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Item Using generalized estimating equation (gee) to analyse the influence of some factors on the state of health of diabetes patients(2018-04) Adepoju, A. A.; Afolabi, K.In longitudinal studies, observations measured repeatedly from the same subject over time are serially correlated. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. Generalized Estimating Equation (GEE) is a general statistical approach to fit a marginal model for longitudinal/clustered data analysis, and it has been popularly applied into clinical trials and biomedical studies. Generalized linear Model (GLM)on the other hand has been widely used in fitting a regression to a set of data of dependent variables depending solely on a/some set of covariates with the different set of distributions and their link function and its use has been extended to longitudinal data. This paper examines the effects of some factors; age, sex, Body Mass Index (BMI), blood pressure, exercise and glucose tolerance on the health status of 840 diabetes patients attending clinic over a period of five years using the generalized linear model and the generalized estimating equations methods. The GEE performs better than the GLM. The result reveals that glucose tolerance, blood pressure and BMI are the important factors that affect the state of health of these patientsItem Regression methods in the presence of heteroscedasticity and outliers(Academia Publishing, 2017-12) Adepoju, A. A .; Ogundunmade, T.P .; Adebayo, K. B.It has been observed over the years that real life data are usually non-conforming to the classical linear regression assumptions. One of the stringent assumptions that is unlikely to hold in many applied settings is that of homoscedasticity. When homogenous variance in a normal regression model is not appropriate, invalid standard inference procedure may result from the improper estimation of standard error when the disturbance process in a regression model present heteroscedasticity. When both outliers and heteroscedasticity exist, the inflation of the scale estimate can deteriorate. This study identifies outliers under heteroscedastic errors and seeks to study the performance of four methods; ordinary least squares (OLS), weighted least squares (WLS), robust weighted least squares (RWLS) and logarithmic transformation (Log Transform) methods to estimate the parameters of the regression model in the presence of heteroscedasticity and outliers. Real life data obtained from the Central Bank of Nigeria Bulletin and Monte Carlo simulation were carried out to investigate the performances of these four estimators. The results obtained show that the transformed logarithmic model proved to be the best estimator with minimum standard error followed by the robust weighted least squares. The performance of OLS is the least in this orderItem An Application of Bayesian Dynamic Linear Model to Okun’s Law(Scienpress Ltd, 2017) Awe, O. O.; Sanusi, K.A.; Adepoju, A. A.Many authors have used dynamic time series regression models to analyse Okun’s law. This type of models often require first differencing the dependent and independent variables, as well as investigating the maximum lag length required for the model to be efficient. In this paper, we propose a straight-forward time-varying parameter state space model for analyzing Okun’s law. In particular, as a case study, we investigate the validity and stability of Okuns law using a Bayesian Dynamic Linear Model which implicitly describes the time-varying relationship between Gross Domestic Product (GDP) and unemployment rate of a major economy in Africa for three decades. The time-varying parameters of this model are estimated via a modified recursive forward filtering, backward sampling algorithm. We find that Okuns law exhibited structural instability in Nigeria in the period 1970-2011, with the sensitivity of unemployment rate to movements in output growth loosing stability over time, which may have been a contributor to her recent economic declineItem Frequentist and bayesian estimation of parameters of linear regression model with correlated explanatory variables(2017) Adepoju, A. A.; Adebajo, E. O; Ogundunmade, P. T.This paper addressed the popular issue of collinearity among explanatory variables in the context of a multiple linear regression analysis, and the parameter estimations of both the classical and the Bayesian methods. Five sample sizes: 10, 25, 50, 100 and 500 each replicated 10,000 times were simulated using Monte Carlo method. Four levels of correlation p = 0.0,0.1,0.5, and 0.9 representing no correlation, weak correlation, moderate correlation and strong correlation were considered. The estimation techniques considered were; Ordinary Least Squares (OLS), Feasible Generalized Least Squares (FGLS) and Bayesian Methods. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE) of the estimates. In all cases considered, the Bayesian estimators had the best performance. It was consistently most efficient than the other estimators, namely OLS and FGLSItem Effects of atypical observations on the estimation of seemingly unrelated regression model(Science and Education Publishing, 2017) Adepoju, A. A.; Akinwumi, A. OThe Seemingly Unrelated Regression Equation model is a generalization of a linear regression model that consists of several regression equations in order to achieve efficient estimates. Unfortunately, the assumptions underlying most SUR estimators give little/no consideration to outlying observations which may be present in the data. These atypical observations may have some apparent distorting effects on the estimates produced by these estimators. This study thus examined the effect of outliers on the performances of SUR and OLS estimators using Monte Carlo simulation method. The Cholesky method was used to partition the variance-covariance matrix by decomposing it into the upper and lower non-singular triangular matrices. Varying degree of outliers; 0%, 5%, and 10% were each introduced into five sample sizes; 20, 40, 60, 100 and 500 respectively. