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Adaptive Partially Linear Regression Models by Mixing Different Estimates
Magda Mohamed Mohamed Haggag
Issue:
Volume 8, Issue 5, September 2019
Pages:
157-168
Received:
24 June 2019
Accepted:
26 July 2019
Published:
4 September 2019
Abstract: This paper proposes adapting the semiparametric partial model (PLM) by mixing different estimation procedures defined under different conditions. Choosing an estimation method of PLM, from several estimation methods, is an important issue, which depends on the performance of the method and the properties of the resulting estimators. Practically, it is difficult to assign the conditions which give the best estimation procedure for the data at hand, so adaptive procedure is needed. Kernel smoothing, spline smoothing, and difference based methods are different estimation procedures used to estimate the partially linear model. Some of these methods will be used in adapting the PLM by mixing. The adapted proposed estimator is found to be a square root-consistent and has asymptotic normal distribution for the parametric component of the model. Simulation studies with different settings, and real data are used to evaluate the proposed adaptive estimator. Correlated and non-correlated regressors are used for the parametric components of the semiparametric partial model (PLM). Best results are obtained in the case of correlated regressors than in the non-correlated ones. The proposed adaptive estimator is compared to the candidate model estimators used in mixing. Best results are obtained in the form of less risk error and less convergence rate for the proposed adaptive partial linear model (PLM).
Abstract: This paper proposes adapting the semiparametric partial model (PLM) by mixing different estimation procedures defined under different conditions. Choosing an estimation method of PLM, from several estimation methods, is an important issue, which depends on the performance of the method and the properties of the resulting estimators. Practically, it...
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A Comparison of Count Regression Models on Modeling of Instructors Publication Factors: Application of Ethiopian Public Universities
Issue:
Volume 8, Issue 5, September 2019
Pages:
169-178
Received:
10 July 2019
Accepted:
5 August 2019
Published:
23 September 2019
Abstract: Instructors’ publication (IP) is one of a major activity in higher education institutes. Currently, IP faced problem both high prevalence and severity in Ethiopian public universities. Publication was affected approximately around 352 (73.9%) instructors have not done publication in Ethiopian public universities even if there is a problem in both developing and developed countries. Since, the outcomes from IP factors are mostly discrete variable; they are often modeled using advanced count regression models. It is therefore, the purpose of this study was to determine the appropriate count regression model that efficiently fit the IP data and further to identify the key risk factors contributing significantly to IP in public universities in Ethiopian. The data were collected between November 2015 through November 2016 from selected thirteen (13) public universities in Ethiopian through both questionnaires and interview. A cross sectional study design was employed using IP data. A simple random sampling technique was applied to the population of Ethiopian public universities to obtain a sample of 13 universities or 476 individual instructors were selected. The average age of the 476 participants were found to be 30 years with 31 (6.5%) being females and 445 (93.5%) being males. The count outcomes obtained were modeled using count regression models which included Poisson, Negative Binomial, Zero-Inflated Negative Binomial (ZINB), Zero-Inflated Poisson (ZIP) and Poisson Hurdle regression models. In order to compare the performance and the efficiency of the listed count regression models with respect to the IP data, the various model selection methods such as the Vuong Statistic (V) and Akaikes Information Criterion (AIC) were used. The ZINB count regression model with reference to the values of the Vuong Statistic and AIC were selected as the most appropriate and efficient count regression model for modeling IP data. Based on the ZINB model the variables age, experience, average work-load, association member and motivation to work were statistically significant risk factors contributing to IP in Ethiopian public universities.
Abstract: Instructors’ publication (IP) is one of a major activity in higher education institutes. Currently, IP faced problem both high prevalence and severity in Ethiopian public universities. Publication was affected approximately around 352 (73.9%) instructors have not done publication in Ethiopian public universities even if there is a problem in both d...
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Modelling Geometric Measure of Variation About the Population Mean
Troon John Benedict,
Karanjah Anthony,
Alilah Anekeya David
Issue:
Volume 8, Issue 5, September 2019
Pages:
179-184
Received:
17 September 2019
Accepted:
28 September 2019
Published:
12 October 2019
Abstract: Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of this paper was to model a geometric measure of variation about the population mean which could overcome the weaknesses of the existing measures of variation about the population mean. The study was able to formulate the geometric measure of variation about the population mean that obeyed the algebraic laws behind absolute numbers, which was capable of further algebraic manipulations as it could be used further to estimate the average variation about the mean for weighted datasets, probability mass functions and probability density functions. Lastly, the measure was not affected by outliers and skewed datasets. This shows that the formulated measure was capable of solving the weaknesses of the existing measures of variation about the mean.
Abstract: Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measures have allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean ...
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Analysis of Penalized Regression Methods in a Simple Linear Model on the High-Dimensional Data
Zari Farhadi Zari Farhadi,
Reza Arabi Belaghi,
Ozlem Gurunlu Alma
Issue:
Volume 8, Issue 5, September 2019
Pages:
185-192
Received:
29 June 2019
Accepted:
3 September 2019
Published:
16 October 2019
Abstract: Shrinkage methods for linear regression were developed over the last ten years to reduce the weakness of ordinary least squares (OLS) regression with respect to prediction accuracy. And, high dimensional data are quickly growing in many areas due to the development of technological advances which helps collect data with a large number of variables. In this paper, shrinkage methods were used to evaluate regression coefficients effectively for the high-dimensional multiple regression model, where there were fewer samples than predictors. Also, regularization approaches have become the methods of choice for analyzing such high dimensional data. We used three regulation methods based on penalized regression to select the appropriate model. Lasso, Ridge and Elastic Net have desirable features; they can simultaneously perform the regulation and selection of appropriate predictor variables and estimate their effects. Here, we compared the performance of three regular linear regression methods using cross-validation method to reach the optimal point. Prediction accuracy using the least squares error (MSE) was evaluated. Through conducting a simulation study and studying real data, we found that all three methods are capable to produce appropriate models. The Elastic Net has better prediction accuracy than the rest. However, in the simulation study, the Elastic Net outperformed other two methods and showed a less value in terms of MSE.
Abstract: Shrinkage methods for linear regression were developed over the last ten years to reduce the weakness of ordinary least squares (OLS) regression with respect to prediction accuracy. And, high dimensional data are quickly growing in many areas due to the development of technological advances which helps collect data with a large number of variables....
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