Generalized Estimating Equations Models for Rubber Yields in Thailand

Transcription

1 Generalzed Estmatng Equatons Models for Rubber Yelds n Thaland Watcharn Sangma and 2 Suttpong Jumroonrut Industral Engneerng Department, Faculty of Engneerng, Rajamangala Unversty of Technology Phra Nakhon, Bangkok 0800, Thaland. Orcd: , 2 Orcd: Abstract The objectves of ths research are to estmate the monthly rubber yeld n each provnce of Thaland, to nvestgate factors related to the rubber yelds, and to draw the maps of rubber yelds. A generalzed estmatng equaton model (GEE) s used. The estmated rubber yelds are used to draw the rubber yeld maps. The rubber yelds were extracted from the database of the Offce of the Agrcultural Economcs Mnstry of Agrculture and Cooperatves (OAE) and the clmatc factors were extracted from the Tha Meteorologcal Department. The dependent varables are the monthly rubber yelds. The factors consdered are ranfall, averaged temperatures, seasons, and regons. The results reveal that the factors related to the rubber yelds are, averaged temperature, regons, and seasons. The amounts of regonal effects on the rubber yelds, rankng from largest to smallest values, are southern regon, eastern regon, northeastern regon, and central regon, respectvely, where western regon and northern regon have no regonal effect. The amounts of seasonal effects on the rubber yelds, rankng from largest to smallest values, are Aug-Oct, May-July, Nov-Jan, and Feb- Apr. The top ten provnces wth hgh rubber yelds, rankng from largest to smallest values, are Surat Than n August ((6, ton), Yala n September (6, ton), Phatthalung n August (6, ton), Songkhla n August (6,537.2 to (, Chumphon n September (6, ton), Yala n August (6, ton), Phatthalung n September (6,48.09 ton), Pattan n August (6,400.2 ton), Pattan n September (6, ton), Nakhon S Thammarat n August (6, ton), respectvely. The rubber yelds maps are easy for readers to dentfy whch areas have hgh or low yelds. They are useful for rubber plannng producton. Keywords: Generalzed Estmatng Equatons (GEE), Rubber Yelds, Rubber Yeld Mappng. INTRODUCTION Rubber s an essental resource. It s requred n the manufacturng of many ndustral and consumer products, such as tres, gloves, elastcs, and hoses. Thaland has become the world s foremost producer and exporter of hgh-qualty rubber, accountng for 40% of global rubber producton, exportng $3 bllon (USD) worth each year. Its fve key markets are Chna, neghborng Malaysa, Japan, the EU, and the US. And whle plantatons cover 3 mllon hectares of land, 95% of them belong to small landowners (TCEB, 206). Monthly rubber yelds n each provnce of Thaland are reported every year va the webste of Offce of the Agrcultural Economcs Mnstry of Agrculture and Cooperatves (OAE, 206). The reports are n the form of tables and graphs. Those data reports motvated us to do ths research. They wll be more nformatve f those reported data are deeply analyzed. We can see factors assocated wth those rubber yelds or the dstrbuton of the rubber yelds n each area. Snce the reported data can be treated as repeated data. One of the most powerful statstcal model for repeated measures s a Generalzed Estmatng Equaton (GEE), whch was frst ntroduced by Lang and Zeger (986). The generalzed estmatng equatons (GEEs) methodology enables you to analyze correlated data that otherwse could be modeled as a generalzed lnear model. GEEs have become an mportant strategy n the analyss of correlated data. These data sets can arse from longtudnal studes, n whch subjects are measured at dfferent ponts n tme, or from clusterng, n whch measurements are taken on subjects who share a common characterstc, such as belongng to the same ltter (SAS, 204). Umar et al. (207) ndcated that clmatc factors whch were ranfall, maxmum and mnmum temperature mpacted on Latex yeld of hevea braslenss. Golbon et al. (205) used mxed models and mult-model nference technques for rubber yeld predcton by meteorologcal condtons. L et al. (204) found that temperature, precptaton and solar radaton were the three major clmatc factors affectng latex yeld. Zhang et al. (204) presented that average temperature, ranfall, sunshne duraton, relatve humdty and ground temperature were factors on latex yeld. Akpan et al. (2007) studed latex yeld of rubber as nfluenced by clone planted and locatons wth varyng fertlty status. L et al. (204) revewed nfluencng factors on latex yeld of Hevea braslenss. Meske and Esekhade (204) studed ranfall varablty and rubber producton n Ngera. Snce the GEE has never been used before for an analyss of the rubber yelds, t s adopted n ths research. The monthly rubber yelds from OAE (204) are assumed to have a normal dstrbuton. The assocated factors consdered nclude ranfall, average temperature from TMD (206), regon (central, north, north-east, east, south and west), season (Nov

