Nonparametric Regression Modeling of Shape Data Using Ordinary Procrustes Analysis

Author(s):  
Meisam Moghimbeygi ◽  
Mousa Golalizadeh
Inferensi ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 39
Author(s):  
Fadhlul Rahim ◽  
I Nyoman Budiantara ◽  
Erma Oktania Permatasari

2021 ◽  
Vol 1 (1) ◽  
pp. 26-36
Author(s):  
Andrea Tri Rian Dani ◽  
Narita Yuri Adrianingsih

ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia.  Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.


2021 ◽  
Vol 3 (1) ◽  
pp. 26-36
Author(s):  
Andrea Tri Rian Dani ◽  
Narita Yuri Adrianingsih

ABSTRAKPendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R2 dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia.  Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R2 dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R2 sebesar 65,44% dan MSE sebesar 0,19.ABSTRACTThe nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R2, and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R2 value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R2 value of 65.44% and MSE of 0.19.


Risk Analysis ◽  
2013 ◽  
Vol 34 (1) ◽  
pp. 135-151 ◽  
Author(s):  
Walter W. Piegorsch ◽  
Hui Xiong ◽  
Rabi N. Bhattacharya ◽  
Lizhen Lin

Author(s):  
V.N. Voloshin ◽  
I.S. Voloshina ◽  
I.Yu. Vash

The aim of the paper is to study thymus variability in white rats, which were exposed to formaldehyde, and to compare these data with the indicators in control animals. Materials and Methods. The trial enrolled 72 white male rats, initial body weight 40–50 g. The animals were divided into 2 groups (36 rats in each). The first group consisted of control rats. Animals of the second group were exposed to formaldehyde inhalation, 2.766 mg/m3. To characterize the variability of the organ size, centroids were determined. The superposition of landmark configurations was performed using the generalized Procrustes analysis method, MorphoJ 1.06d program. The principal component analysis and canonical analysis of the obtained data were carried out. Results. One-Way ANOVA revealed a high level of intergroup differences in Procrust distance (F=1.34; p<0.0001). The significant effect of the duration of formaldehyde exposure on centroid size was established. The Kruskal-Wallis criterion was 19.778 (p=0.0014). The analysis of the principal components indicated that each of the first 10 components stands for more than 1 % of Procrustes coordinate variance. In this case, the first 7 components compatibly explain 91.398 % of thymus variability. The proportion of the first main component to the total variance of the Procrustes coordinates is 40.236 %. PC1 (-) shows changes in the thymus shape, mostly affecting the tops of its lobes, the middle part of the right boundary and the entire left thymus boundary. The scattering ellipses of the thymus ordinates in rats exposed to formaldehyde, in the first two canonical variables are located higher than those in the control animals. Conclusion. Formaldehyde inhalation leads to thymus changes in white rat. The most significant differences with control data are determined along the second canonical variable. Keywords: thymus, form, rat, formaldehyde, geometric morphometry. Цель. Изучение изменчивости формы тимуса белых крыс, находившихся в условиях влияния формальдегида, и сравнение этих данных с показателями, полученными у контрольных животных. Материалы и методы. Работа выполнена на 72 белых крысах-самцах с начальной массой тела 40–50 г. Животные были разделены на 2 серии (по 36 крыс). Первую серию составляли контрольные крысы. Животные второй серии подвергались ингаляционному воздействию формальдегида (ФА) в концентрации 2,766 мг/м3. Для характеристики изменчивости размеров органов определяли размер их центроидов. Процедуру суперимпозиции конфигураций ландмарок выполняли методом генерализованного прокрустова анализа с использованием программы MorphoJ 1.06d. Проводили анализ главных компонент и канонический анализ полученных данных. Результаты. Однофакторный дисперсионный анализ выявил высокий уровень межгрупповых различий по показателю прокрустовых расстояний (F=1,34; р<0,0001). Установлено значительное влияние продолжительности нахождения животных в условиях воздействия ФА на размер центроида. Критерий Краскела–Уоллиса составил 19,778 (р=0,0014). Анализ главных компонент указывал на то, что каждая из первых 10 компонент объясняет более 1 % дисперсии прокрустовых координат. При этом первые 7 компонент совместно объясняют 91,398 % изменчивости формы тимуса. Вклад первой главной компоненты в общую дисперсию прокрустовых координат составляет 40,236 %. РС1 (–) показывает изменения формы тимуса, в большей степени затрагивающие верхушки его долей, среднюю часть правого контура и весь левый контур тимуса. Эллипсы рассеивания ординат тимусов, принадлежащих крысам, подвергавшимся влиянию ФА, в пространстве первых двух канонических переменных расположены выше по отношению к таковым контрольных животных. Заключение. Ингаляционное воздействие формальдегида приводит к изменению формы тимуса белых крыс. Наибольшие различия с контрольными данными определяются вдоль второй канонической переменной. Ключевые слова: тимус, форма, крыса, формальдегид, геометрическая морфометрия.


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