Evaluation Of Logistic Regression In Classification Of Drug Data In Kwara State

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1 Intrnational Journal Of Computational Enginring Rsarch (icronlin.com) Vol. 3 Issu. 3 Evaluation Of Logistic Rgrssion In Classification Of Drug Data In Kwara Stat, O.S. Balogun, 2 T.J. Aingbad, A.A. Ainrfon Dpartmnt of Statistics and Oprations Rsarch, Modibbo Adama Univrsity of Tchnology, P.M.B. 276, Yola, Adamawa Stat, Nigria 2 Dpartmnt of Mathmatical Scincs, Kogi Stat Univrsity, Anyigba, Kogi Stat, Nigria Abstract Th classification of individuals who ngag in illicit drugs into drug pddlrs and non-pddlrs on th basis of oral vidnc, typ and th quantity of xhibit found with thm usually pos problm for th purpos of proscution. This papr uss logistic rgrssion to classify offndrs into th two dichotomous dpndnt variabl (pddlrs or non-pddlrs) in ordr to as th wor of th agncy, National Drug Law Enforcmnt Agncy (NDLEA), rsponsibl for illicit drugs. Th data usd in this study includ ag of offndrs, typ and wight of xhibit collctd from th agncy. Th discriminant analysis was first usd by Abduladir and Emmanul (2) to classify th illicit drug offndrs into pddlrs and non-pddlrs basd on th data and thn usd by Balogun t tal (22) including som othr variabl to it. In litratur th author discovrd that th discriminant analysis cannot handl mixd data (discrt and continuous data) ffctivly instad logistic rgrssion bttr fit th data. Th modl corrctly classifid 95.4% original groupd cass with positiv and ngativ prdictiv valus 92.44% and 97.9% rspctivly, which ar highr than valus obtaind undr th discriminant analysis. It was discovrd that larg quantity of xhibit has mor ffct than othr variabls, yt thir inclusion significantly improvs th outcom of th findings. Kyword: Logistic rgrssion, classification, odds ratio, discriminant Analysis.. Introduction Logistic rgrssion is a mathmatical modling approach that can b usd to dscrib th rlationship btwn indpndnt or prdictor variabls to dichotomous dpndnt variabl (Klinbaum t al.998). Th modl has traditional bn appaling du to its prformanc in classification, th potntial to us its output as probabilistic stimats sinc thy ar in th rang[, ], and intrprtation of th cofficints in trms of th logodds ratio. It is spcially in biostatistical application whr binary classification tass occur frquntly (Hasti t al.2).agrsti (996) assrtd that rlationships btwn th probability of succss (x) and X ar usually nonlinar rathr than linar. Thrfor a fixd chang in X may hav lss impact whn (x) is nar or than (x) is in th middl of its rang.logistic rgrssion is oftn chosn if th prdictor variabls ar a mixtur of continuous and catgorical variabls and/or if thy ar not nicly distributd, that is, logistic rgrssion mas no assumptions about th distribution of prdictor variabls. Th logit analysis is usually mployd if all th prdictors ar catgorizd whil discriminant function analysis is usd if all th prdictors ar continuous and nicly distributd (s This paragraph motivatd th author to ranalyz th data obtaind on illicit drug using logistic rgrssion analysis (Abduladri, 22). Th data was first usd in a papr by Balogun t al, 22 using discriminant analysis whil th data includs both qualitativ and catgorizd prdictor variabls. In th papr th authors blivd that th agncy, Th National Drug Law Enforcmnt Agncy chargd with th rsponsibility of daling with drug and drug rlatd offncs, in som occasion, may not b abl to distinguish btwn drug pddlrs and non- pddlrs on th basis of oral vidnc on possssion