2 Jan, May July, Oct - Nov and Feb - May). The results of ths study are useful for plannng to ncrease the rubber producton. METHOD The GEE model s the model used for the varables accordng to the observed values correlated. Let Y, j,..., n,,..., M, represent the observaton value of unt at tme j and N denote the total number of observatons, K N n... p Y s related to the ntal varable X (, X,..., X ) T and the parameter β (,,..., ) T accordng to the followng lnk 0 p functons, dentty lnk: g( a) a, natural log lnk: g( a) log( a), logt lnk: g( a) logt( a) log( a /( a)). The relatonshp between Y and X (,.,...,. ) T X X p s expressed as T g( E( Y x )) g( ) x β whch s the margnal regresson model. The covarance Matrx of Y ( Y,..., Y ) T s V A R( ) A / 2 / 2. When s dsperson parameter, A s Dagonal matrx of a varance functon and R( ) s correlaton matrx. The correlaton matrx shows the pattern of data relatons of Y ( Y,..., Y ) T Exchangeable structure:, whch has the followng forms. R( ) Frst-order autoregressve (AR()) structure: ( ) j j2, j j2 R, Unstructured structure: ( ) 2 j 2 2 j j j2 R. For the estmaton of the parameter β, the Quas-lkelhood s usually used. The estmates are from the Quas-lkelhood equatons, whch are called generalzed estmatng equatons (GEE). For fndng the solutons of that equaton, the numercal terators are appled. The functon of β s represented as U T ( ) ( ) β D V Y μ 0, D, k,2,..., p. k For the model n ths research, we let Y be the number of rubber yelds n provnce at moth j where,..., 62 and j,...,2. In provnce at moth j, X. s ranfall (mm), X.2 s temperature (degree Celsus),.3 X s the provnce n Northern regon, X.4 s the provnce n Northeastern regon. X.5 s the provnce n Southern regon. X.6 s the provnce n eastern regon. X.7 s the provnce n Western regon. X.8 s the season from Nov to Jan. X.9 s the season from May to July. X.0 s the season from Oct to Nov. s Intercept 0 and,..., 0 are regresson coeffcents of ranfall, temperature, North, Northern, South, East, West, season wthn No-Jan, May to July and Oct to No, respectvely. Central s a reference regon, and Feb to Apra s also a reference regon. The correlaton structure wthn the subject ( Y ) resulted from repeated measures, the same as tme seres data, s assumed to have a frst-order autoregressve form. The GEE model has the followng form, E( Y ) X X X X X X X X X X 0.0 The R, a statstcal software, s used for parameter estmaton. The sgnfcance of 0.5 s used as a crteron. 6348

3 RESULTS AND DISCUSSION The factors effectng to rubber yelds are shown n Table. The estmated coeffcents are presented n Table 2. emphaszes hgh productvty areas. It s easer to see whch areas produce hgh yelds. It s a beneft n agrculture n desgnng and plannng for rubber producton. Table: Factors effectng rubber yelds Source Wald Ch-Square Sg. (Intercept) 3.6 <0.000 regon <0.000 season <0.000 ranfall 3.38 <0.000 temperature At the sgnfcance of 0.05, factors effected rubber yelds are ranfall, temperature, Northeast regon, Southern regon, Western regon, Eastern regon where central regon s a reference. Season n Nov to Jan, May to July, Oct to Oct where Feb to Apr s the reference. If the ranfall ncreases mm, the rubber yelds wll decrease 3.23 tons. If the temperature ncreases Celsus, the rubber yelds wll decrease tons.provnce n Northern regon produces Rubber yelds tons more than provnces n central regon.. Provnce n Southern regon produces Rubber yelds 5, tons more than provnces n central regon. Provnce n Eastern regon produces Rubber yelds tons more than provnces n central regon. Provnce n Western regon produces Rubber yelds tons more than provnces n central regon. The rubber yeld n Nov to Jan s tons more than n Feb to Apr. The rubber yeld n Aug to Oct s tons more than n Feb to Apr. The rubber yeld n May to Jul s tons more than n Feb to Apr. The estmated rubber yelds n each month are used to produce maps as shown n Fg. to Fg. 6. It s easy to see the dstrbuton of rubber yelds n each month. If the ranfall ncreases, the rubber yeld wll decrease. That s because durng the rany season, f t s rans contnuously, the rubber trees cannot be tapped. Moreover, the outbreak of the dsease whch usually occurs wth rubber trees durng the rany season s a problem. Although t s not too severe to make the rubber tree de, t makes the plant not grow well, then the rubber yeld wll decreasng. In rany season, f there s flood, ths may cause damage to the rubber trees as well. The approprate temperature for rubber trees s about degrees Celsus (Economc Offce Agrculture, 206). Thaland's average temperature s not less than 25 degrees Celsus. The hgher temperature wll lower the rubber yelds. There s a regonal effect because the weather n each regon of Thaland vares. Seasonal factors occurs when the rany season ends, t s consdered to be a good tme to tap rubber trees. In wnter, the latex wll flow longer and be obtaned more than the other. A rubber yeld map shows the average monthly rubber yeld expressng n dfferent colors. It Parameter CONCLUSIONS Table 2: The estmated coeffcents Beta Std. Error Lower Upper Wald Ch- Square Sg. Intercept North Eastern South <0.00 East West Central Nov-Jan May-July <0.00 Aug-Oct <0.00 Feb-Apr Ranfall <0.00 Temp The objectves of ths research are to estmate the rubber yeld n each month of 63 provnces growng rubber trees n Thaland, to nvestgate factors nfluencng on the rubber yelds, and to construct the maps of rubber yelds. The generalzed estmatng equaton model (GEE) s used. The estmated rubber yelds are used to construct the rubber yeld maps. The dependent varables are the rubber yeld n each month of the provnces. The factors consdered are ranfall, averaged temperatures, seasons, and regons. The results show that the factors nfluencng on the rubber yelds are, averaged temperature, regons, and seasons. The rubber yelds maps are easy for readers to dentfy whch areas have hgh or low yelds. They are a useful tool for plannng rubber producton. ACKNOWLEDGMENTS 95% Wald Confdence Interval Hypothess Test Authors gratefully acknowledge the Rajamangala unversty of technology Phra Nakhon, Insttute of Research and Development Rajamangala Unversty of Technology Phra Nakhon and the faculty of Engneerng for ther techncal and fnancal support. 6349

