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Marriage Migration Associated with Distance inBangladesh: An Application of Polynomial ModelMODEL AND SYSTEM OF PRIMARY CAREABSTRACT36In this study an effort has been madeto fit mathematical model to marriagemigration associated with distanceof Comilla district in Bangladesh.For this, data have been taken fromYadava, Soni and Sabina (2002) butthe data is also available in Hosain(2000). It is to be noted that Hossain(2000) applied pareto exponentialmodel (Morril and Pitts, 1967). Yadava,Soni and Sabina (2002) alsoapplied exponenial distribution to thesame data and they showed that exponentialdistribution provided goodapproximation. In this study an attempthas been given attention toshow that the polynomial model isalso applicable to the same data set.It is found that marriage migration associatedwith distance follows polynomialmodel. To verify the stabilityof the model, cross validity predictionpower is employed to the model.Keywords and Phrases: Marriagemigration Mathematical modelingPolynomial Variance explained (R 2 )Cross validity prediction power(CVPP) F-test.Md. Rafiqul Islam, Associate ProfessorCorrespondence to:Dept. of Population Science and Human Resource Development, Rajshahi University,Bangladesh.E-mail: rafique_pops@yahoo.comIntroductionIt is to be mentioned here thatmathematical modeling in PopulationStudies especially in Demography(Fertility, Mortality, Migration) inBangladesh have been workedvery limited scale. In the era ofglobalization, mathematical modelsare very realistic and sophisticatedmechanisms to express data inMathematics. Mathematical modelsare of great useful to demographers inrealizing the process in differentiatingamong various variables to find outthe functional relationships and theirdynamic behaviors among variousdemographic phenomena. Finally,model is important for predictionpurposes Mathematical models indemography are mainly two groups:stochastic and deterministic.Deterministic model has only beendiscussed in the present study.Deterministic models are used todescribe the functional relationshipbetween variables that take definitevalues. Traditionally, one candraw graphs of the demographicparameters but very few of us knowin the context of Bangladesh whichmodels are more appropriate for theparameters.Islam and Ali (2004) found thatage specific fertility rates (ASFRs)follows slightly modified biquadraticpolynomial model where as forwardand backward cumulative ASFRsfollow quadratic and cubic polynomialmodel, respectively in the ruralcommunity of Bangladesh. To observethe distribution or pattern of marriagemigration associated with distance inBangladesh, India and other countriesof the world a number of models havebeen fitted to the data set (Libbee andSopher, 1975; Morril and Pitts, 1967;MIDDLE EAST JOURNAL OF FAMILY MEDICINE • VOLUME 6, ISSUE 6Perry, 1969a and 1969b; Samuel,1994; Sharma, 1984; Yadava et. al.1988). Hossain gave an atention tobuild up the model of Sharma (1984)and Yadava et. al (1988).But these models did not supplygood fit and then Hossain used thePareto-Exponential model proposedby Morril and Pitts (1967) to presentthe marriage migration related todistance for his data of Bangladesh.Although Pareto-Exponential modelsupplied better approximation than themodels of Sharma (1984) and Yadavaet. al. (1988) but not significantly fit tothe utilised data set. It is to be notedthat proposed models of Sharma(1984) and Yadava et. al (1988) aresuitable for Hinda community in India.For this, Yadava et. al. (2002) triedto show that exponential distributionprovides a better fit to the distributionof marriage migration associated withdistance than pareto-Exponentialfunction as applied by Hossain (2000).Also Yadava et. al (2002) comparedwith pareto-exponential functinapplied by Yadava et. al (1998).In this study an effort has beengiven attention to build mathematicalmodel to total marriage migrationassociated with distance, that is,the same data aggregate which wasalready used by Yadava et. al. (2002).For this purpose, a polynomial modelis chosen to applied here. A briefdiscussion about polynomial model isgiven below:A general expression of the formy = f(x)=a 0+a 1x+a 2x 2 +a 3x 3 +...+a nx n(a n0) (Waerden, 1948)where a 0is the constant term; a iisthe coefficient of x i (i =1, 2, 3, ..., n)but a 1, a 2,..., an are also constants butthese belong to a field (field meansa nonempty set in which group for
