Statistics

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Statistical theory and methods
(2002) Shangodoyin, D. K.; Olubusoye, O. E.; Shittu, O. I.; Adepoju, A A.
STA: 332 Laboratory/fieldwork on experimental design I
(Distance Learning Centre, University of Ibadan, 2007) Udomboso, C. G.
Comparative performance of the limited information techniques in a two equation structural model
(2007) Adepoju, A. A.
The samples with which we deal in practice are rather small. seldom exceeding 80 observations and frequently much smaller. 'Thus, it is of great interest to inquire into the properties of estimators for the typical sample sizes encountered in practice. The performances of three simultaneous estimation method using a model consisting of a mixture of an identified and over identified equations with correlated error terms and compared. The result of the Monte Carlo study revealed that the Two Stage least Squares (2SLS) and the Limited Information Maximum Likelihood (LIML) estimates are similar and in most cases identical in respect of the just-identified equation. The Total Absolute Biases (TAB) of 2SLS and LIML revealed asymptotic behavior under (upper triangular matrix) P1 while those of Ordinary Least Squares (OLS) exhibited no such behavior. For both upper and lower triangular matrices (P, and P2), 2SI.S estimates showed asymptotic behavior in the middle interval. The OI.S is the only stable estimator with a stable behavior of Root Mean Square Error (RM3F.) as its estimates increase (decrease) consistently for equation 1(equation 2) for P, (for P2).
Statistical computing: STA 231
(Distance Learning Centre, University of Ibadan, 2007) Udomboso, C. G.
On the maximization of the likelihood function against Iogarithmic transformation
(2008) Obisesan, K. O.; Udomboso, C. G.; Osowole, O. I.; Alaba, O. O.
We consider maximum likelihood estimation logarithmic transformation irrespective of mass of density functions. The estimators are assumed to be consistent, convergent and existing. They are referred to as asymptotically minimum-variance sufficient unbiased estimators (AMVSU). We find that the likelihood function gives accurate result when maximized than the log-likelihood. This is because logarithmic transformation has potential problems. We consider a uniform case where the parameter 0 cannot be estimated by calculus but order-statistics. We fit a truncated Poison distribution into data on damaged done after estimating λ by a Newton-Raphson Iterative Algorithm.
The effect of students' pre-admission performance on post-admission performance
(2008) Olayiwola, O. M.; Adepoju, A. A.; Okunlade, A.; Akomolafe, A.
This study uses canonical correlation analysis to investigate the effect of pre-admission performance (performance in SSCE/GCE and JAMB) on the post-admission performance (performance in 1OOlevel to 400 Level). The study population comprised of a set of students that were admitted in the same year in the department of computer science. University of Ibadan, Nigeria. The students’ SSCE/GC, JAMB. 100 Level to 400 level results were studied. The result shows that students ' pre-admission performance are highly correlated with their 100 level to 300 level, but uncorrelated with 400 level result. This may due to: complexity of the course as they are moving higher, effect of the project work. Strike, riot, lack of relevant textbooks, social activities. etc. This study then recommends that the University should introduce or assign level advisers to advice the students; they should ensure that they provide relevant textbooks to the library for the students.
A comparison of least squares dummy variable (LSDV) and the pooled estimator in fixed effect model
(2008) Olayiwola, O. M.; Adepoju, A.A.; Olajide, J. T
This paper examines a comparison of Least Squares Dummy Variable and a pooled estimator in a fixed effect model. The aims of the research are: to estimate the individuals firms parameters by using least squares dummy variables. To estimate parameter of the pooled observations using ordinary least squares. To estimate the behavioral relationship between individuals variables and to test for the significance différence across the groups. The framework was based on a fixed effect model. The analysis of a panel model was carried out using the Ordinary Least Squares (OLS) and Least Squares Dummy Variable (LSDV) methods. various tests were carried out to determine which of the methods to use when dealing with a panel data. The results of the analysis showed significant différence across the different groups effect. F is also significant at 95% level by using either the fixed effect or pooled model in a panel data. Also, a measure of fit of the model carried out showed that the fixed effect model significantly explained the variation in the dependent variable while pooling the model explained a very small proportion of the total variation in the dépendent variable. In the light of the above, it will be appropriate to use a fixed effect least squares dummy variable rather than pooling the data in the analysis of a panel data
Ranking of simultaneous equation techniques to small sample properties and correlated random deviates
(Science Publications, 2009) Adepoju, A.A; Olaomi, J.O
Problem statement: All simultaneous equation estimation methods have some desirable asymptotic properties and these properties become effective in large samples. This study is relevant since samples available to researchers are mostly small in practice and are often plagued with the problem of mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The objective of this research was to study the small sample properties of these estimators when the errors are correlated to determine if the properties will still hold when available samples are relatively small and the errors were correlated. Approach: Most of the evidence on the small sample properties of the simultaneous equation estimators was studied from sampling (or Monte Carlo) experiments. It is important to rank estimators on the merit they have when applied to small samples. This study examined the performances of five simultaneous estimation techniques using some of the basic characteristics of the sampling distributions rather than their full description. The characteristics considered here are the mean, the total absolute bias and the root mean square error. Results: The result revealed that the ranking of the five estimators in respect of the Average Total Absolute Bias (ATAB) is invariant to the choice of the upper (P1) or lower (P2) triangular matrix. The result of the FIML using RMSE of estimates was outstandingly best in the open-ended intervals and outstandingly poor in the closed interval (- 0.05
Ranking of simultaneous equation techniques to small sample properties and correlated random deviates
(Science Publications, 2009) Adepoju, A.A.; Olaomi, J.O.
