Modeling Nigerian Covid-19 cases: A comparative analysis of models and estimators.

COVID-19 remains a major pandemic currently threatening all the countries of the world. In Nigeria, there were 1, 932 COVID-19 confirmed cases, 319 discharged cases and 58 deaths as of 30th April 2020. This paper, therefore, subjected the daily cumulative reported COVID-19 cases of these three variables to nine (9) curve estimation statistical models in simple, quadratic, cubic, and quartic forms. It further identified the best of the thirty-six (36) models and used the same for prediction and forecasting purposes. The data collected by the Nigeria Centre for Disease Control for sixty-four (64) days, two (2) months and three (3), were daily monitored and eventually analyzed. We identified the best models to be Quartic Linear Regression Model with an autocorrelated error of order 1 (AR(1)); and found the Ordinary Least Squares, Cochrane Orcutt, Hildreth-Lu, and Prais-Winsten and Least Absolute Deviation (LAD) estimators useful to estimate the models' parameters. Consequently, we recommended the daily cumulative forecast values of the LAD estimator for May and June 2020 with a 99% confidence level. The forecast values are alarming, and so, the Nigerian Government needs to hastily review her activities and interventions towards COVID-19 to provide some tactical and robust structures and measures to avert these challenges.

Two-Parameter Modified Ridge-Type M-Estimator for Linear Regression Model.

The general linear regression model has been one of the most frequently used models over the years, with the ordinary least squares estimator (OLS) used to estimate its parameter. The problems of the OLS estimator for linear regression analysis include that of multicollinearity and outliers, which lead to unfavourable results. This study proposed a two-parameter ridge-type modified M-estimator (RTMME) based on the M-estimator to deal with the combined problem resulting from multicollinearity and outliers. Through theoretical proofs, Monte Carlo simulation, and a numerical example, the proposed estimator outperforms the modified ridge-type estimator and some other considered existing estimators.

The efficiency of Raphia hookeri adsorbent in indigo carmine dye removal: Economy depth via chemometrics.

The remediation of dye pollutants remains a concern in contemporary water management practices. Hence, the need for efficient and cost-effective techniques for dye removal from wastewater. In this study, the epicarp of Raphia hookeri fruits was treated with orthophosphoric acid for enhanced porosity and efficiency in the uptake of Indigo carmine dye (ICD). Treated Raphia hookeri fruit waste (RHPW) presented morphologically distributed pores as well as high porosity with Branneur-Emmet-Teller (BET) surface area of 945.43 m2/g. RHPW displayed functional groups suitable for adsorption. The maximum ICD uptake was observed at pH 5 while the maximum uptake (qmax) was 20.41 mg/g in the concentration range of 2-10 mg/L. Freundlich isotherm and Pseudo-second order kinetics well-described equilibrium and kinetics data respectively. This indicated a multilayered adsorption. The Dubinin-Radushkecich model energy value was 40.82 kJ/mol, indicating chemical adsorption. The ridge regression, the Lasso and the Elastic net statistical models were used to establish a positive relationship between the various adsorption operational parameters studied. Lasso provided the best result based on the estimated mean squared error. The RHPW-ICD adsorption system was more favorable at room temperature, as the removal efficiency decreased with temperature rise. The findings established Raphia hookeri fruit epicarp as an economical and sustainable precursor for the preparation of potent adsorbent for Indigo carmine dye removal. This can find possible application in wastewater treatment.

Robust-stein estimator for overcoming outliers and multicollinearity.

Linear regression models with correlated regressors can negatively impact the performance of ordinary least squares estimators. The Stein and ridge estimators have been proposed as alternative techniques to improve estimation accuracy. However, both methods are non-robust to outliers. In previous studies, the M-estimator has been used in combination with the ridge estimator to address both correlated regressors and outliers. In this paper, we introduce the robust Stein estimator to address both issues simultaneously. Our simulation and application results demonstrate that the proposed technique performs favorably compared to existing methods.

Modified ridge-type for the Poisson regression model: simulation and application.