and daling with illicit drugs. Thrfor, thr is nd for a scintific mthod to mploy in ordr to classify futur offndrs into pddlr or non-pddlr if som variabls such as ag of offndrs, lngth of daling in illicit drugs, typ of xhibit, wight of xhibit and so on ar nown. Th involvmnt in illicit drug has so many social implications som of which includ prostitution, thft, sxual assaults on fmal fols. According to Odid (992), thos involvd in pddling ar ignorant of th problm manating from it. It is tru that a small numbr of popl, mainly thos organizing th illicit drug trad, ma larg profits from illicit crop cultivation, but th vast maority of popl, including most of thos bnfiting from such trad, ar advrsly affctd by th illicit activity. In th long trm, th illicit industry causs maor problm that vntually affct th conomic dvlopmnt of th country concrn. ( On this prmis th author bliv offndrs, spcially pddlrs/trafficrs dsrv stiff pnalty than th usrs, bcaus without sllr buyr will not xist and invariably rducs or liminat th activity in th systm. Thrfor, th laws concrning th illicit drug nd to b rformd to rflct th nw ida of trating pddlrs with stiffr pnalty than non-pddlrs. This will b th rsponsibility of th lgislators to appropriat th nabling laws. 54 Issn (Onlin) March 23

2 Evaluation Of Logistics Rgrssion In In USA th amount of quantity of illicit drug dtrmins th lngth of sntnc pass on th offndrs. Howvr, th larg quantity or numbrs of itm sizd usually ma th calculation of total quantity cumbrsom, hnc th us of statistical sampling such as multistag, composit and simpl random samplings hav bn adoptd. A rul of tumbl dvlopd by Iznman (2) for dtrmination of sampl siz is squar root of N, N, whr N is th numbr of itms in a containr is popular. A 95% confidnc intrval is dvlopd to rduc th rror for using th rul.sinc th aim of th study is to dtrmin whthr or not an offndr can b classifid as a pddlr/trafficr on th bass of ag of offndr, typ, and wight of substanc, thrfor larg quantity as nvr bn rportd in litratur to hav influncd th logistic rgrssion modl. Howvr, som larg quantity which could hav bn considrd as outlirs in th data collctd was includd/rmovd to dtrmin th ffct on th rsult of th study. Th logistic rgrssion is mployd for classification of obcts into binary variabl as Drug pddlr Y = Non pddlr According to Gansalingam (989), classification of obcts to groups is usually thought of as partition of obcts into substs in which th mmbrs ar mor similar. Classifying individuals into groups such that thr is rlativ homognity within th groups and htrognity btwn th groups is a problm which has bn considrd for many yars. For this papr th author intnts to r-classify obcts into groups in which thy wr nown to blong using logistic rgrssion analysis. 2. Logistic Modl Lt X, X 2,..., X p b prdictor variabls which consist of qualitativ and quantitativ variabls and Y as a dichotomous dpndnt variabl, whr Y is codd as or for its two catgoris as indicatd abov. E (X) = () xp[ ( B B x )] This quation can b writtn in a form that dscribs th probability of occurrnc of on of th two possibl outcoms of Y, as follow P(Y=) = (2) xp[ ( B B x )] In gnral, f(z) = z whr z = B + B X Th function f(z) is calld logistic function. This function is wll suitd to modling a probability, sinc th valus of f(z) varis from- to +. Th logistic modl, thrfor, is st up to nsur that, whatvr stimat of ris w gt, it always falls btwn and. This is not tru for othr modls, which is why th logistic modl is oftn usd whn a probability must b stimatd. 