Problem statement: All simultaneous equation estimation methods have some desirable asymptotic properties and these properties become effective in large samples. This study is relevant since samples available to researchers are mostly small in practice and are often plagued with the problem of mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The objective of this research was to study the small sample properties of these estimators when the errors are correlated to determine if the properties will still hold when available samples are relatively small and the errors were correlated. Approach: Most of the evidence on the small sample properties of the simultaneous equation estimators was studied from sampling (or Monte Carlo) experiments. It is important to rank estimators on the merit they have when applied to small samples. This study examined the performances of five simultaneous estimation techniques using some of the basic characteristics of the sampling distributions rather than their full description. The characteristics considered here are the mean, the total absolute bias and the root mean square error. Results: The result revealed that the ranking of the five estimators in respect of the Average Total Absolute Bias (ATAB) is invariant to the choice of the upper (P1) or lower (P2) triangular matrix. The result of the FIML using RMSE of estimates was outstandingly best in the open-ended intervals and outstandingly poor in the closed interval (- 0.05
Application of ordinal logistic regression model to occupation data
(Duncan Science Company, 2009) Adepoju, A. A.; Adegbite, M.
People's occupational choices might be influenced by their parents' occupation, gender, previous experiences, ages, and their own education level. We can study the relationship of one's occupation choice with education level and father's occupation. The occupational choices will be the outcome variable which consists of categories of occupations. The regression methods are capable of allowing researchers to identify explanatory variables related to organizational programs and services that contribute to the overall staff status. These methods also permit researchers to estimate the magnitude of the effect of the explanatory variables on the outcome variable. Therefore, regression methods seem to be superior in studying the relationship between the explanatory and outcome variables. This study used ordinal logistic regression method to examine the relationship between the ordinal outcome variable, different levels of staff status in the Lagos State Civil Service of Nigeria, the explanatory variables are Gender, Indigenous status, Educational Qualification, Previous Experience and Age. The outcome variable was measured on an ordered, categorical, and three-point Likert scale as Junior staff Middle Management staff, and Senior Management staff. Within the complete models, the legit link was the better choice because of its satisfying parallel lines assumption and larger model- fitting statistics. The study revealed that two explanatory variables namely, Education Qualification and Previous Working Experience significantly predicted the probability of an individual staff being a member of any of the three levels of staff status
Performances of the full information estimators in a two-equation structural model with correlated disturbances
(Bachudo Science, 2009) Adepoju, A. A.
The performances of two full information techniques, Three Stage Least Squares (3SLS) and Full Information Maximum Likelihood (FIML) of simultaneous equation models with correlated disturbance terms are compared with the Ordinary Least Squares (OLS) method in small samples. Comparative performance evaluation of the estimators was done using Average of Estimates, Total Absolute Bias (TAB) of Estimates, Root Mean Squared Error (RMSE) and Sum of Squared Residuals (RSS) of parameter estimates. The results of the Monte Carlo experiment showed that OLS is best with large negative or positive correlation, while 3SLS is best with feebly correlated error terms in the case of replication-based averages. The total absolute biases increase consistently as the sample size increases for OLS while FIML estimates reveal no distinct pattern. The magnitudes of the estimates yielded by two estimators, OLS and 3SLS, exhibited fairly consistent reaction to changes in magnitudes and direction of correlations of error terms
Efficiency in linear model with AR (1) and correlated error-regressor
(African Research Review, 2009-04) Olutunji., O.J.; Adepoju., A.A
In this study, we conduct several Monte-Carlo experiments to examine the sensitivity of the estimators relative to OLS using the Variance and RMSE criteria, in the presence of first order autocorrelated error terms which are also correlated with geometric regressor. We examine the of efficiency to ı, _, as well as, its asymptotic behaviour, N, when the above two assumptions are violated. We observe that CORC and HILU give similar result, same for ML and MLGRID. OLS is more efficient than CORC and HILU while ML and MLGRID dominate OLS. In the scenarios, efficiency does increase with increase in autocorrelation level, only ML and MLGRID at _ = 0.05 show that efficiency increases with increase in autocorrelation level. All estimators show that efficiency reducesas significant level increases only when the autocorrelation value and samplesize are small (_ = 0.4, N = 20). There is more efficiency gain when N and _are large at all significant correlation levels. Asymptotically, the efficiency of FGLS estimators increase with increasing autocorrelation but it is in different to the correlation levels. The asymptotic ranking is CORC and HILU followed by MLGRID and ML.
