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Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation Masjkur, Mohammad; Folmer, Henk
Journal of the Indonesian Mathematical Society Volume 24 Number 1 (April 2018)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.24.1.516.27-50

Random parameter models have been found to outperform xed pa-rameter models to estimate dose-response relationships with independent errors. Amajor restriction, however, is that the responses are assumed to be normally andsymmetrically distributed. The purpose of this paper is to analyze Bayesian infer-ence of random parameter response models in the case of independent responseswith normal and skewed, heavy-tailed distributions by way of Monte Carlo simu-lation. Three types of Bayesian estimators are considered: one applying a normal,symmetrical prior distribution, a second applying a Skew-normal prior and, a thirdapplying a Skew-t-distribution. We use the relative bias (RelBias) and Root MeanSquared Error (RMSE) as valuation criteria. We consider the commonly applied lin-ear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. Onesimulation examines the performance of the estimators in the case of independent,normally and symmetrically distributed responses; the other in the case of indepen-dent responses following a heavy-tailed, Skew-t-distribution. The main nding isthat the estimator based on the Skew-t prior outperforms the alternative estima-tors applying the normal and Skew-normal prior for skewed, heavy-tailed data. Fornormal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more ecient than its alternatives.Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal fordose-response modeling.

Upaya untuk memacu produktivitas padi salah satunya dengan cara pemupukan. Untuk mendapatkan pengaruh pupuk yang berinteraksi positif dengan lokasi tertentu dilakukan uji lokasi ganda. Salah satu metode yang dapat digunakan untuk menganalisis interaksi pemupukan dengan lokasi adalah analisis AMMI. Tujuan penelitian ini adalah mengetahui penggunaan model AMMI dalam analisis interaksi pemupukan N, P, K dan lokasi. Hasil penelitian menunjukkan bahwa pupuk N berinteraksi positif pada Cilamaya-Karaw Mohammad Masjkur; Niken Dyah Septiastuti
FORUM STATISTIKA DAN KOMPUTASI Vol. 14 No. 1 (2009)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

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Upaya untuk memacu produktivitas padi salah satunya dengan cara pemupukan. Untuk mendapatkan pengaruh pupuk yang berinteraksi positif dengan lokasi tertentu dilakukan uji lokasi ganda. Salah satu metode yang dapat digunakan untuk menganalisis interaksi pemupukan dengan lokasi adalah analisis AMMI. Tujuan penelitian ini adalah mengetahui penggunaan model AMMI dalam analisis interaksi pemupukan N, P, K dan lokasi. Hasil penelitian menunjukkan bahwa pupuk N berinteraksi positif pada Cilamaya-Karawang dan Bumiayu-Brebes, pupuk NP berinteraksi positif pada Sungapan-Pemalang, Perak-Jombang, dan Mayang-Jember, sedangkan pupuk NPK berinteraksi positif pada Rengasdengklok-Karawang, Dempet-Demak, Balen-Bojonegoro, Pungging-Mojokerto, dan Tanggul-Jember. Selain itu, meskipun respon berat kering padi tertinggi pada pemupukan NPK, namun tidak semua lokasi membutuhkan pupuk lengkap NPK.

ALGORITMA GENETIK PENDUGAAN PARAMETER MODEL NONLINEAR JERAPAN FOSFOR (Genetic Algorithm for Parameter Estimation of Phosphorus Adsorption Nonlinear Model) Mohammad Masjkur
FORUM STATISTIKA DAN KOMPUTASI Vol. 15 No. 2 (2010)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

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Expectation Maximization (EM) was the best method used to estimate the parameters of phosphorus adsorption in a nonlinear model. However, it is questionable whether the optimum value obtained was exactly a global optimum value. Genetic algorithm is an alternative procedure to estimate the phosphorus adsorption’s parameters in a nonlinear model. The objective of this study was to have a better understanding in the use of genetic algorithm in maximum likelihood estimation of phosphorus adsorption nonlinear model parameters and compare it with the EM algorithm. This study used data of P adsorption isotherms of kaolinitic and smektitic soil in three locations. Phosphorus adsorption nonlinear models used are Freundlich and Langmuir. Results showed that the genetic algorithm and EM method produced different values of estimated phosphorus maximum adsorption and bonding energy parameters. AIC and SBC values of genetic algorithm is lower than EM algorithm, both on the Langmuir and Freundlich models. AIC and SBC values of Langmuir model is lower than Freundlich model both for genetic algorithms and EM algorithm. Hence, the best model for phosphorus adsorption is Langmuir nonlinear model with genetic algorithm. Keywords: nonlinear model, EM, Freundlich, Langmuir, genetic algorithm