MODEL AND SYSTEM OF PRIMARY CAREaddition, group for multiplication andleft as well as right distributive lawhold) and n is the positive integer,is called a polynomial of degreen and the symbol x is called anindeterminate.An effort has been made here tofind out what types of models aremore appropriate to total marriagemigration by distance in Comilla ofBangladesh. Thus, the fundamentalobjectives of this study are brieflymentioned below:i) to build up mathematical modelsto total marriage migration by distanceandii) to apply cross-validity predictionpower (CVPP), , to the model toverify how much the model is valid ornot.Data and MethodologySources of DataThe data on total marriage migrationassociated with distance of Comilladistrict in Bangladesh have beentaken from Yadava et. al. (2002). Thisdata was also available in Hossain(2000) and prohibited in Table 1.Mathematical Model FittingUsing the scattered plot of marriagemigration associated with distance ofBangladesh (Fig. 1), it is observedthat marriage migration can be fittedby polynomial model with respect todistance. Therefore, an nth degreepolynomial model is considered andthe form of the model is(Gupta and Kapoor, 1997)where, x is distance; y is marriagemigration; is the constant; is thecoefficient of (i =1, 2, 3, ..., n) and u isthe stochastic error term of the model.Here a suitable n has been selectedfor which the error sum of square isminimum.The software STATISTICA wasused to fit the mathematical model.Checking Model ValidationTo check how much the model isstable, the cross validity predictionpower(CVPP),, is applied. Here,where, n is the number of cases, k= the number of regressors in themodel and the cross-validated R isthe correlation between observed and(1-Rpredicted values of the dependent2 );variable (Stevens, 1996). Theshrinkage of the model is the absolutevalue of the difference of and R 2 . Thestability of R 2 of this model is equal to1- shrinkage.F-testTo verify the measure of the overallsignificance of the fitted model aswell as the significance of R 2 , the F-test is employed to this model. Theformula for F-test in mathematics isas follows:where k is the number of parametersto be estimated, n is the number ofcases and R 2 is the coefficient ofdetermination in the model (Gujarati,1998).Applicationof the modeland resultsThe polynomial model is assumedfor marriage migration due to distancein Comilla of Bangladesh and thefitted equation isy = 1025.557 - 169.5126x +9.613215x 2 - 0.182286x 3t-stats- (105.562) (-47.561) (27.80423)(-19.2117)p-value- (0.000) (0.000) (0.00001)(0.0000)providing R 2 =0.999714324 and= 0.998875. This is the polynomialof degree three i.e. cubic polynomial.From this statistics we see that thefitted model is highly cross-validatedand its shrinkage is 0.000839.These imply that the fitted model is99.8875% stable. Moreover, all theparameters of the fitted model arealso highly statistically significant with99.9714324% of variance explained.Moreover, the stability of R 2 of thismodel is also more than 99%.In this study the calculated valueof F-test is 4665.96, that is, largequantity which means that the fittedmodel is overall highly significant at1% level of significance. Therefore,from these statistics we see that thefitted model and corresponding R2are highly statistically significance.As a result, the model is good fit.Thereafter, the prediction is dine andthe predicted values of the model arealso demonstrated in the last.ConclusionIn this paper it is found that thirddegree polynomial model is fittedto the distribution of marriagemigration associated with distanceof Muslim community in Bangladesh.The results show that this model isalso applicable or suitable even ifHossain fitted pareto exponentialmodel and Yadava et. al. showedthat exponeutial distribution providedbetter approximation than Hossain.Hence it is concluded that the patternof marriage migration due to distancefollow 3rd degree polynomial model.ReferencesGujarati, Damodar N. (1998). BasicEconometric, Third Edition, McGrawHill, Inc., New York.Gupta, S. C. & Kapoor, V. K. (1997).Fundamentals of MathematicalStatistics, Ninth Extensively RevisedEdition, Sultan Chand & Sons,Educational Publishers, New Delhi.Hossain, M.Z. (2000). SomeDemographic Models and theirApplications with Special Referenceto Bangladesh. An Unpublished Ph.D. Thesis in Statistics, Banaras HinduUniversity, Varanasi, India.Islam, Md. Rafiqul & Ali, M. Korban.MIDDLE EAST JOURNAL OF FAMILY MEDICINE • VOLUME 6, ISSUE 6 37
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