A Topological Approach of Principal Component Analysis
Issue:
Volume 7, Issue 2, April 2021
Pages:
20-31
Received:
10 January 2021
Accepted:
29 January 2021
Published:
20 April 2021
Abstract: Large datasets are increasingly widespread in many disciplines. The exponential growth of data requires the development of more data analysis methods in order to process information more efficiently. In order to better visualize the data, many methods such as Principal Component Analysis (PCA) and MultiDimensional Scaling (MDS) allow to extract a low-dimensional structure from high-dimensional data set. The proposed approach, called Topological Principal Component Analysis (TPCA), is a multidimensional descriptive method witch studies a homogeneous set of continuous variables defined on the same set of individuals. It is a topological method of data analysis that consists of comparing and classifying proximity measures from among some of the most widely used proximity measures for continuous data. Proximity measures play an important role in many areas of data analysis, the results strongly depend on the proximity measure chosen. So, among the many existing measures, which one is most useful? Are they all equivalent? How to identify the one that is most appropriate to analyze the correlation structure of a set of quantitative variables. TPCA proposes an appropriate adjacency matrix associated to an unknown proximity measure according to the data under consideration, then analyzes and visualizes, with graphic representations, the relationship structure of the variables relating to, the well known PCA problem. Its uses the concept of neighborhood graphs and compares a set of proximity measures for continuous data which can be more-or-less equivalent a topological equivalence criterion between two proximity measures is defined and statistically tested according to the topological correlation between the variables considered. An example on real data illustrates the proposed approach.
Abstract: Large datasets are increasingly widespread in many disciplines. The exponential growth of data requires the development of more data analysis methods in order to process information more efficiently. In order to better visualize the data, many methods such as Principal Component Analysis (PCA) and MultiDimensional Scaling (MDS) allow to extract a l...
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Repeated Measure Analysis for the CD4+ Cell Counts of HIV-Positive Patients Initiated to ART: A Case Study at Ambo Hospital
Endale Alemayehu,
Tsigereda Tilahun
Issue:
Volume 7, Issue 2, April 2021
Pages:
32-38
Received:
8 February 2021
Accepted:
24 March 2021
Published:
20 April 2021
Abstract: Introduction: HIV is a virus that causes Acquired Immunodeficiency Syndrome (AIDS) by reducing a person's ability to fight the infection. It attacks an immune cell called the CD4 cell which is responsible for the body's immune response to infectious agents. Now a days anti retro viral therapy treatment is avail to elongate the life of patients. The treatment is given for patients to increase the CD4 counts of patients to keep the ability of body preventing the disease. Objectives: This study was aimed to identify the potential associated risk factors with CD4 counts of patients under ART treatment at public hospital in Ethiopia. The other was to fit linear mixed model by handling missing value of the data during follow up time. Method: To see the structure of the data, exploratory data analysis was conducted. Of the familiar variance structures, unstructured variance covariance is selected to be best and to fit the data under study, step-by-step procedure was passed to obtain best model. Results: The descriptive statistics directed that the progressive change in CD4 counts of females seems better than that of males. On the other hand, the output of the fitted model indicated that covariates significant with 5% level of significance is that baseline CD4, time, weight and interaction of Sex, baseline CD4 with time. Allowing the significance level to increase to 25% increases most covariates to be significant that help patients in a better awareness. Conclusion: With this result, full linear mixed with random intercept and slop is found to best model. There was high variability within patients over time and between patients and the interaction of time with covariates was also significant. Generally, the data was fitted by handling the missing value using multiple imputation technique.
Abstract: Introduction: HIV is a virus that causes Acquired Immunodeficiency Syndrome (AIDS) by reducing a person's ability to fight the infection. It attacks an immune cell called the CD4 cell which is responsible for the body's immune response to infectious agents. Now a days anti retro viral therapy treatment is avail to elongate the life of patients. The...
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Statistical Analysis of the Influence of Financial Education Expenditure on Economic Growth in Shandong Province
Issue:
Volume 7, Issue 2, April 2021
Pages:
39-50
Received:
14 January 2021
Accepted:
2 February 2021
Published:
26 April 2021
Abstract: Education is a country’s livelihood plan. It provides manpower and technology for development. The role of education in promoting the economy has been recognized by most countries, and the mutual influence of education and economic growth will increase with the improvement of the country’s economic level. Obviously, the leading role of education in the economy has been valued by more countries. Shandong Province, being a big economic province is also a big province for college entrance examination, but there is still the problem of uneven distribution of economic resources. In order to make suggestions for the financial education expenditure in Shandong Province, it is of far-reaching significance to analyze the relationship between financial education expenditure and economic growth (gross regional product). Therefore, this article proposes two research questions. Question 1: Calculated on a per capita basis, is there a long-term equilibrium relationship among the four variables of fiscal education expenditure, scientific undertaking expenditure, total investment in fixed assets of the whole society, and gross regional product? To solve this problem, this article proposes two hypotheses. H0: There is no long-term equilibrium relationship between the four variables. H1: There is a long-term equilibrium relationship between the four variables. Question 2: On a per capita basis, what kind of work does fiscal education expenditure have on economic growth? To solve this problem, this paper proposes two hypotheses. H0: Fiscal education expenditures promote economic growth. H1: Financial education expenditure has a restraining effect on economic growth. In response to question 1, this paper uses Eivews to find a long-term equilibrium relationship between the four variables through the use of ADF test, E-G two-step method, and theoretical research. Aiming at problem 2, this paper uses Eviews software to establish an error correction model and finds that fiscal education expenditure has a promoting effect on economic growth, and for every increase of per capita fiscal education expenditure by one unit, the average per capita GDP increases by 6.688. And theoretical research also supports the results of data analysis. At the end of the article, policy recommendations for the development of financial education are put forward.
Abstract: Education is a country’s livelihood plan. It provides manpower and technology for development. The role of education in promoting the economy has been recognized by most countries, and the mutual influence of education and economic growth will increase with the improvement of the country’s economic level. Obviously, the leading role of education in...
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