scholarly journals On the Unlikely Case of an Error-Free Principal Component From a Set of Fallible Measures

2017 ◽  
Vol 78 (4) ◽  
pp. 708-712 ◽  
Author(s):  
Tenko Raykov ◽  
George A. Marcoulides ◽  
Tenglong Li
Keyword(s):  
Principal Component Analysis ◽  
Measurement Error ◽  
Principal Component ◽  
Component Analysis ◽  
Correlated Errors ◽  
Two Measures ◽  
Error Terms

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component—and in particular for the first principal component—to be error-free. In conjunction with the findings in Raykov et al., it is concluded that in practice no principal component can be perfectly reliable for a set of observed variables that are not all free of measurement error, whether or not their error terms correlate, and hence no principal component can practically be error-free.

scholarly journals Application of Characteristic Model-Based Principal Component Analysis in Optimization of Flowmeter Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Wenping Jiang ◽  
Zhencun Jiang ◽  
Lingyang Wang ◽  
Jun Min ◽  
Yi Zhu ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Measurement Error ◽  
Measurement Accuracy ◽  
Structural Parameters ◽  
Principal Component ◽  
Component Analysis ◽  
Characteristic Model ◽  
Industrial Systems ◽  
Model Based ◽  
High Level

In complex industrial processes, it is necessary to perform modeling analysis on some industrial systems and find and optimize the factors that have the greatest impact on the results, in order to achieve the optimization of the industrial systems. However, due to the high-level nature or complex working mechanism of complex industrial systems, traditional principal component analysis methods are difficult to apply. Therefore, this paper proposes a characteristic model-based principal component analysis (CMPCA) to perform principal component analysis on complex industrial systems. The differential pressure flowmeter is taken as an example to verify the effectiveness of the method. Flowmeter is an indispensable instrument in measurement, and its accuracy depends on its own structural parameters. However, the measurement accuracy of some flow meters is not high, and the measurement error is large, which affects the normal industrial production process. This method is used to analyze the influence of the structural parameters of the flowmeter on its measurement accuracy, and the four most important structural parameters are found and optimized. The measurement error of the Bitoba flowmeter is reduced from 1% to 0.2%, and the measurement repeatability is reduced from 0.3 to 0.06, which proves the effectiveness of the method.

scholarly journals Improving PET Receptor Binding Estimates from Logan Plots Using Principal Component Analysis

2007 ◽  
Vol 28 (4) ◽  
pp. 852-865 ◽  
Author(s):  
Aniket Joshi ◽  
Jeffrey A Fessler ◽  
Robert A Koeppe
Keyword(s):  
Principal Component Analysis ◽  
Intervention Studies ◽  
Simulated Data ◽  
Volume Ratio ◽  
Principal Component ◽  
Component Analysis ◽  
Correlated Errors ◽  
Post Intervention ◽  
Positron Emission ◽  
Distribution Volume Ratio

This work reports a principal component analysis (PCA)-based approach for reducing bias in distribution volume ratio ( DVR) estimates from Logan plots in positron emission tomography (PET). Comparison has been made of all existing bias-removal methods with the proposed PCA method, for both single-estimate PET studies and intervention studies where pre- and post-intervention estimates are made. Bias in Logan-based DVR estimates is because of the noise in the PET timeactivity curves (TACs) that propagates as correlated errors in dependent and independent variables of the Logan equation. Intervention studies show this same bias but also higher variance in DVR estimates. In this work, noise in the TACs was reduced by fitting the curves to a low-dimension PCA-based linear model, leading to reduced bias and variance in DVR. For validating the approach, TACs with realistic noise were simulated for a 11C-labeled tracer with carfentanil (CFN)-like kinetics for both single-measurement and intervention studies. Principal component analysis and existing methods were applied to the simulated data and their performance was compared by statistical analysis. The results indicated that existing methods either removed only part of the bias or reduced bias at the expense of precision. The proposed method removed ∼90% of the bias while also improving precision in both single- and dual-measurement simulations. After validation of the proposed method in simulations, PCA, along with the existing methods, was applied to human [11C]CFN data acquired for both single estimation of DVR and dual-estimation intervention studies. Similar results were observed in human scans as were seen in the simulation studies.

