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data science course

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data science course

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  1. Advanced Regression Nega)ve Binomial Poisson Regression ZeroInflated Mul)nomial Regression AGENDA © 2013 ExcelR Solutions. All Rights Reserved

  2. Multinomial Regression •  Logis'cregression(Binomialdistribu'on)isusedwhenoutputhas‘2’categories •  Mul'nomialregression(classifica'onmodel)isusedwhenoutputhas>‘2’categories •  Extensiontologis'cregression •  Nonaturalorderingofcategories Modeof transport Car Carpool Bus Rail Allmodes Count 218 32 81 122 453 •  Responsevariablehas>‘2’categories&henceweapplymul'logit Probability 0.48 0.07 0.18 0.27 1 •  Understandtheimpactofcost&'meonthevariousmodesoftransport © 2013 ExcelR Solutions. All Rights Reserved

  3. Multinomial Regression Whetherwehave‘Y’(response)or‘X’(predictor),whichiscategoricalwith‘s’categories ü  Lowestinnumerical/lexicographicalvalueischosenasbaseline/reference ü  Missinglevelinoutputisbaselinelevel ü  Wecanchoosethebaselinelevelofourchoicebasedon‘relevel’func'oninR ü  Modelformulatestherela'onshipbetweentransformed(logit)Y&numericalXlinearly ü  Modelingquan'ta'vevariableslinearlymightnotalwaysbecorrect •  © 2013 ExcelR Solutions. All Rights Reserved

  4. Multinomial Regression - Output Itera'onHistory: •  Itera'veprocedureisusedtocomputemaximumlikelihoodes'mates •  #itera'ons&convergencestatusisprovided •  -2logL=2*nega'veloglikelihood •  -2logLhasχ2distribu'on,whichisusedforhypothesistes'ngofgoodnessoffit #parameters=27 © 2013 ExcelR Solutions. All Rights Reserved

  5. Multinomial Regression - Output ‘car’hasbeenchosenasbaseline •  x=vectorrepresen'ngthevaluesofallinputs •  Log(P(choice=carpool|x)/P(choice=car|x)=β20+β21*cost.car+β22*cost.carpool+……………. Thisequa'oncomparesthelogofprobabili'esofcarpooltocar Theregressioncoefficient0.636indicatesthatfora‘1’unitincreasesthe‘cost.car’,thelogoddsof‘carpool’to‘car’ increasesby0.636 •  Interceptvaluedoesnotmeananythinginthiscontext •  •  IfwehaveacategoricalXalso,sayGender(female=0,male=1),thenregressioncoefficient(say0.22)indicates thatrela'vetofemales,malesincreasethelogoddsof‘carpool’to‘car’by0.22 © 2013 ExcelR Solutions. All Rights Reserved

  6. Probability •  Letp=p(x|A)betheprobabilityofanyevent(sayairi'on)undercondi'onA(say gender=female) Odds •  Thenp(x|A)÷(1-p(x|A)iscalledtheoddsassociatedwiththeevent Odds Ratio •  Iftherearetwocondi'onsA(gender=female)&B(gender=male)thenthera'o p(x|A)÷(1-p(x|A)/p(x|B)÷(1-p(x|B)iscalledasoddsra'oofAwithrespecttoB Relative Risk •  p(x|A)÷p(x|B)iscalledasrela'verisk hips://en.wikipedia.org/wiki/Rela've_risk © 2013 ExcelR Solutions. All Rights Reserved

  7. Odds Ratio •  Oddsra'oiscomputedfromthecoefficientsinthelinearmodelequa'onbysimply exponen'a'ng •  Exponen'atedregressioncoefficientsareoddsra'oforaunitchangeinapredictor variable •  Theoddsra'oforaunitincreaseincost.caris1.88forchoosingcarpoolvscar © 2013 ExcelR Solutions. All Rights Reserved

  8. Goodness of fit Linear AnalysisofVariance ResidualDeviance OLS GLM AnalysisofDeviance ResidualSumofSquares MaximumLikelihood •  ResidualDevianceis-2logL •  AddingmoreparameterstothemodelwillreduceResidualDevianceevenifitisnot goingtobeusefulforpredic'on •  Inordertocontrolthis,penaltyof“2*numberofparameters”isaddedtoto Residualdeviance •  Thispenalizedvalueof-2logLiscalledasAICcriterion •  AIC=-2logL+2*numberofparameters Note:“Mul'logitModelwithInterac(on” © 2013 ExcelR Solutions. All Rights Reserved

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