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE). The results showed that at 0% outliers (when outliers were absent), the ABIAS and MSE of the SUR and OLS estimators showed similar results. At 5% and 10% outliers, the magnitude in ABIAS and MSE for both estimators increased but the SUR estimator showed better performance than the OLS estimator. As the sample size increases, ABIAS and MSE of the estimators decreased consistently for the various degrees of outliers considered with SUR consistently better than OLSItem On the modification of M-out-of-N bootstrap method for heavy-tailed distributions(Global Society of Scientific Research and Researchers, 2015) Opayinka, H. F.; Adepoju, A.A.This paper is on the modification of 𝑚-out-of-𝑛 bootstrap method for heavy-tailed distributions such as income distribution. The objective of this paper is to present a modified 𝑚-out-of-𝑛 bootstrap method (𝑚𝑚𝑜𝑛) and compare its performance with the existing m-out-of-n bootstrap method (𝑚𝑜o𝑛). The nature of the upper tail of a distribution is the major reason for the poor performance of classical bootstrap methods even in large samples. The ‘𝑚𝑚𝑜𝑛’ bootstrap method was therefore, proposed as an alternative method to ‘𝑚𝑜𝑛’ bootstrap method. The distribution involved has finite variance. The simulated data sets used was drawn from Singh-Maddala distribution. The methodology involved decomposing the empirical distribution and sampling only n⃛ times with replacement from a sample size n, such that n⃛ →∞ as n→∞, and n⃛/n →0. The performances are judged using standard error; absolute bias; coefficient of variation and root mean square error. The findings showed that ‘𝑚𝑚𝑜𝑛’ performed better than 𝑚𝑜𝑛 in moderate and larger samples and it converged fasterItem Fractional integration and structural breaks in bank share prices in Nigeria(Elsevier, 2015) Gil-Alana, L. A.; Yaya, O.S.; Adepoju, A. A.The paper employs both fractional integration and structural break techniques in studying the daily share prices structure of the banking sector in Nigeria. Our data span between 2001 and 2012, covers periods before and after the global financial crisis. The results obtained using both parametric and semi parametric methods indicate little evidence of mean reversion since most of the orders of integration are equal to or higher than1. Long memory is found in the absolute and squared return series. The possibility of structural breaks is also taken into account and the results show a different number of breaks depending on the bank examined. In general, an increase in the degree of dependence across time is noticed, and the most common break took place in December 2008, probably being related with the world financial crisis affecting also the banking system in NigeriaItem A time varying parameter state-space model for analyzing money supply-economic growth nexus(2015-03) Awe, O.O.; Crandell, I.; Adepoju, A.A.; Leman, S.In this paper, we propose a time-varying parameter state space model for analyzing predictive nexus of key economic indicators such as money supply and Gross Domestic Product (GDP). Economic indicators are mainly used for measuring economic trends. Policy makers in both advanced and developing nations make use of economic indicators like GDP to predict the direction of aggregate economic activities. We apply the Kalman filter and Markov chain Monte Carlo algorithm to perform posterior Bayesian inference on state parameters specified from a discount Dynamic Linear Model (DLM), which implicitly describes the relationship between response of GDP and other economic indicators of an economy. In our initial exploratory analysis, we investigate the predictive ability of money supply with respect to economic growth, using the economy of Nigeria as a case study with an additional evidence from South African economy. Further investigations reveal that leading variables like capital expenditure, the exchange rate, and the treasury bill rate are also useful for forecasting the GDP of an economy. We demonstrate that by using these various regressors, there is a substantial improvement in economic forecasting when compared to univariate random walk modelsItem Bayesian optimal filtering in dynamic linear models: an empirical study of economic time series data(2015) Awe, O. O.; Adepoju, A. A.This paper reviews a recursive Bayesian methodology for optimal data cleaning and filtering of economic time series data with the aim of using the Kalman filter to estimate the parameters of a specified state space model which describes an economic phenomena under study. The Kalman filter, being a recursive algorithm, is ideal for usage on time-dependent data. As an example, the yearly measurements of eight key economic time series data of the Nigerian economy is used to demonstrate that the integrated random walk model is suitable for modeling time series with no clear trend or seasonal variation. We find that the Kalman filter is both predictive and adaptive, as it looks forward with an estimate of the variance and mean of the time series one step into the future and it does not require stationarity of the time series data consideredItem On the comparative study of estimators in seemingly unrelated regression equation(2015) Adepoju, A. A.; Olamide, E. I.This work examined the efficiencies of Ordinary Least Squares (OLS) and Seemingly Unrelated Regression (SUR) estimators in lagged and unlagged models. Literature has shown gain in efficiency of SUR estimator over OLS estimator when the errors are correlated across equations. This paper studied the efficiencies of these estimators in a lagged and unlagged models and also sought a comparative study of these estimators in both models. Data was simulated for sample sizes 50, 100 and 1000 with 5000 bootstrapped replicates in each case with the predictors having Gaussian distribution. Results from the study showed that both estimators were efficient in each model with the SUR estimator being consistently more efficient than the OLS estimator as the sample size increased. On the assessment of the models, the unlagged model was found to be more efficient than the lagged model in small sample but converged as sample size increased.