Distinguishing between Leptidea sinapis and L. reali (Lepidoptera: Pieridae) using a morphometric approach: impact of measurement error on the discriminative characters

Zootaxa ◽  
2008 ◽  
Vol 1819 (1) ◽  
pp. 40 ◽  
Author(s):  
MICHELE FUMI
Keyword(s):  
Principal Component Analysis ◽  
Discriminant Analysis ◽  
Measurement Error ◽  
Principal Component ◽  
Component Analysis ◽  
Data Sets ◽  
Discriminative Power ◽  
Size And Shape ◽  
Species Variability ◽  
Shape Data

A morphometric approach was used to test the possibility of discriminating between L. sinapis and L. reali by taking into account some new genitalic characters in addition to those used in previous surveys. Principal component analysis, performed on the size-and-shape data sets and on the size-adjusted data sets, has allowed two completely separate morphotypes to be detected, both in males and in females. Discriminant analysis has confirmed the separation of previously detected morphotypes and has correctly classified 100% of the specimens in both sexes with six discriminative characters being identified in males and two in females. However, some of these discriminative characters were not considered reliable enough because of the high associated measurement error and the scarce discriminative power. Reliable discriminative characters were: vinculum (≈ valve) width, length of phallus (≈ aedoeagus ≈ aedeagus), saccus and uncus in males and ductus bursae length in females. The main topics discussed are: a comparison of the discriminative characters with previous studies, the sources of measurement error and the devices used to reduce it, as well as the between and within-species variability of the characters.

A German version of the Intermittent Claudication Questionnaire (ICQ): cultural adaptation and validation

VASA ◽  
2012 ◽  
Vol 41 (5) ◽  
pp. 333-342 ◽  
Author(s):  
Kirchberger ◽  
Finger ◽  
Müller-Bühl
Keyword(s):  
Principal Component Analysis ◽  
Intermittent Claudication ◽  
Completion Time ◽  
Short Form ◽  
Principal Component ◽  
Component Analysis ◽  
German Version ◽  
Average Completion Time ◽  
Sf 36 ◽  
Related Quality

Background: The Intermittent Claudication Questionnaire (ICQ) is a short questionnaire for the assessment of health-related quality of life (HRQOL) in patients with intermittent claudication (IC). The objective of this study was to translate the ICQ into German and to investigate the psychometric properties of the German ICQ version in patients with IC. Patients and methods: The original English version was translated using a forward-backward method. The resulting German version was reviewed by the author of the original version and an experienced clinician. Finally, it was tested for clarity with 5 German patients with IC. A sample of 81 patients were administered the German ICQ. The sample consisted of 58.0 % male patients with a median age of 71 years and a median IC duration of 36 months. Test of feasibility included completeness of questionnaires, completion time, and ratings of clarity, length and relevance. Reliability was assessed through a retest in 13 patients at 14 days, and analysis of Cronbach’s alpha for internal consistency. Construct validity was investigated using principal component analysis. Concurrent validity was assessed by correlating the ICQ scores with the Short Form 36 Health Survey (SF-36) as well as clinical measures. Results: The ICQ was completely filled in by 73 subjects (90.1 %) with an average completion time of 6.3 minutes. Cronbach’s alpha coefficient reached 0.75. Intra-class correlation for test-retest reliability was r = 0.88. Principal component analysis resulted in a 3 factor solution. The first factor explained 51.5 of the total variation and all items had loadings of at least 0.65 on it. The ICQ was significantly associated with the SF-36 and treadmill-walking distances whereas no association was found for resting ABPI. Conclusions: The German version of the ICQ demonstrated good feasibility, satisfactory reliability and good validity. Responsiveness should be investigated in further validation studies.

Sign in / Sign up

Export Citation Format

Share Document