FACULTY OF SCIENCE
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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 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 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 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.Item Evaluation of simultaneous equation techniques in the presence of misspecification error: a Monte Carlo approach(2014) Ojo, O. O.; Adepoju, A. A.One of the assumptions of Classical Linear Regression Model (CLRMA), is that the regression model be ‘correctly’ specified. If the model is not ‘correctly’ specified, the problem of model misspecification error arises. The objective of the study is to know the performances of the estimator and also the estimator that is greatly affected by misspecification error due to omission of relevant explanatory variable. Four simultaneous equation techniques (OLS, 2SLS, 3SLS, LIML) were applied to a two-equation model and investigated on their performances when plagued with the problem of misspecification error. A Monte Carlo method simulation method was employed to investigate the effect of these estimators due to misspecification of the model. The findings revealed that the estimates obtained by 2SLS and 3SLS are similar and variances by all the estimates reduced consistently as the sample size increases. The study had revealed that 2 3 SLS performed best using average of parameter criterion while OLS generated the least variances. LIML is mostly affected by misspecificationItem Bootstrap approach for estimating seemingly unrelated regressions with varying degrees of autocorrelated disturbances(2013) Ebukuyo, O. B.; Adepoju, A. A.; Olamide, E. I.The Seemingly Unrelated Regressions (SUR) model proposed in 1962 by Arnold Zellner has gained a wide acceptability and its practical use is enormous. In this research, two methods of estimation techniques were examined in the presence of varying degrees of _rst order Autoregressive [AR(1)] coefficients in the error terms of the model. Data was simulated using bootstrapping approach for sample sizes of 20, 50, 100, 500 and 1000. Performances of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators were examined under a definite form of the variance-covariance matrix used for estimation in all the sample sizes considered. The results revealed that the GLS estimator was efficient both in small and large sample sizes. Comparative performances of the estimators were studied with 0.3 and 0.5 as assumed coefficients of AR(1) in the first and second regressions and these coefficients were further interchanged for each regression equation, it was deduced that standard errors of the parameters decreased with increase in the coefficients of AR(1) for both estimators with the SUR estimator performing better as sample size increased. Examining the performances of the SUR estimator with varying degrees of AR(1) using Mean Square Error (MSE), the SUR estimator performed better with autocorrelation coefficient of 0.3 than that of 0.5 in both regression equations with best MSE obtained to be 0.8185 using _ = 0:3 in the second regression equation for sample size of 50. Key words: Autocorrelation||Bootstrapping||Generalized least squares||Ordinary least squares||Seemingly unrelated regressionsItem Simultaneous equation estimation with first order auto correlated disturbances(2013-08) Ojo, Y. O.; Adepoju, A. A.The estimation of the parameters of simultaneous equation problem is usually affected by the existence of mutual correlation between pairs of random deviates, which is a violation of the assumption of no autocorrelation between the error terms. In practice the form of correlation between the pairs of random deviates is not known. This study therefore examined a two-equation model in which the correlation between the random deviates is assumed to follow a first-order Autoregressive [AR (1)] process. Data was simulated using Monte Carlo approach with varying sample sizes each replicated 1000 times. The behaviour of OLS, 2SLS, LIML and 3SLS were evaluated using Variance, Root Mean Square Error (RMSE) and Absolute Bias (AB). The absolute bias estimates decrease in most cases as the sample size increases. The variances obtained by all the estimators reduced consistently as the sample size increases. There was no clear pattern in the behaviour of the RMSE across sample sizes. The results for = 0.3 were better than when = 0.0 with respect to each criterion but retained the same pattern. This work established that when was different from zero, the estimators performed better, hence the choice of should be carefully made as this may significantly affect the performances of the estimators