scholarly journals PRINCIPAL COMPONENT ANALYSIS FOR WEIGHTED DATA IN THE PROCEDURE OF MULTIDIMENSIONAL STATISTICAL FORECASTING

2021 ◽  
Author(s):  
А. Kaplina ◽  
О. Loboda
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Statistical Forecasting ◽  
Weighted Data

scholarly journals Principal Component Analysis for Weighted Data in the Procedure of Multidimensional Statistical Forecasting

2021 ◽  
Vol 18 (2) ◽  
pp. 4-11
Author(s):  
V. V. Nikitin ◽  
D. V. Bobin
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Confidence Interval ◽  
Time Lag ◽  
Principal Component ◽  
Component Analysis ◽  
Data Set ◽  
Modified Method ◽  
Weighted Data ◽  
Main Component

Purpose of the research. Let’s assume that the dynamics of the state of some object is being investigated. Its state is described by a system of specified indicators. Among them, some may be a linear combination of other indicators. The aim of any forecasting procedure is to solve two problems: first, to estimate the expected forecast value, and second, to estimate the confidence interval for possible other forecast values. The prediction procedure is multidimensional. Since the indicators describe the same object, in addition to explicit dependencies, there may be hidden dependencies among them. The principal component analysis effectively takes into account the variation of data in the system of the studied indicators. Therefore, it is desirable to use this method in the forecasting procedure. The results of forecasting would be more adequate if it were possible to implement different forecasting strategies. But this will require a modification of the traditional principal component analysis. Therefore, this is the main aim of this study. A related aim is to investigate the possibility of solving the second forecasting problem, which is more complex than the first one. Materials and research methods. When estimating the confidence interval, it is necessary to specify the procedure for estimating the expected forecast value. At the same time, it would be useful to use the methods of multidimensional time series. Usually, different time series models use the concept of time lag. Their number and weight significance in the model may be different. In this study, we propose a time series model based on the exponential smoothing method. The prediction procedure is multidimensional. It will rely on the rule of agreed upon data change. Therefore, the algorithm for predictive evaluation of a particular indicator is presented in a form that will be convenient for building and practical use of this rule in the future. The principal component analysis should take into account the weights of the indicator values. This is necessary for the implementation of various strategies for estimating the boundaries of the forecast values interval. The proposed standardization of weighted data promotes to the implementation of the main theorem of factor analysis. This ensures the construction of an orthonormal basis in the factor area. At the same time, it was not necessary to build an iterative algorithm, which is typical for such studies. Results. For the test data set, comparative calculations were performed using the traditional and weighted principal component analysis. It shows that the main characteristics of the component analysis are preserved. One of the indicators under consideration clearly depends on the others. Therefore, both methods show that the number of factors is less than the number of indicators. All indicators have a good relationship with the factors. In the traditional method, the dependent indicator is included in the first main component. In the modified method, this indicator is better related to the second component. Conclusion. It was shown that the elements of the factor matrix corresponding to the forecast time can be expressed as weighted averages of the previous factor values. This will allow us to estimate the limits of the confidence interval for each individual indicator, as well as for the complex indicator of the entire system. This takes into account both the consistency of data changes and the forecasting strategy.

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.

Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans

2020 ◽  
Vol 4 (11) ◽  
pp. 676-681
Author(s):  
V.V. Sapozhnikova ◽  
◽  
A.L. Bondarenko ◽  
Keyword(s):  
Principal Component Analysis ◽  
Lyme Borreliosis ◽  
Clinical Laboratory ◽  
Acute Infection ◽  
Erythema Migrans ◽  
Principal Component ◽  
Component Analysis ◽  
Control Group ◽  
Multifactorial Analysis ◽  
Specific Antibodies

Aim: to determine the association between clinical laboratory parameters, the production of cytokines (IL-17A, -23, -33, -35), and specific IgM and IgG in the serum of patients with Lyme borreliosis without erythema migrans. Patients and Methods: complete blood count, the concentrations of IL-17A, -23, -33, -35, and the levels of specific IgM and IgG were measured during acute infection and convalescence (n=30). The control group included age- and sex-matched healthy individuals (n=30). Statistical analysis was performed using the StatSoft Statistica v 10.0 software (parametric and non-parametric methods and multifactorial analysis, i.e., principal component analysis). Results: most (80%) patients with Lyme borreliosis without erythema migrans are the people of working age. In most patients, the combination of the specific antibodies against Borrelia afzelii and Borrelia garinii (76.7%) and severe intoxication and inflammatory process (100%) were detected. Moderate and severe disease associated with meningism was diagnosed in 90% and 10%, respectively. The mean duration of hectic period was 8.3±1.27 days. Abnormal ECG was reported in 40% of patients, i.e., conduction abnormalities in 20%, sinus bradycardia in 16.7%,and sinus tachycardia in 3.3%. The clinical laboratory signs of hepatitis without jaundice were identified in 26.7%. During treatment, the significant reduction in band and segmented neutrophil counts as well as the significant increase in platelet count were revealed compared to these parameters at admission. Abnormal cytokine levels (i.e., the increase in IL-17A, -23, -33 and the deficiency of IL-35) were detected. Conclusions: multifactorial analysis has demonstrated that the severity of immunological abnormalities in patients with Lyme borreliosis without erythema migrans is associated with fever, cardiac and liver disorders, the high levels of IL-23 and IL-33, and the lack of IL-35 and specific IgM and IgG. KEYWORDS: tick-borne borreliosis, Lyme disease without erythema migrans, clinical laboratory signs, cytokines, specific antibodies, multifactorial analysis, principal component analysis. FOR CITATION: Sapozhnikova V.V., Bondarenko A.L. Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans. Russian Medical Inquiry. 2020;4(11):676–681. DOI: 10.32364/2587-6821-2020-4-11-676-681.

Oxypropylation of Brazilian Pine-Fruit Shell Evaluated by Principal Component Analysis

2018 ◽  
Vol 6 (7) ◽  
pp. 715-723 ◽  
Author(s):  
Stephany C. de Rezende ◽  
Jo鉶 A. Pinto ◽  
Isabel P. Fernandes ◽  
Fernanda V. Leimann and Maria-Filomena Barreiro
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis
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