The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood estimator (PMLE). There is a tendency that the explanatory variables grow together, which results in the problem of multicollinearity. The variance of the PMLE becomes inflated in the presence of multicollinearity. The Poisson ridge regression (PRRE) and Liu estimator (PLE) have been suggested as an alternative to the PMLE. However, in this study, we propose a new estimator to estimate the regression coefficients for the PRM when multicollinearity is a challenge. We perform a simulation study under different specifications to assess the performance of the new estimator and the existing ones. The performance was evaluated using the scalar mean square error criterion and the mean squared error prediction error. The aircraft damage data was adopted for the application study and the estimators' performance judged by the SMSE and the mean squared prediction error. The theoretical comparison shows that the proposed estimator outperforms other estimators. This is further supported by the simulation study and the application result.

Modeling the relationship between malaria prevalence and insecticide-treated bed net coverage in Nigeria using a Bayesian spatial generalized linear mixed model with a Leroux prior.

OBJECTIVES: To evaluate malaria transmission in relation to insecticide-treated net (ITN) coverage in Nigeria. METHODS: We used an exploratory analysis approach to evaluate variation in malaria transmission in relation to ITN distribution in 1,325 Demographic and Health Survey clusters in Nigeria. A Bayesian spatial generalized linear mixed model with a Leroux conditional autoregressive prior for the random effects was used to model the spatial and contextual variation in malaria prevalence and ITN distribution after adjusting for environmental variables. RESULTS: Spatial smoothed maps showed the nationwide distribution of malaria and ITN. The distribution of ITN varied significantly across the 6 geopolitical zones (p<0.05). The North-East had the least ITN distribution (0.196±0.071), while ITN distribution was highest in the South-South (0.309±0.075). ITN coverage was also higher in rural areas (0.281±0.074) than in urban areas (0.240±0.096, p<0.05). The Bayesian hierarchical regression results showed a non-significant negative relationship between malaria prevalence and ITN coverage, but a significant spatial structured random effect and unstructured random effect. The correlates of malaria transmission included rainfall, maximum temperature, and proximity to water. CONCLUSIONS: Reduction in malaria transmission was not significantly related to ITN coverage, although much could be achieved in attempts to curtail malaria transmission through enhanced ITN coverage. A multifaceted and integrated approach to malaria control is strongly advocated.

A new estimator for the multicollinear Poisson regression model: simulation and application.

The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation.

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

A New Ridge-Type Estimator for the Gamma Regression Model.

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

Spatial regression and geostatistics discourse with empirical application to precipitation data in Nigeria.

In this study, we propose a robust approach to handling geo-referenced data and discuss its statistical analysis. The linear regression model has been found inappropriate in this type of study. This motivates us to redefine its error structure to incorporate the spatial components inherent in the data into the model. Therefore, four spatial models emanated from the re-definition of the error structure. We fitted the spatial and the non-spatial linear model to the precipitation data and compared their results. All the spatial models outperformed the non-spatial model. The Spatial Autoregressive with additional autoregressive error structure (SARAR) model is the most adequate among the spatial models. Furthermore, we identified the hot and cold spot locations of precipitation and their spatial distribution in the study area.

Unbiased K-L estimator for the linear regression model.

Background: In the linear regression model, the ordinary least square (OLS) estimator performance drops when multicollinearity is present. According to the Gauss-Markov theorem, the estimator remains unbiased when there is multicollinearity, but the variance of its regression estimates become inflated. Estimators such as the ridge regression estimator and the K-L estimators were adopted as substitutes to the OLS estimator to overcome the problem of multicollinearity in the linear regression model. However, the estimators are biased, though they possess a smaller mean squared error when compared to the OLS estimator. Methods: In this study, we developed a new unbiased estimator using the K-L estimator and compared its performance with some existing estimators theoretically, simulation wise and by adopting real-life data. Results: Theoretically, the estimator even though unbiased also possesses a minimum variance when compared with other estimators.  Results from simulation and real-life study showed that the new estimator produced smaller mean square error (MSE) and had the smallest mean square prediction error (MSPE). This further strengthened the findings of the theoretical comparison using both the MSE and the MSPE as criterion. Conclusions: By simulation and using a real-life application that focuses on modelling, the high heating values of proximate analysis was conducted to support the theoretical findings. This new method of estimation is recommended for parameter estimation with and without multicollinearity in a linear regression model.

