In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels (n>p) considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.
In this article, we study the mathematical characteristics of the inverse power Pranav distribution. The proposed distribution has three special cases namely Pranav, inverse Pranav and inverse power Pranav distributions. In addition with the basic properties of the distribution, the maximum likelihood method was employed in computing the parameters of the distribution. The 95% confidence interval was estimated for each of the parameters and finally, the distribution was applied to 128 bladder cancer patients to illustrate its applicability, and compared to Pranav distribution, inverse power Lindley distribution and inverse Ishita distribution. However, the inverse power Pranav distribution proved superiority over the competing models.
This study examined the probability distribution that best described the quarterly economic growth rate of Nigeria between 1960- 2015. The study collected secondary data from Central Bank of Nigeria (CBN) Statistical Bulletin 2015 on Gross Domestic Product to compute the economic growth rate of Nigeria. Six theoretical statistical distributions were fitted via Normal Distribution, Logistic Distribution, Laplace Distribution, Cauchy Distribution, Gumbel (Largest Extreme Value) Distribution and Generalized Logistic Distribution. The Laplace Distribution fitted the data as confirmed by Kolmogorov Simonov goodness of fit test, Akaike Information Criteria and Bayes Information Criteria. The probabilities of economic growth rate behaviours were obtained from the best fit distribution. The analysis showed that the chance of obtaining a negative quarterly economic growth rate is 28%. The chance of an economic recession is 8%. Also, the probability of having a positive single digit quarterly economic growth rate is 46%. In addition, having a double digit positive quarterly economic growth rate is 26%.
In this study, we examine factor analysis as a multivariate statistical tool, starting from the origin of factor analysis with regards to Spearman's approach of 1904 to the three phases of factor analysis. This is done with a view of determining the similarities and individual contributions of each of the three phases of factor analysis. This was achieved by examining the algorithms used in parameter estimations of the three phases of factor analysis. By inputting data into the algorithms and examining their outcomes and proffering recommendations based on the respective findings.
In this paper, we proposed the generalized method and algorithms developed for estimation of parameters and best model fits of log linear model for n-dimensional contingency table. For purpose of this work, the method was used to provide parameter estimates of log-linear model for three-dimensional contingency table. In estimating parameter estimates and best model fit, computer programs in R were developed for the implementation of the algorithms. The iterative proportional fitting procedure was used to find the parameter estimates and goodness of fits of the log linear model. Akaike information criteria (AIC) and Bayesian information criteria (BIC) were used to check the adequacy of the model of the best fit. Secondary data were used for illustration and the result obtained showed that the best model fit for three-dimensional contingency table had a gene-rating class: [CA, AB]. This showed that the best model fit had sufficient evidence to fit the data without loss of information. This model also revealed that breed was independent of chick loss given age. The best model in harmony with the hierarchy principle is
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