Logit vs Probit Models: Differences, Examples - Data Analytics

Logit and probit models are statistical models that are used to model binary or dichotomous dependent variables. This means that the outcome ... DataAnalytics Data,DataScience,MachineLearning,AI SelectapageHome MachineLearning     DeepLearning     Python InterviewPreparation FreeAI/MLOnlineCourses Shop LogitvsProbitModels:Differences,Examples April1,2022byAjiteshKumar·1Comment Logitandprobitmodelsarestatisticalmodelsthatareusedtomodelbinaryordichotomousdependentvariables.Thismeansthattheoutcomeofinterestcanonlytakeontwopossiblevalues.Inmostcases,thesemodelsareusedtopredictwhetherornotsomethingwillhappen.Forexample,abusinessmightwanttoknowifaparticularadvertisingcampaignwillleadtoanincreaseinsales.Inthisblogpost,wewillexplainwhatlogitandprobitmodelsare,andwewillprovideexamplesofhowtheycanbeused.Asdatascientists,itisimportanttounderstandtheconceptsoflogitandprobitmodelsandwhenshouldtheybeused. TableofContents WhatareLogitmodels?WhatareProbitmodels?WhatisthedifferencebetweentheLogitandProbitmodels? WhatareLogitmodels? Logitmodelsareaformofastatisticalmodelthatisusedtopredicttheprobabilityofaneventoccurring.Logitmodelsarealsocalledlogisticregressionmodels.Thelogitmodelisbasedonthelogisticfunction(alsocalledthesigmoidfunction),whichisusedtomodelsituationswheretherearetwopossibleoutcomes.Thelogisticfunctioncanbeusedtomodelavarietyofsituations,includingbinarydependentvariables,dichotomousdependentvariables,andcategoricaldata. Thelogitmodelisusedtomodeltheoddsofsuccessofaneventasafunctionofindependentvariables.Thefollowingisthestartingpointofarrivingatthelogisticfunctionwhichisusedtomodeltheprobabilityofoccurrenceofanevent. Alogitfunctioncanbewrittenasfollows: logit(I)=log[P/(1-P)]=Z=b0+b1X1+b2X2+…..+bnXn wherePistheprobabilityofaneventoccurring,andlistheoddsofaneventoccurring.Zisthelinearcombinationofindependentvariableswithcoefficients.Theaboveequationcanbesolvedfurthertoarriveatthefollowingfunctionwhichcanbeusedtodeterminetheprobabilityofoccurrenceoftheevents. $$P=\sigma(z)=\frac{1}{1+e^{-Z}}$$ Theσ(Z)isalsocalledalogisticorsigmoidfunction.AsthevalueofZapproaches-infinity,thevalueofσ(Z)orPapproaches0.And,asthevalueofZapproaches+infinity,thevalueofσ(Z)orPapproaches1. WhatareProbitmodels? Probitmodelsareaformofastatisticalmodelthatisusedtopredicttheprobabilityofaneventoccurring.Probitmodelsaresimilartologitmodels,buttheyarebasedontheprobitfunctioninsteadofthelogisticfunction.TheProbitmodeldeterminesthelikelihoodthatanitemoreventwillfallintooneofarangeofcategoriesbyestimatingtheprobabilitythatobservationwithspecificfeatureswillbelongtoaparticularcategory.InthecaseoftheProbitmodel,thedependentvariableiscategoricalandcanonlytakeononeofthetwovalues,suchasyesorno,trueorfalse. TheProbitmodelcanberepresentedusingthefollowingformula: Pr(Y=1|X)=Φ(Z)=Z=Φ(b0+b1X1+b2X2+…..+bnXn) Where,Yisthedependentvariableandrepresentstheprobabilitythattheeventwilloccur(hence,Y=1)giventhevariablesX.