Pensuaian Model Taklinear Gompertz Terhadap Pertumbesaran Pokok Koko

Authors

  • Md. Yunus Jaafar

DOI:

https://doi.org/10.11113/matematika.v15.n.376

Abstract

Pensuaian model taklinear sigmoid Gompertz mencapai pengoptimuman wajar menggunakan tatacara peminimuman Levenburg-Marquardt. Bilangan lelaran parameter model, pengiraan yang dikehendaki dan penstabilan titik pegun bergantung bererti pada hampiran asal titik mula. Data yang digunakan untuk mensuai model taklinear ini ialah data cerapan pertumbesaran daun koko di bawah tiga naungan 30%, 60%, dan 90% mengikut masa (hari). Penganggaran model terhadap data itu menerapkan pakej SAS, PROC NLIN pada komputer kerangka utama MARDI. Titik mula ad hoc membantu algoritma peminimuman meraih titik pegun dalam 11, 8, dan 10 lelaran dalam penganggaran parameter model Gompertz terhadap masing-masing pertumbesaran daun koko bawah naungan 30%, 60%, dan 90%. Model tersuai itu telah didiagnosis menggunakan pentaksiran kesuaian model taklinear yang merangkumi ujian nisbah-t, selang keyakinan, matriks korelasi parameter, analisis reja, dan ujian kenormalan varians reja. Penganatomian model tersuai menampilkan kelok Gompertz merupakan model paling sesuai menerangkan ciri pertumbesaran pokok koko bawah tiga naungan itu. Kadar pertumbesaran relatif di bawah naungan-naungan 30%, 60%, dan 90% masing-masing ialah 0.061, 0.032 dan 0.031 mm Katakunci: Model taklinear Gompertz; anggaran parameter; titik mula; algoritma penumpuan; dan kadar pertumbesaran bandingan. The fitting of Gompertz nonlinear sigmoid model attains optimization using the Levenburg-Marquardt minimization procedure. The number of parameter iterations and estimations required and the stability of the stationary point or convergence criterion met depend significantly on the initial approximations of the starting values. The Gompertz nonlinear model was fitted on the shaded cocoa leaf growth using SAS package, PROC NLIN on MARDI's mainframe computer. Ad hoc initialization values helped the minimization algorithm to reach stationary points in 11, 8, and 10 iterations for parameter estimations of the Gompertz model on 30%, 60%, and 90% shaded cocoa leaf expansion respectively. The fitted models were diagnosed using nonlinear model adequacy measures constituting t-ratio test, confidence interval, parameter correlation matrix, analysis of residuals, and normality test. An anatomy of the estimated models indicates that the three Gompertz model representing three cocoa leaf growth is the most apt functions to describe the growth of the cocoa plant. The relative growth rate of the cocoa plant under 30%, 60%, and 90% shades are 0.061, 0.032, and 0.031 mm respectively. Keywords: Nonlinear Gompertz model; parameter estimations; starting values; convergence algorithm; stationary points; model anatomy and relative growth rate.

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Published

1999-06-01

Issue

Section

Mathematics