PERBANDINGAN MODEL RESPON PEMUPUKAN NITROGEN PADA PADI SAWAH Mohammad Masjkur; Maman Rusman
FORUM STATISTIKA DAN KOMPUTASI Vol. 13 No. 1 (2008)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

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Model statistika linier plateau, kuadratik plateau, dan kuadratik umumnya digunakan dalam penentuan dosis optimum pemupukan. Penelitian ini membandingkan model linier plateau, kuadratik plateau, dan kuadratik respons pemupukan Nitrogen pada padi sawah. Perbandingan model menunjukkan bahwa model kuadratik lebih baik daripada model-model lainnya. Hal ini berdasarkan pada perilaku sisaan respon, pengujian asumsi kenormalan sisaannya, nilai koefisien determinasi (R2) serta nilai dugaan respon maksimum. Kata kunci : linier plateau, kuadratik plateau, kuadratik, dosis pemupukan, optimum.

RANDOM PARAMETER MODELS OF FERTILIZER RESPONSE FOR CORN USING SKEWED DISTRIBUTIONS Mohammad Masjkur
FORUM STATISTIKA DAN KOMPUTASI Vol. 20 No. 2 (2015)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (903.57 KB)

Random parameter models have been found to better determine the optimum dose of fertilizer than fixed parameter. However, a major restriction of it is the normality assumption.. The purpose of this study the introduction of random parameter models of fertilizer response using skewed distributions from a Bayesian perspective. The method is applied to data sets of multilocation trials of potassium fertilization on corn. We compare the Linear Plateau, Spillman-Mitscherlich, and Quadratic random parameter models with different random errors distribution assumption, i.e. as normal, skew-normal, Student-t and Skew-t distribution using the Deviance Information Criterion (DIC). The results show that the smallest DIC value is obtained for the normal linear plateau model compare with the other models. The correlation between observed and fitted values was significant.Key words : fertilizer response model, mixed effects, skewed distributions, DIC.

Covariance Analysis of Heterogenous Group Data Mohammad Masjkur; M. Sjarkani Musa; . Aunuddin; Oetit Koswara
Forum Pasca Sarjana Vol. 18 No. 2 (1995): Forum Pascasarjana
Publisher : Forum Pasca Sarjana

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This paper discussed the important of concomitant variables in regression analysis. Particularly, it was shown that without considering concomitant variables none of the combined regression models was reliable. In fact, the highest coefficient of determination R' was obtained from Mediterran soil group of data (65.8%). although R' for each specimen varied from 72.8% to 97.7%. Considering K-soil contents as concomitant variables, it was shown that the coefficient of determination increased by 18 2% to 85.3%. The resulting R* for each model was ranging from 67.1% to 93.6%. Another important finding from the research was the incorporation of concomitant variables resulted in more symmetric data distributions, smaller variances, and substantial increase in the regression slopes.

Correlation between Soil Test Phosphorus of Kaolinitic and Smectitic Soils with Phosphorus Uptake of Lowland Rice Mohammad Masjkur
JOURNAL OF TROPICAL SOILS Vol 14, No 3: September 2009
Publisher : UNIVERSITY OF LAMPUNG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5400/jts.2009.v14i3.205-209

Correlation between soil test phosphorus (P) and plant-available P parameters were affected by soil properties, such as soil pH, particle-size composition, and mineralogy. The objectives of this research were: (1) to determine P concentration extracted by several soil P test method in kaolinitic and smectitic soil, and (2) to determine correlation between soil P test and soil properties, P fractions, P sorption parameters, and P uptake of lowland rice. The soil P test in kaolinitic and smectitic soil used solutions of HCl 25%, Truog, Olsen, Bray1, Mehlich1, and Morgan Venema and were correlated with P uptake of lowland rice in field experiment. Concentration of Truog-P in kaolinitic soil was significantly higher than smectitic soil, while concentration of Morgan-P in kaolinitic soil was significantly lower than smectitic soil. Concentration differences of HCl 25%-P, Olsen-P, Bray1-P, and Mehlich1-P between kaolinitic and smectitic soil were not significant. In kaolinitic soil correlation between HCl 25%-P, Olsen-P, Bray1-P, and Mehlich1-P, and Morgan-P with P uptake of lowland rice were not significant. In smectitic soil HCl 25%-P, Olsen-P, Bray1-P, and Mehlich1-P correlated significantly with P uptake of lowland rice, while Morgan-P was not significant.