Φisthecumulativestandardnormaldistributionfunction. Zisthelinearcombinationofindependentvariables(X)withcoefficients(b0,b1,b2…bn).Inthecaseofthelogitmodel,weuselogisticorsigmoidfunctioninsteadofΦwhichiscumulativestandardnormaldistributionfunction. WhatisthedifferencebetweentheLogitandProbitmodels? ThefollowingaresomeofthekeydifferencesbetweentheLogitandProbitmodels: Thelogitmodelisusedtomodeltheoddsofsuccessofaneventasafunctionofindependentvariables,whiletheprobitmodelisusedtodeterminethelikelihoodthatanitemoreventwillfallintooneofarangeofcategoriesbyestimatingtheprobabilitythatobservationwithspecificfeatureswillbelongtoaparticularcategory. Inthecaseofthelogitmodel,weusealogisticorsigmoidfunctioninsteadofΦwhichisacumulativestandardnormaldistributionfunction. Logisticregressionmodelsarealsocalledlogitmodels,whileprobitregressionmodelsarealsocalledprobitmodels. LogitmodelsareusedtomodelLogisticdistributionwhileprobitmodelsareusedtomodelthecumulativestandardnormaldistribution. ThepicturebelowrepresentstheLogit&Probitmodels: Probitmodelsaslikethelogitmodelsareusedtopredicttheprobabilityofaneventoccurring.Probitmodelsaresimilartologitmodels,buttheyarebasedonprobitsinsteadlogisticfunctions.Theprobitmodeldeterminesthelikelihoodthatanitemoreventwillfallintooneofarangeofcategoriesbyestimatingtheprobabilitythatobservationwithspecificfeatureswillbelongtoaparticularcategory.Theprocessforcalculatingprobabilitiesinlogitandprobitsdifferfromeachotherbecauselogisticfunctionsuselinearcombinationswhileprobityusescumulativestandardnormaldistributionfunction. AuthorRecentPostsFollowmeAjiteshKumarIhavebeenrecentlyworkingintheareaofDataanalyticsincludingDataScienceandMachineLearning/DeepLearning.IamalsopassionateaboutdifferenttechnologiesincludingprogramminglanguagessuchasJava/JEE,Javascript,Python,R,Julia,etc,andtechnologiessuchasBlockchain,mobilecomputing,cloud-nativetechnologies,applicationsecurity,cloudcomputingplatforms,bigdata,etc.Forlatestupdatesandblogs,followusonTwitter.IwouldlovetoconnectwithyouonLinkedin.CheckoutmylatestbooktitledasFirstPrinciplesThinking:BuildingwinningproductsusingfirstprinciplesthinkingFollowmeLatestpostsbyAjiteshKumar(seeall) LearningCurvesPythonSklearnExample-September9,2022 MachineLearningSklearnPipeline–PythonExample-September9,2022 SequenceModelsQuiz1–TestYourUnderstanding-September5,2022 AjiteshKumar IhavebeenrecentlyworkingintheareaofDataanalyticsincludingDataScienceandMachineLearning/DeepLearning.IamalsopassionateaboutdifferenttechnologiesincludingprogramminglanguagessuchasJava/JEE,Javascript,Python,R,Julia,etc,andtechnologiessuchasBlockchain,mobilecomputing,cloud-nativetechnologies,applicationsecurity,cloudcomputingplatforms,bigdata,etc.Forlatestupdatesandblogs,followusonTwitter.IwouldlovetoconnectwithyouonLinkedin. CheckoutmylatestbooktitledasFirstPrinciplesThinking:Buildingwinningproductsusingfirstprinciplesthinking PostedinDataScience,MachineLearning,statistics.TaggedwithDataScience,machinelearning. ←LinearvsLogisticRegression:Differences,Examples StepsforEvaluating&ValidatingTime-SeriesModels→ OneResponse ObedChanda August29,2022at12:56am Thanks.Thisisquiteinformative.IfeelconfidentthatIcanusethesemodelsinresearchnow. 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