scholarly journals An Eigenvalue Test for spatial Principal Component Analysis

2017 ◽  
Author(s):  
V. Montano ◽  
T. Jombart
Keyword(s):  
Principal Component Analysis ◽  
Spatial Patterns ◽  
Statistical Power ◽  
Principal Component ◽  
Component Analysis ◽  
Type I ◽  
Type I Errors ◽  
Spatial Principal Component Analysis ◽  
Local Test ◽  
Global And Local

AbstractBackgroundThe spatial Principal Component Analysis (sPCA, Jombart 2008) is designed to investigate non-random spatial distributions of genetic variation. Unfortunately, the associated tests used for assessing the existence of spatial patterns (global and local test; Jombart et al. 2008) lack statistical power and may fail to reveal existing spatial patterns. Here, we present a non-parametric test for the significance of specific patterns recovered by sPCA.ResultsWe compared the performance of this new test to the original global and local tests using datasets simulated under classical population genetic models. Results show that our test outperforms the original global and local tests, exhibiting improved statistical power while retaining similar, and reliable type I errors. Moreover, by allowing to test various sets of axes, it can be used to guide the selection of retained sPCA components.ConclusionsAs such, our test represents a valuable complement to the original analysis, and should prove useful for the investigation of spatial genetic patterns.

Exploring competitiveness and wellbeing in Italy by spatial principal component analysis

2021 ◽  
pp. 141-146
Author(s):  
Carlo Cusatelli ◽  
Massimiliano Giacalone ◽  
Eugenia Nissi
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Well Being ◽  
Component Analysis ◽  
Measurement Model ◽  
Statistical Technique ◽  
Multivariate Statistical ◽  
Spatial Principal Component Analysis ◽  
Italian Provinces ◽  
Reflective Measurement

Well being is a multidimensional phenomenon, that cannot be measured by a single descriptive indicator and that, it should be represented by multiple dimensions. It requires, to be measured by combination of different dimensions that can be considered together as components of the phenomenon. This combination can be obtained by applying methodologies knows as Composite Indicators (CIs). CIs are largely used to have a comprehensive view on a phenomenon that cannot be captured by a single indicator. Principal Component Analysis (PCA) is one of the most popular multivariate statistical technique used for reducing data with many dimension, and often well being indicators are obtained using PCA. PCA is implicitly based on a reflective measurement model that it non suitable for all types of indicators. Mazziotta and Pareto (2013) in their paper discuss the use and misuse of PCA for measuring well-being. The classical PCA is not suitable for data collected on the territory because it does not take into account the spatial autocorrelation present in the data. The aim of this paper is to propose the use of Spatial Principal Component Analysis for measuring well being in the Italian Provinces.

scholarly journals Analisis Partial Least Square Menghasilkan Output Alternatif Antarmuka Tambahan Dari Kansei Engineering

2020 ◽  
Vol 17 (2) ◽  
pp. 67
Author(s):  
Arief Ginanjar ◽  
Awan Setiawan
Keyword(s):  
Principal Component Analysis ◽  
Factor Analysis ◽  
Correlation Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Partial Least Square ◽  
Least Square ◽  
Type I ◽  
Kansei Engineering ◽  
Coefficient Corrélation

Ketika menggunakan Kansei Engineering dalam mencari kandidat terbaik untuk menentukan model perancangan antarmuka website, peneliti menggunakan metode analisis Partial Least Square (PLS) yang dilakukan secara berulang hingga ditemukan elemen terbaik yang dapat diimplementasikan. PLS sebagai alat bantu untuk menentukan nilai terbaik antara elemen website. Output perbandingan yang dihasilkan akan dikelompokkan berdasarkan Kansei Word sebagaimana yang telah ditentukan dalam rencana awal implementasi Kansei Engineering, output perbandingan PLS iterasi pertama mempunyai kemungkinan mendapatkan nilai usulan terbaik jika digabung dengan melakukan iterasi kedua terhadap asimilasi dua atau tiga elemen yang mempunyai nilai tertinggi. Metodologi yang digunakan mengacu kepada Kansei Engineering Type I dengan melalui pengolahan data menggunakan Cronbach’s Alpha untuk menguji kelayakan responden, kemudian untuk mengetahui hubungan Kansei Words dapat menggunakan Coefficient Correlation Analysis (CCA), sedangkan hubungan antara Kansei Words dengan spesimen dapat menggunakan Principal Component Analysis (PCA), sedangkan mencari pengaruh Kansei Words paling kuat dapat menggunakan Factor Analysis (FA) dan analisis Partial Least Square (PLS) namun harus dilakukan iterasi proses PLS hingga variabel rekomendasi model perancangan antarmuka yang dihasilkan menjadi lebih bervariatif.

scholarly journals Identifying the Informational/Signal Dimension in Principal Component Analysis

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 269 ◽  
Author(s):  
Sergio Camiz ◽  
Valério Pillar
Keyword(s):  
Principal Component Analysis ◽  
Type I Error ◽  
Bootstrap Method ◽  
Simulated Data ◽  
Principal Component ◽  
Component Analysis ◽  
Stopping Rules ◽  
Multidimensional Data ◽  
Type I ◽  
Zero Eigenvalue

The identification of a reduced dimensional representation of the data is among the main issues of exploratory multidimensional data analysis and several solutions had been proposed in the literature according to the method. Principal Component Analysis (PCA) is the method that has received the largest attention thus far and several identification methods—the so-called stopping rules—have been proposed, giving very different results in practice, and some comparative study has been carried out. Some inconsistencies in the previous studies led us to try to fix the distinction between signal from noise in PCA—and its limits—and propose a new testing method. This consists in the production of simulated data according to a predefined eigenvalues structure, including zero-eigenvalues. From random populations built according to several such structures, reduced-size samples were extracted and to them different levels of random normal noise were added. This controlled introduction of noise allows a clear distinction between expected signal and noise, the latter relegated to the non-zero eigenvalues in the samples corresponding to zero ones in the population. With this new method, we tested the performance of ten different stopping rules. Of every method, for every structure and every noise, both power (the ability to correctly identify the expected dimension) and type-I error (the detection of a dimension composed only by noise) have been measured, by counting the relative frequencies in which the smallest non-zero eigenvalue in the population was recognized as signal in the samples and that in which the largest zero-eigenvalue was recognized as noise, respectively. This way, the behaviour of the examined methods is clear and their comparison/evaluation is possible. The reported results show that both the generalization of the Bartlett’s test by Rencher and the Bootstrap method by Pillar result much better than all others: both are accounted for reasonable power, decreasing with noise, and very good type-I error. Thus, more than the others, these methods deserve being adopted.

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