PERBANDINGAN FUNGSI RESPONS STOKASTIK HASIL KEDELAI TERHADAP PEMUPUKAN KALIUM Mohammad Masjkur
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 15, No 1 (2015)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v15i1.1405

Abstrak Fungsi respons stokastik hasil tanaman terhadap pemupukan diketahui lebih baik daripada versi deterministik bagi penentuan dosis optimum rekomendasi pemupukan suatu wilayah. Namun demikian, pemilihan bentuk fungsi yang sesuai bagi kondisi pertanaman tertentu juga perlu dievaluasi secara kritis. Kajian ini ditujukan untuk mengetahui model terbaik fungsi respons stokastik hasil kedelai terhadap pemupukan kalium. Penelitian ini dilakukan berdasarkan pada data percobaan multilokasi respons hasil kedelai terhadap pemupukan kalium. Model parameter tetap (M1) linear plateau, Spillman-Mitscherlich, kuadratik, dan logistik dibandingkan dengan model parameter acak dengan 1 (M2) atau 2 pengaruh acak (M3) menggunakan -2 log-likelihood, Akaike information criterion, dan Bayesian information criterion. Hasil penelitian menunjukkan bahwa nilai AIC model parameter tetap (M1) secara berurutan adalah logistik < Spillman-Mitscherlich < linear plateau < kuadratik. Adapun nilai AIC model parameter acak (M2) secara berurutan adalah kuadratik <. Spillman-Mitscherlich < logistik < linear plateau. Model parameter acak (M3) secara berurutan adalah linear plateau < Spillman-Mitscherlich < logistik. Model terbaik bagi respons hasil kedelai terhadap pemupukan kalium adalah model linear plateau stokastik dengan pengaruh acak intersep dan plateau.

Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation Mohammad Masjkur; Henk Folmer
Journal of the Indonesian Mathematical Society Volume 24 Number 1 (April 2018)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.24.1.516.27-50

Random parameter models have been found to outperform xed pa-rameter models to estimate dose-response relationships with independent errors. Amajor restriction, however, is that the responses are assumed to be normally andsymmetrically distributed. The purpose of this paper is to analyze Bayesian infer-ence of random parameter response models in the case of independent responseswith normal and skewed, heavy-tailed distributions by way of Monte Carlo simu-lation. Three types of Bayesian estimators are considered: one applying a normal,symmetrical prior distribution, a second applying a Skew-normal prior and, a thirdapplying a Skew-t-distribution. We use the relative bias (RelBias) and Root MeanSquared Error (RMSE) as valuation criteria. We consider the commonly applied lin-ear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. Onesimulation examines the performance of the estimators in the case of independent,normally and symmetrically distributed responses; the other in the case of indepen-dent responses following a heavy-tailed, Skew-t-distribution. The main nding isthat the estimator based on the Skew-t prior outperforms the alternative estima-tors applying the normal and Skew-normal prior for skewed, heavy-tailed data. Fornormal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more ecient than its alternatives.Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal fordose-response modeling.

Dekomposisi Ensemble untuk Peramalan Harga Bawang Merah DKI Jakarta Febie Tri Lestari; Farit Mochamad Afendi; Mohammad Masjkur; Budi Waryanto
Xplore: Journal of Statistics Vol. 8 No. 1 (2019): 30 April 2019
Publisher : Department of Statistics, IPB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/xplore.v8i1.120

Onions are one of the vegetable commodities that are not distributed and included as seasonal crops. Onions are commonly used as cooking spices and traditional medicine. At the time of the religious holidays or non-harvest season, the stock of onions is not able to meet the demand, hence the government has to import them, but that increase the fluctuations of onion prices on the market. Actually, by utilizing the price fluctuation, information about the factors, will be obtained by reviewing the price movement and precise forecasting of the price of onions. Ensamble Empirical Mode Decomposition (EEMD) method can be applied to examine that. EEMD is a decomposition method that can be used to convert a series of time functions from a data signal into several sub-signals resulting from flattening, otherwise known as Intrinsic Mode Function (IMF) and IMF remaining. In this research, this concept applied to data on weekly onion prices in DKI Jakarta from July 2008 to April 2018 as many as 521 data. Based on the results of data processing, as many as 7 IMF and IMF remaining were used as IMF forecasting and the IMF remaining in the future. The forecast was performed by choosing the best model of each IMF component and IMF remaining, used ARIMA. In the end, the weekly price forecast for onion in Jakarta from May - July 2018 ranged from Rp34295.67, - to Rp36133.36, - with average forecasting prices for May-July 2018 amounting to Rp34482.39 - Rp 35207.12 and Rp 36024.88 with a MAPE value of 1.85%.

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