The gender of the person being chatted up significantly predicted whether they went home with the person or gave no Tesponse, b = —5.63, Wald y~(1) = 17.93, p< .001. Sex: The sexual content of the chat-up line significantly predicted whether you went home with the date or got a slap in the face, D = 0.42, Wald y*(1) = 11.68, p< .01, FunnyxGender: The success of funny chat-up lines depended on Whether they were delivered to a man or a woman because in interaction these variables predicted whether or not you went home with the date, b = 1.17, Wald y%(1) = 34.63, p< .001. Sexx Gender: The success of chat-up lines with sexual content depended on whether they were delivered to a man or a woman because in interaction these variables predicted whether or not you went home with the date, b = —0.48, Wald (1) = 8.51, p <.01. 

صفحه 39:
44 How 10 report mutinomial logistic regression. Phone Numba vs, No Fesporse Intercept 76 ‏وم‎ ‎Good Mato 2 609۴ Funny 14017 Gender 1.65 0.80)* Sexual Content 26 (009)"* Gonder » Funny 0 04۳ Gender x Sex 35 (0.11)** Going Homa va. No Responce Intercept 4.29 ‏موم‎ ‎Good Mete 19 (0.08) Funay 22 (0.19) Gender B63 1.39)¢4" ‏ادمع‎ Content 220.412)" Gender x Furry 7 0 Gender Sex 48 (010)