4 Fgure : Rubber yelds n January (top) and February (bottom) Fgure 2: Rubber yelds n March (top) and Aprl (bottom) 6350

5 Fgure 3: Rubber yelds n May (top) and June (bottom) Fgure 4: Rubber yelds n July (top) and August (bottom) 635

6 Fgure 5: Rubber yelds n September (top) and October (bottom) Fgure 6: Rubber yelds n November (top) and December (bottom) 6352

7 REFERENCES [] Akpan, A.U., Edem, S.O. and Ndaeyo,N.U., 2007, Latex Yeld of Rubber (Hevea braslenss Muell Argo) as Influenced by Clone Planted and Locatons wth Varyng Fertlty Status, Journal of Agrculture and Socal Scences, vol. 3(): pp [2] C. S. Meskeand T. U. Esekhade Ranfall varablty and rubber producton n Ngera. Afrcan Journal of Envronmental Scence and Technology, vol.8(): pp [3] Golbon R, Author, E., Joseph Ocheng, O., Cotter, M, Sauerborn, J, 205, Rubber yeld predcton by meteorologcal condtons usng mxed models and mult-model nference technques, Internatonal Journal of Bometeorology,59 (2): [4] Guo-yao, L., Quan-bao, W., Yu-yng, L., Shuang-x, Z., Ha-yng, Y., 204, A revew of nfluencng factors on latex yeld of Hevea braslenss. Chnese Journal of Ecology,, 33(2), pp [5] L, G-y., Wang, Q-b., L, Y-y. and et al., 204, A revew of nfluencng factors on latex yeld of Hevea braslenss.[j]. Chnese Journal of Ecology, vol. 33(2): pp [6] Lang, K.Y., Zeger, S.L., 986, Longtudnal data analyss usng generalzed lnear models. Bometrka, vol. 73: pp [7] Offce of Agrcultural Economcs (OAE), 206, Rubber. 4 Feb [8] SAS., 204, Generalzed Estmatng Equatons. Avalable: gee.pdf), 4 Feb [9] TCEB., 206, Rubber. Avalable: thaland/key-mcendustry/rubber., 4 Feb [0] TMD., 206, Ranfall and temperature data. Avalable: 4 Feb [] Umar, H. Y, Okore, N.E, Toryla, M., Asemota, B., Okore, I.K., 207, Evaluaton of the Impact of Clmatc Factors on Latex Yeld of Hevea Braslenss, Internatonal Journal of Research Studes n Agrcultural Scences (IJRSAS), 3 (5): [2] Zhang, H., Zhang, L., Ge, Y., Hua, Y., Lan, Z. and Huang, H., 204, Short Communcaton: Clmate and Latex Producton of Rubber Tree (Hevea Braslenss Muell. Arg.) n Wannng, Southeastern Part of Hanan Provnce, Chna. Journal of Rubber Research, Volume 7(4) (5), pp