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All Journal Inferensi Journal Focus Action of Research Mathematic (Factor M)
Kurnia Ahadiyah
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Perbandingan Model Generalized Ammi (Gammi) dengan Row Column Interaction Model pada Interaksi Genotipe dan Lingkungan Kurnia Ahadiyah; Ardiana Fatma Dewi
Journal Focus Action of Research Mathematic (Factor M) Vol. 4 No. 2 (2022)
Publisher : IAIN Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (536.535 KB) | DOI: 10.30762/factor_m.v4i2.4189

Abstract

Model Generalized AMMI (GAMMI) merupakan perluasan dari model AMMI (Additive Main Effect and Multiplicative Interaction). Model GAMMI melibatkan konsep Generalized Linear Model (GLM) pada variabel responnya. Pada penelitian ini, model GAMMI digunakan untuk data interaksi antara genotipe dan lingkungan yang mempunyai distribusi poisson. Sama halnya dengan model AMMI, model GAMMI juga digunakan untuk menganalisis kestabilan genotipe pada lingkungan yang beragam dengan pengaruh utama perlakuan dimodelkan dengan model aditif sedangkan pengaruh interaksi dimodelkan dengan model multiplikatif (bilinier). Metode lain yang memiliki kemiripan dengan model GAMMI adalah Row Column Interaction Model (RCIM). Model ini juga dapat digunakan untuk data yang berdistribusi poisson. Kedua model ini akan dibandingkan nilai analisis devian dan biplotnya. Interpretasi kedua model ditunjukkan melalui biplot dengan penguraian Singular Value Decompotition (SVD) pada matriks interaksi. Data yang digunakan untuk membandingkan kedua metode tersebut adalah data hama kedelai yang berisi empat genotipe dan lima jenis hama kedelai. Penelitian ini lebih ditekankan pada perbandingan hasil pemodelan dengan cara yang berbeda. Kedua metode menunjukan nilai peluang yang hampir sama yaitu untuk model GAMMI dengan regresi bolak-balik sebesar 0,0541, sedangkan model RCIM sebesar 0,0548. Keduanya sama-sama signifikan pada model GAMMI2 karena nilai peluang <0,06.   Generalized AMMI (GAMMI) model is a development of the AMMI (Additive Main Effect and Multiplicative Interaction) model. Model GAMMI involves the concept of Generalized Linear Model (GLM) on the response variable. In this research, GAMMI model used for interaction of genotype and environment data that have poisson distribution. Similar to the AMMI model, GAMMI model also used to analyze the stability of the genotype in any different environment with the main effect of treatment is modeled by additive model, while the effect of the interaction is modeled by multiplicative model (bilinear). Another method which is similar to GAMMI model is Row Column Interaction Model (RCIM). This model also can used for the data that have poisson distribution. These two models will be compared with the analysis value of the deviance and biplot. Interpretation of the model is shown through the biplot with Singular Value Decompotition (SVD) toward interaction matrix. The data used to compare the two methods is soybean pest data which contains four genotypes and five of soybean pests. This research emphasizes on comparing the results of modeling in different ways. The results of the analysis of the two methods show that the probability value is almost the same, for the GAMMI model with alternating regression is 0.0541, while the RCIM model is 0.0548. Both are equally significant in the GAMMI2 model because the probability value is <0.06.
Analisis Regresi Spline Truncated pada Indeks Pembangunan Manusia (IPM) di Provinsi Jawa Timur tahun 2021 Ardiana Fatma Dewi; Kurnia Ahadiyah
Inferensi Vol 6, No 1 (2023)
Publisher : Department of Statistics ITS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j27213862.v6i1.14107

Abstract

The increase in the achievement of the Human Development Index cannot be separated from the improvement of each of its constituent components. Currently, the components of the HDI also show an increase from year to year. To be able to participate in the development process, of course, Indonesian people are needed who are not only superior in terms of quantity, but also superior in terms of quality. HDI is used as a tool to achieve national goals, so that many things are related between humans and the development around them. This is to find out what factors can affect the HDI in East Java so that the provincial government can pay attention to several programs which can later be used to continue to maintain and improve development so that it can become an achievement for the Province of East Java. One of the analyzes that can be used is modeling, one of which is regression analysis. Nonparametric regression is a regression that is flexible in use because it can find its own data pattern. One of the truncated spline approaches to nonparametric regression can be used to predict the Human Development Index (HDI). HDI and several factors that influence it will be estimated at various knot points to get the best model. In the Spline Truncated nonparametric regression modeling which is applied to HDI data in East Java Province in 2021 several knot points are tried, namely 1 knot point, 2 knot point, and 3 knot point. The results obtained showed that the best model was found in the 3 knots experiment with a minimum GCV value of 5.40 and an R2 value of 89.875%.
Co-Authors Ardiana Fatma Dewi Ardiana Fatma Dewi