scholarly journals PRINCIPAL COMPONENTS TO OVERCOME MULTICOLLINEARITY PROBLEM

2019 ◽  
Vol 4 (1) ◽  
pp. 79-91 ◽  
Author(s):  
Abubakari S. Gwelo
Keyword(s):  
Principal Component Analysis ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Combination ◽  
Principal Components ◽  
Linear Regression Model ◽  
Principal Component ◽  
Component Analysis ◽  
Ordinary Least Squares ◽  
The Impact

The impact of ignoring collinearity among predictors is well documented in a statistical literature. An attempt has been made in this study to document application of Principal components as remedial solution to this problem. Using a sample of six hundred participants, linear regression model was fitted and collinearity between predictors was detected using Variance Inflation Factor (VIF). After confirming the existence of high relationship between independent variables, the principal components was utilized to find the possible linear combination of variables that can produce large variance without much loss of information. Thus, the set of correlated variables were reduced into new minimum number of variables which are independent on each other but contained linear combination of the related variables. In order to check the presence of relationship between predictors, dependent variables were regressed on these five principal components. The results show that VIF values for each predictor ranged from 1 to 3 which indicates that multicollinearity problem was eliminated. Finally another linear regression model was fitted using Principal components as predictors. The assessment of relationship between predictors indicated that no any symptoms of multicollinearity were observed. The study revealed that principal component analysis is one of the appropriate methods of solving the collinearity among variables. Therefore this technique produces better estimation and prediction than ordinary least squares when predictors are related. The study concludes that principal component analysis is appropriate method of solving this matter.

scholarly journals Estimating an NBA player’s impact on his team’s chances of winning

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Sameer K. Deshpande ◽  
Shane T. Jensen
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Combination ◽  
Linear Regression Model ◽  
High Impact ◽  
The Other ◽  
Evaluation Metrics ◽  
Score Statistics ◽  
Bayesian Linear Regression ◽  
The Impact

AbstractTraditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams’ chances of winning. We propose a Bayesian linear regression model to estimate an individual player’s impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics.

scholarly journals Climate indices for the Baltic states from principal component analysis

2017 ◽  
Vol 8 (4) ◽  
pp. 951-962 ◽  
Author(s):  
Liga Bethere ◽  
Juris Sennikovs ◽  
Uldis Bethers
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Climate Models ◽  
Regional Climate ◽  
Principal Component ◽  
Component Analysis ◽  
Climate Indices ◽  
Baltic States ◽  
The Baltic ◽  
The Impact

Abstract. We used principal component analysis (PCA) to derive climate indices that describe the main spatial features of the climate in the Baltic states (Estonia, Latvia, and Lithuania). Monthly mean temperature and total precipitation values derived from the ensemble of bias-corrected regional climate models (RCMs) were used. Principal components were derived for the years 1961–1990. The first three components describe 92 % of the variance in the initial data and were chosen as climate indices in further analysis. Spatial patterns of these indices and their correlation with the initial variables were analyzed, and it was detected (based on correlation coefficient between principal components and initial variables) that higher values in each index corresponded to locations with (1) less distinct seasonality, (2) warmer climate, and (3) wetter climate. In addition, for the pattern of the first index, the impact of the Baltic Sea (distance to coast) was apparent; for the second, latitude and elevation were apparent, and for the third elevation was apparent. The loadings from the chosen principal components were further used to calculate the values of the climate indices for the years 2071–2100. An overall increase was found for all three indices with minimal changes in their spatial pattern.

scholarly journals Principal Component Analysis in Biometric, Pulp Quality and Anatomical Properties of Thronless Bamboo (Bambusa balcooa)

2019 ◽  
pp. 350-355
Author(s):  
N. Krishnakumar ◽  
S. Umesh Kanna ◽  
K. T. Parthiban
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Tamil Nadu ◽  
Principal Component ◽  
Component Analysis ◽  
Vessel Diameter ◽  
Pulp Yield ◽  
Bambusa Balcooa ◽  
Anatomical Characters ◽  
The Impact

Aims: To estimate the impact, connection and association among the biometric attributes, pulping qualities and anatomical characters in Bambusa balcooa. Place and Duration of Study: The study was conducted across the agro climatic regions viz., North Eastern Zone, Northern Zone, Western Zone, Cauvery Delta Zone and Southern Zone of Tamil Nadu, India during 2017-2018. Methodology: The Principal Components Analysis (PCA) was examined to establish the numbers of clusters using Statistical Package for Social Studies (SPSS) version 16.0.1 software in order to identify the patterns of variation (PCA). The principal component analysis was computed using the equation PCA = Σa jXj. Results: The PCA separated into three cluster principal components among the nineteen parameters studied. Out of nineteen principal components generated, twelve principal components had contributed positively on pulp yield. Among these twelve traits, maximum contribution to the pulp yield was observed by the traits viz., numbers of culms, hollocellulose, kappa number, tear index, burst index, fibre wall thickness and vessel diameter with respect to Bambusa balcooa. Conclusion: The results showed some relationships between the biometric attributes, pulping qualities and anatomical characters in Bambusa balcooa. PCA was shown to be a useful tool for assessing the impact and connection for further research.