3. Estimating Th Odds Ratio Using Logistic Rgrssion Th rgrssion cofficints B in th logistic modl givn in () play an important rol in providing information about th rlationships of th prdictors in th modl to th xposur variabl. Th qualification of this rlationship involvs a paramtr calld th odd ratio (Klinbaum t.al, 998) Th odd ratio is a masur of ffct bcaus it is a masur that compars two or mor groups in prdicting th outcom variabl. Th odd of an vnt D = {Y=} Pr( D) Odds (D) = Pr( D) Any odds ratio is dfind as a ratio of two odds. Th logistic rgrssion is writtn as Logit [Pr(Y=)] = log [odds(y=)] 55 Issn (Onlin) March 23

3 Evaluation Of Logistics Rgrssion In Pr( Y ) = log. Pr( Y ) Thus, quation () bcoms B X Logit [Pr(Y=)] = B + Th odds ratio, say, for groups A and B can b dfind as ( X A X B ) B In gnral th odds ratio for groups A and B in givn by ( X A Odds for X A Odds for X B X B = ) B ( B ( B B X B X A B ) ) =.. (3) Th constant trm B in th logistic modl () drops out of th odds ratio xprssion in (3). Th xprssion (3) dscribs a population odds ratio paramtr bcaus th B trms in th xprssion ar thmslvs unnown population paramtr. An stimat of this population odds ratio is obtaind by fitting th logistic modl using maximum lilihood stimation and substitut in th ML stimats B, togthr with th valus of X A and X B, into th formula (3) to obtaind a numrical valu for th odds ratio. 4. Rsults And Discussion A total numbr of 262 cass of illicit drugs which compriss of 9 drug pddlrs and 43 nonpddlrs was xtractd from th rcord of NDLEA in Kwara and considrd for this study. Th avrag ag of th pddlrs is 27.76yars with a standard dviation of 8.6 whil th avrag ag of non-pddlrs is 28.7 yars with standard dviation of Th xhibit typ for th pddlrs and non-pddlrs ar.4 and.6 rspctivly. Th avrag wights of xhibit caught with pddlrs and non-pddlrs ar grams and grams rspctivly.th tabl blow dpicts th Naglr R squar of 88% of th total variation in th outcom variabl (drug status- pddlrs and non-pddlrs) xplaind by th logistic rgrssion modl fittd into th data. Tabl : Modl summary Stp -2 Log lilihood Cox & Snll R Squar Naglr R Squar Th stimats of th logistic rgrssion modl paramtrs ar prsntd in Tabl 2blow. Th Wald statistics for ag xhibit wights and gndr ar 2.345, and 8.88 rspctivly. Ths show that th thr ar important ris factors to dtrmin th status of illicit drug offndrs. Th xhibit wight and gndr ar mor important that th ag going by th valu of th Wald statistic, bsids th Wald valu for ag is not significant whil that of xhibit wight and gndr is highly significant (P-valu of. and.3)rspctivly. Th odds ratio for ag is.65 maning that an incras in ag by on yar ag will incras th rat of pddling by.65 (95% C.I..983 to.54). 56 Issn (Onlin) March 23

4 Evaluation Of Logistics Rgrssion In Tabl 2: Estimats of th Logistic Rgrssion Modl 95% C.I. for Exp(B) B S.E. Wald df Sig Exp(B) Lowr Uppr Exhibit typ Ag Exhibit Wight Gndr Constant Th ovrall accuracy of this modl (logistic rgrssion) to prdict bcoming a drug pddlr, with a (prdictd probability of.5 or gratr) is 95.4% as shown in Tabl 3.Th prdictiv modl is z = ag+2.65gndr -.726Exhibit Typ -.Exhibit Wight. Th intrst is to us this modl (logistic rgrssion) to prdict th outcom for a nw cas. To dtrmin how good th modl is w computd th followings: Th snsitivity from Tabl 3is 96.35% Tabl 3: Classification Rsult (for logistic modl) Obsrvd Prdictd % Corrct 3 4 Ovrall % % of th original groupd cass corrctly classifid. and spcificity is 93.96%. Th positiv prdictiv valu (PPV) is 92.44% and th ngativ prdictiv valu (NPV) is 97.9%. Ths