# MULTILEVEL NON-LINIER REGRESSION FOR REPEATED MEASURMENT DATA AS STUDY OF PEANUT GROWTH

• Arie Purwanto Mathematic Study Program, Faculty of Teacher Training and Education, Mercu Buana Yogyakarta University
• Umul Aiman Agrotechnology, Faculty of Agroindustry, Mercu Buana Yogyakarta University
Keywords: peanut, regression, multilevel

### Abstract

Peanut is one of the most important legume commodities in Indonesia. In its implementation, a lot of research has been done related to this plant. However, in studies conducted by growth models, it is very rarely studied. Therefore, researchers are interested in modeling the growth of peanuts. One of the models that can be used is a multilevel regression model for the case of repeated measurement data. Multilevel regression was chosen because it is considered to provide more information than other regression models. On the other hand, the nonlinear model was chosen based on the tendency of the initial plot of the data obtained. The research method used is a case study in the study of peanut growth. This study aims to build the best model based on the tested model. The Restricted Estimator Maximum Likelihood (REML) parameter estimation method was chosen because it is considered to have unbiased parameter estimates. The best model is based on the lowest Akaike Information Criterion (AIC) generated from a predetermined model. The results obtained indicate that the multilevel parabolic regression model is the model with the best AIC size. In addition, it was found that there was an Interclass Correlation (ICC) of 81.19% which indicated a difference in variability between levels.

### References

A. F., “Peranan Matematika Dan Statistika Dalam Pertanian Industrial Untuk Mewujudkan Ketahanan Pangan Nasional,” in Prosiding Seminar Nasional Matematika, Jember, 2014.

E. e. a. ] Respati, “Kacang tanah. Buletin Konsumsi Pangan,” Pusdatin, vol. 4 (1), no. Buletin Konsumsi Pangan, pp. 6-15, 2013.

C. R. R. V. O. &. V. R. Kumar, “Correlation and path coefficient analysis in groundnut (Arachis hypogaea L.),” International Journal of Applied Biology and Pharmaceutical Technology, vol. 5 (1), pp. 8-11, 2014.

R. V. D. Leeden, “Multilevel Analysis of Repeated Measure Data,” Kluwer Academic Publisers, vol. 32, pp. 15-29, 2010.

J. P.-M. M. D. L.-G. E. M. P.-O. a. J. J. T. José F Molina-Azorín, “Multilevel research: Foundations and opportunities in management,” Business Research Quarterly , vol. 23 (4), p. 319 –333, 2020.

G. e. a. Weinmayr, “Multilevel regression modelling to investigate variation in disease prevalence across locations,” International Journal of Epidemiology, vol. 46 (1), p. 336–347 , 2017.

A. J. F. N. e. a. Hubbard AE, “To GEE or not to GEE: comparing population average and mixed models for estimating the associations between neighborhood risk factors and health,” Epidemiology, vol. 21 (4), pp. 467-474, 210.

N. a. C. Breslow, “Aproximate Inference in GLMM,” Journal of American statistical Association, vol. 88, pp. 95-25, 1993.

N. S. e. al, “Analisa Metode Forward dan Backward Untuk Menentukan Persamaan,” Saintia Matematika, vol. 2 (4), pp. 235-360, 2014.

M. Elff, J. P. Heisig, M. Schaeffer and S. Shikano, “Multilevel Analysis with Few Clusters: Improving Likelihood-Based Methods to Provide Unbiased Estimates and Accurate Inference,” British Journal of Political Science, vol. 51 , p. 412–426, 2021.

e. a. Carly A. Bobak, “Estimation of an inter-rater intra-class correlation coefficient that over comes commonassumption violations in the assessment of health measurement scales,” MC Medical Research , vol. 18 (1), pp. 1-11, 2018.

‎. F. H. Richard B. Darlington, Regression Analysis and Linear Models, New York: Guildford Press, 2016.

O. Korosteleva, Advanced Regression Models with SAS and R, Florida: CRC Press, 2018.

M. Faturahman, “Pemilihan Model Regresi Terbaik Menggunakan Akaike’s Information Criterion,” Eksponensial, vol. 1 (2), pp. 26-33, 2010.

R. Bickel, Multilevel Analysis for Applied Research: It's Just Regression, New York: Guilford Press, 2013.

Published
2022-09-01
How to Cite
[1]
A. Purwanto and U. Aiman, “MULTILEVEL NON-LINIER REGRESSION FOR REPEATED MEASURMENT DATA AS STUDY OF PEANUT GROWTH”, BAREKENG: J. Math. & App., vol. 16, no. 3, pp. 861-868, Sep. 2022.
Section
Articles