Stormwater inflow prediction using radar rainfall data compressed by principal component analysis

2006 ◽  
Vol 1 (1) ◽  
Author(s):  
K. Katayama ◽  
K. Kimijima ◽  
O. Yamanaka ◽  
A. Nagaiwa ◽  
Y. Ono
Keyword(s):  
Principal Component Analysis ◽  
Prediction Model ◽  
Principal Components ◽  
Prediction Method ◽  
Principal Component ◽  
Component Analysis ◽  
Rainfall Data ◽  
Radar Rainfall ◽  
Input Variables ◽  
Inflow Prediction

This paper proposes a method of stormwater inflow prediction using radar rainfall data as the input of the prediction model constructed by system identification. The aim of the proposal is to construct a compact system by reducing the dimension of the input data. In this paper, Principal Component Analysis (PCA), which is widely used as a statistical method for data analysis and compression, is applied to pre-processing radar rainfall data. Then we evaluate the proposed method using the radar rainfall data and the inflow data acquired in a certain combined sewer system. This study reveals that a few principal components of radar rainfall data can be appropriate as the input variables to storm water inflow prediction model. Consequently, we have established a procedure for the stormwater prediction method using a few principal components of radar rainfall data.

Evaluation of the Aging Behavior of High Density Polyethylene in Thermal Oxidative Environment by Principal Component Analysis

2017 ◽  
Vol 727 ◽  
pp. 447-449 ◽  
Author(s):  
Jun Dai ◽  
Hua Yan ◽  
Jian Jian Yang ◽  
Jun Jun Guo
Keyword(s):  
Principal Component Analysis ◽  
Impact Strength ◽  
High Density Polyethylene ◽  
Tensile Modulus ◽  
Principal Component ◽  
Component Analysis ◽  
High Density ◽  
Aging Behavior ◽  
Data Set ◽  
The Impact

To evaluate the aging behavior of high density polyethylene (HDPE) under an artificial accelerated environment, principal component analysis (PCA) was used to establish a non-dimensional expression Z from a data set of multiple degradation parameters of HDPE. In this study, HDPE samples were exposed to the accelerated thermal oxidative environment for different time intervals up to 64 days. The results showed that the combined evaluating parameter Z was characterized by three-stage changes. The combined evaluating parameter Z increased quickly in the first 16 days of exposure and then leveled off. After 40 days, it began to increase again. Among the 10 degradation parameters, branching degree, carbonyl index and hydroxyl index are strongly associated. The tensile modulus is highly correlated with the impact strength. The tensile strength, tensile modulus and impact strength are negatively correlated with the crystallinity.

Cognition predicts days-alive-out-of-hospital after LVAD implantation

2021 ◽  
pp. 039139882110184
Author(s):  
Marykay A Pavol ◽  
Amelia K Boehme ◽  
Melana Yuzefpolskaya ◽  
Mathew S Maurer ◽  
Jesus Casida ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Left Ventricular ◽  
Motor Speed ◽  
Ventricular Assist ◽  
Hospitalization Rates ◽  
Left Ventricular Assist ◽  
Patient Groups ◽  
The Impact

Objective: Cognition influences hospitalization rates for a variety of patient groups but this association has not been examined in heart failure (HF) patients undergoing left ventricular assist device (LVAD) implantation. We used cognition to predict days-alive-out-of-hospital (DAOH) in patients after LVAD surgery. Methods: We retrospectively identified 59 HF patients with cognitive assessment prior to LVAD. Cognitive tests of attention, memory, language, and visual motor speed were averaged into one score. DAOH was converted to a percentage based on total days from LVAD surgery to either heart transplant or 900 days post-LVAD. Variables significantly associated with DAOH in univariate analyses were included in a linear regression model to predict DAOH. Results: A linear regression model including LVAD type (continuous or pulsatile flow) and cognition significantly predicted DAOH (F(2,54) = 6.44, p = 0.003, R2 = .19). Inspection of each variable revealed that cognition was a significant predictor in the model (β = .11, SE = .04, p = 0.007) but LVAD type was not ( p = 0.08). Conclusions: Cognitive performance assessed prior to LVAD implantation predicted how much time patients spent out of the hospital following surgery. Further studies are warranted to identify the impact of pre-LVAD cognition on post-LVAD hospitalization.

The Design of Index about Corporate Governance Based on PCA Method

2014 ◽  
Vol 926-930 ◽  
pp. 4085-4088
Author(s):  
Chuan Jun Li
Keyword(s):  
Principal Component Analysis ◽  
Corporate Governance ◽  
Principal Components ◽  
Principal Component ◽  
Component Analysis ◽  
Contribution Rate ◽  
Variance Contribution ◽  
Pca Method

This article uses the PCA method (Principal component analysis) to evaluate the level of corporate governance. PCA is used to analyze the correlation among 10 original indicators, and extract some principal components so that most of the information of the original indicators is extracted. The formulation of the index of corporate governance can be got by calculating the weight based on the variance contribution rate of the principal component, which can comprehensively evaluate corporate governance.

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