A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications.

The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.

COVID-19 prevalence estimation: Four most affected African countries.

The world at large has been confronted with several disease outbreak which has posed and still posing a serious menace to public health globally. Recently, COVID-19 a new kind of coronavirus emerge from Wuhan city in China and was declared a pandemic by the World Health Organization. There has been a reported case of about 8622985 with global death of 457,355 as of 15.05 GMT, June 19, 2020. South-Africa, Egypt, Nigeria and Ghana are the most affected African countries with this outbreak. Thus, there is a need to monitor and predict COVID-19 prevalence in this region for effective control and management. Different statistical tools and time series model such as the linear regression model and autoregressive integrated moving average (ARIMA) models have been applied for disease prevalence/incidence prediction in different diseases outbreak. However, in this study, we adopted the ARIMA model to forecast the trend of COVID-19 prevalence in the aforementioned African countries. The datasets examined in this analysis spanned from February 21, 2020, to June 16, 2020, and was extracted from the World Health Organization website. ARIMA models with minimum Akaike information criterion correction (AICc) and statistically significant parameters were selected as the best models. Accordingly, the ARIMA (0,2,3), ARIMA (0,1,1), ARIMA (3,1,0) and ARIMA (0,1,2) models were chosen as the best models for SA, Nigeria, and Ghana and Egypt, respectively. Forecasting was made based on the best models. It is noteworthy to claim that the ARIMA models are appropriate for predicting the prevalence of COVID-19. We noticed a form of exponential growth in the trend of this virus in Africa in the days to come. Thus, the government and health authorities should pay attention to the pattern of COVID-19 in Africa. Necessary plans and precautions should be put in place to curb this pandemic in Africa.

Predictive modelling of COVID-19 confirmed cases in Nigeria.

The coronavirus outbreak is the most notable world crisis since the Second World War. The pandemic that originated from Wuhan, China in late 2019 has affected all the nations of the world and triggered a global economic crisis whose impact will be felt for years to come. This necessitates the need to monitor and predict COVID-19 prevalence for adequate control. The linear regression models are prominent tools in predicting the impact of certain factors on COVID-19 outbreak and taking the necessary measures to respond to this crisis. The data was extracted from the NCDC website and spanned from March 31, 2020 to May 29, 2020. In this study, we adopted the ordinary least squares estimator to measure the impact of travelling history and contacts on the spread of COVID-19 in Nigeria and made a prediction. The model was conducted before and after travel restriction was enforced by the Federal government of Nigeria. The fitted model fitted well to the dataset and was free of any violation based on the diagnostic checks conducted. The results show that the government made a right decision in enforcing travelling restriction because we observed that travelling history and contacts made increases the chances of people being infected with COVID-19 by 85% and 88% respectively. This prediction of COVID-19 shows that the government should ensure that most travelling agency should have better precautions and preparations in place before re-opening.

Evaluation of the scholastic performance of students in 12 programs from a private university in the south-west geopolitical zone in Nigeria.

Cumulative grade point average (CGPA) is a system for calculation of GPA scores and is one way to determine a student's academic performance in a university setting. In Nigeria, an employer evaluates a student's academic performance using their CGPA score. For this study, data were collected from a student database of a private school in the south-west geopolitical zone in Nigeria. Regression analysis, correlation analysis, and analysis of variance (F-test) were employed to determine the study year that students perform better based on CGPA. According to the results, it was observed that students perform much better in year three (300 Level) and year four (400 Level) compared to other levels. In conclusion, we strongly recommend the private university to introduce program that will improve the academic performance of students from year one (100 level).

Data on expenditure, revenue, and economic growth in Nigeria.

This article describes the data for examining the influence of government expenditure and revenue on Nigerian economic growth. Data were extracted from the World Bank database and Central Bank of Nigeria (CBN) Statistical bulletin. The data are available with this article. The data is related to the research article "Newly proposed estimator for ridge parameter: an application to the Nigerian economy" (Lukman and Arowolo, 2018) but not discussed in detail. This data article will assist economists in identifying factors that will affect the economy of a country, especially in the African region.