rsults show that whnvr w hav a nw subct, w can us logistic modl to prdict his probability of bcoming a drug pddlr. For instanc, if givn th gndr, ag of a nw subct, th wight and th typ of xhibit caught with him and if th prdictiv modl givs a low probability, it mans that th subct is vry unlily to bcom a drug pddlr bcaus th NPV rvals that w should b 97.9% confidnt and on th othr hand if th modl givs high probability it mans that th subct is vry lily to bcom a drug pddlr bcaus th PPV givs 92.44% confidnc. Th summary rsults obtaind undr th discriminant analysis ar prsntd in Tabl 4 and 5 to ustify th nd to us logistic rgrssion whn variabls contain both discrt and continuous data. Tabl 4: Tst for Equality of Group Mans (through Discriminant Analysis ANOVA tsts) Wils Lambda F Df Df2 Sig Y Y Y Y Th abov Tabl4 contains th rsults obtaind whn discriminant analysis was mployd to classify th drug trafficrs. In th tabl th Y rprsnts typ of xhibit, Y 2 th ag of offndr, Y 3 th wight of xhibit and Y 4 th gndr of th offndr. All th four variabls usd in th modl xcpt on, Y 3, is significant. This implis that only wight of xhibit can b usd to prdict whthr a drug offndr is a pddlr of illicit drug or not. 57 Issn (Onlin) March 23

5 Evaluation Of Logistics Rgrssion In Tabl 5: Classification Rsults (for Discriminant Analysis) Obsrvd Prdictd % Corrct Ovrall % % of original groupd cass corrctly classifid. Comparing Tabls 3 and 5 of classification abov th ovrall prcnt groupd cass corrctly classifid is highr whn logistic rgrssion modl was mploy to classify th illicit drug offndrs. Th positiv prdictiv valu is 56.3% whil th ngativ prdictiv valu is 84.62% Conclusion Th logistic rgrssion modl and discriminant analysis wr usd to classify data collctd on illicit drug offndrs. Th rsults obtaind whn logistic rgrssion was mployd shows that 95.6% of th original groupd cass corrctly classifid whil discriminant analysis corrctly classifid 46.45% of th sam group. Morovr, th discriminant analysis rsults indicat that only wight of xhibit is significant in classification of offndrs, but th logistic rgrssion includs, in addition, th typ of xhibit and ag of offndrs as important variabls in th classification. Although th larg quantity of xhibit has mor ffct than othr variabls, yt thir inclusion significantly improvs th outcom of th findings. Rfrncs [] Abduladir,.S.S. and Emmanul,.T.(2),Discriminant Analysis and Classification of Drug Pddlrs and Non-Pddlrs.Journal of Rsarch in National Dvlopmnt.Vol8() [2] Abduladir,.S.S., Assssmnt of Logistics Rgrssion for Classification of Drug Data. Intrnational Journal of Scinc and Tchnology Volum No., Octobr, 22 [3] Agrsti,.A. (996), An Introduction to Catgorical Data Analysis. John Wily and Sons.Nw Yor [4] Balogun,.O.S.; Oyola,.B.A.;Aingbad,.T.J. (22), Us of Discriminant Analysis in Classification of Drug Pddlrs and Non-Drug Pddlrs in Kwara. Intrnational Journal of Enginring Rsarch and Application. Vol.2, Issu 5, Pp [5] Gansalingam,.S. (989), Classification and Mixtur Approachs to Clustring via Maximum lilihood. Applid Statistics,38.no 3,Pp [6] Hasti,.T. ;Tibshirani,R;and Fridman,.J.H.(2), Th Elmnts of Statistical Larning.Springr. [7] Iznman,.A.J.(2),Lgal and Statistical aspct of th fornsic study of illicit drugs,statistical Scinc,6. [8] Klinbaum,.D.G; Kuppr,.L.L;Mullr,.K.E.,and Nizam,.A.(998) Applid Analysis and Multivariat Mthods. Third Edition. Duxbury Prss. [9] Odid, A.O. (992), Drugs in th Third World. In Drugs and Socity to Yar 2, Ed by Vamos and CorrivanPp 6 9. [] [] 58 Issn (Onlin) March 23