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JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 1, JUNE, 2010


DISCRIMINANT ANALYSIS AND CLASSIFICATION OF DRUG PEDDLERS AND NON- PEDDLERS

S. S. Abdulkadir and Torsen Emmanuel
Department of Statistics and Operations Research, Federal University of Technology, Yola
E-mail: saidusauta@yahoo.com

Abstract.
It is sometimes difficult to classify individuals who engaged in drug activities into drug peddlers and non-peddlers on the basis of oral evidence and amount of substances found with them. This paper considers the use of dicriminant analysis and classification procedure to group persons arrested for drug related offences. The data on type, weight of exhibit and age of offenders collected from National Drug Law Enforcement Agency (NDLEA) were used for discrimination and classification. The discriminant score obtained was used for classifying the training samples and the analysis shows that 71.8% of the grouped cases were correctly classified.

Keywords: Classification, misclassification, heterogeneity, drug-peddler

 


Introduction
Discriminant analysis is a descriptive procedure of separation in which linear functions of the variables are used to describe or elucidate the differences between the two or more groups. That is, the aim of this analysis includes identifying the relative contribution of say, p variables to separation of groups and finding the optimal plane on which the points can be projected to best illustrate the configuration of the groups (Rencher,2002).

The classification of objects to groups is usually thought of as partition of the objects into subsets in which the members are more similar. Classifying individuals into groups such that there is a relative homogeneity between the groups and heterogeneity between the groups is a problem which has been considered for many years ( Ganesalingam, 1989). The National Drug Law Enforcement Agency (NDLEA) in Nigeria is not an exception. Some drugs are prohibited from open market either because of their side-effect or abuse by public. The drug could be in the  tablet or liquid form such as Marijuana,Heroin,Cocaine etc. To restrict the use government placed ban on them and offenders are penalized.

A socially undesirable class, including prostitutes, thieves and hoodlums had been known to use the forbidden drugs. The use also leads to violence among the users and also stimulates sexual assaults on female folks. According to Odejide (1992), those in peddling are ignorant of the magnitude of problems caused by drugs.  Persons or individuals arrested for drug related offences are taken to court and convicted based on the oral evidence supplied and amount of substances caught with them. It is taken as given that peddlers deserve a more stiff penalty than users. The reason being that dealing with prohibited drugs could be drastically reduced if those peddling face stiff penalties. These individuals are very difficult to classify into peddlers and non-peddlers on the basis of possession and dealing and other variables.
The current effort is believed to be the  first time a scientific method will be used to classify drug related offenders.
 Model
The discriminant function
  We assume that two populations (drug peddlers and non-peddlers) have the same covariance matrix . Furthermore, let ,…,  and ,..,  be samples from the two populations. Each vector Y consists of measurements on P variables(where P =3). The discriminant function is defined by


 

 

D( ) =  a y ….……………………………………………………(1)


The maximum of (1) occurs when a = S (  or when a is a multiple of S (   where ( ) is a 1 x n vector of discriminant scores, a  is a 1xp vector discriminant weight,and  Y is a p x n matrix containing the values of the n individuals on the p independent variables .S is the inverse of the pooled sample variance-covariance matrix.

Classification procedure
The classification procedure due to Fisher’s procedure is used in this paper. The principal assumption for Fisher’s procedure is that the two populations have the same covariance matrix ( . Normality is not required.
The classification is based on the discriminant function.


D( )=a  = (  S  ……………………………………………(2)

Classification rule
Assign an individual into group one (peddler) if
D( )=( S >  (  S  ( ………………………..(3)


And if otherwise assign to group two (non-peddler). Alternatively one can use the optimal classification rule discussed below to obtain similar results

The optimal classification rule
 Suppose  and are any two normal populations. Also P and P are the corresponding prior distributions for the populations with P + P  = 1 and probability density function f(x). Suppose that we assign an item X  into  if it is from region R  and to  if it is in region R where R U R = R. The expected cost of misclassification is given by


ECM = c(2|1) P  + c(1|2) P …………….(4)


The optimal rule is obtained if R is minimized
According to Johnson and Wichern (1988) the regions R  and R  that minimize the ECM are defined by the values x for which the following inequalities hold.


R :        and       R : < ………(5)
Thus, the optimal classification rule is classifies an item with response X  into  if         ……………………………………(6)
Otherwise classify the item into , we assume that P = P =  and c(1|2) =
c(2|1), then the ECM is minimized. Using these assumptions the optimal rule becomes  1……………………………………………..(7)


Results and discussion
The data used for the analysis were collected from NDLEA Yola office on the variables Y (type of exhibit), Y (age of offender) and Y (weight of exhibit). SPSS version 15.0 was employed for the analysis. The mean (standard deviation) obtained for the variables in the first group (drug peddler) are respectively 1.20424(0.20230), 27.5339(01.5046),and 5493.7797(3.8904) , while the values in the second group( non-drug peddler) are 1.0833(0.27735),28.0347(4.3343) and 2537.1374 respectively. The unweighted and weighted are the same and equal to 118 for each variable.  


Table 1: Test for equality of group means( through DA ANOVA tests)

 

Wilks’ Lambda

  F

Df 1

Df 2

Sig

Y

0.993

1.792

1

260

0.182

Y

0.999

0.193

1

260

0.661

Y

0.925

21.114

1

260

000


The Table 1 test which variable is statistically different between the two groups ( Peddler and non-peddler).It is obvious from the table that variable Y  is significantly different from the two groups. This implies that an offender can be classified as peddler or non-peddler on the basis of the weight of exhibit found with the offender.

We verified the relationship between pairs of variables and the results (correlation between Y and Y  is -0.107; Y and Y  is 0.032 and between Y and Y  is-0.028). The result obtained shows that they are not highly correlated. This is inconsonance with discriminate analysis (DA) assumption. The normality assumption and independence of variables were equally carried out and found conformed DA guard line of DA.
The prior probability of 0.5 was assumed for each group. Then the discriminant score   obtained using DA is 1.408 - 1.286 Y  -0.011 Y  + 0.100 Y . This was used to reclassify the training sample and 71.8% of the group cases were correctly classified.

Summary
Discriminant analysis was employed to classify drug related offenders into peddlers and non-peddlers on the basis of three variables, namely: type of exhibit, age of offender and weight of exhibit which we believe is more scientificant than the oral evidence obtained in law court to sentence them. A discriminant score obtained was used for classifying drug offenderss into the groups.

Conclusion
The discriminant score obtained was able to classify 71.8% of originally classified offenders  correctly .Also we have shown that the groups differ with  regard to the mean of variables which in turn can be  used to predict group membership of any new offender(s). Also to the best of our knowledge this is the first time a scientific method is employed to classify drug offenders

Reference
Fisher, R.A. (1936),”The Use of Multiple Measurements in Taxonomic Problems,” Annals of Eugenics, 7,179-188

Ganesalingam S., (1989), “Classification and Mixture Approaches to Clustering via Maximum likelihood.” Applied Statistics, 38, no. 3, 455 – 466.
Johnson R.A. and Wichern D.W.(1988), Applied Multivariate Statistic Analysis. Second Edition. Prentice Hall Inc.

Odejide A.O. (1992), Drugs in the Third World. In Drugs and Society to Year 2000, Ed by Vamos and Corrivean Pg 116 – 119

Rencher,A.C.(2002), Method of Multivariate Analysis. Second Edition. John Wiley and Sons, Inc