An alternative technique to ordinal logistic regression model under failed parallelism assumption
(2009-12) Adeleke, K.A .; Adepoju, A.A
Maternal health status is often measured in medical studies on an ordinal scale but data of this type arc generally reduced for analysis to a single dichotomy. Several statistical models have been developed to make full use of information in ordinal response data, but have not been much used in analyzing pregnancy outcomes. The authors discussed two of these statistical models the ordinal logistic regression model and the multinomial logistic regression model. Logistic regression models are used to analyze the dependent variable with multiple outcomes which can either be ranked or not. In this study, we described two logistic regression models for analyzing the categorical response variable. The first model uses the proportion-! odds model while the second uses the multinomial logistic regression model. The fits of these models using data on delivery from a Nigerian State hospital record/database were illustrated and compared to study the pregnancy outcomes. Analyses based on these models were carried out using STATA statistical package. The Multinomial logistic regression was found to be an important alternative to the ordinal regression technique when proportional odds assumption failed. The weight of the baby and the mother's history of disease (treated or not treated) were found to be important in determining the pregnancy outcome.
Factors affecting learning in an open and distance learning programme
(2010) Dontwi, I. K.; Amahia, G. N.; Chukwu, A. U.; Udomboso, C. G.
There is bound to be a shift towards those courses that will provide the knowledge and skills for economic relevance and earning power. Commerce, science and technology are likely to be oversubscribed, once driven world, seems to be diminishing steadily. When designing instruction for distance education, attention is often focused on the cognitive domain, as it is in "traditional" (face-to-face) instruction. What do the students need to know? Which instructional strategies will be most appropriate? Upon what performance criteria will learners be evaluated?
The use of gamma and weibull distributions in modeling rainfall data in Nigeria (a comparative analysis)
(2010) Udomboso, C. G.; Chukwu, A. U.; Nja, M. E.
The distribution of rainfall in Nigeria is not uniform due to the slight differences in the climatic conditions from one geographical region to the other. The climatic conditions ranges from the ‘very wet’ mangrove forest zone of the coastal areas, especially the South-South, to the semi arid regions of the North- West and North-East that share boundaries with the ‘very hot’ desert zone of the North Africa subcontinent. Rainfall data are examples of environmental data, which generally can be modeled by the family of exponential distributions. The Weibull probability function is the most widely used in fitting the distribution of rainfall. This study compares the results obtained by this function with another distribution proposed to the African scientists, that is, the gamma probability function by employing the Kolmogorov- Smimov (K-S) one sample test in testing the goodness- of-fit of these distributions. The results provided are useful tools for decision makers in hydrological and related establishments.
Ordinal logistic regression model: an application to pregnancy outcomes
(Science Publications, 2010) Adeleke, K.A.; Adepoju, A.A.
Problem statement: This research aimed at modeling a categorical response i.e., pregnancy outcome in terms of some predictors, determines the goodness of fit as well as validity of the assumptions and selecting an appropriate and more parsimonious model thereby proffered useful suggestions and recommendations. Approach: An ordinal logistic regression model was used as a tool to model the three major factors viz., environmental (previous cesareans, service availability), behavioral (antenatal care, diseases) and demographic (maternal age, marital status and weight) that affected the outcomes of pregnancies (livebirth, stillbirth and abortion). Results: The fit, of the model was illustrated with data obtained from records of 100 patients at Ijebu-Ode, State Hospital in Nigeria. The tested model showed good fit and performed differently depending on categorization of outcome, adequacy in relation to assumptions, goodness of fit and parsimony. We however see that weight and diseases increase the likelihood of favoring a higher category i.e., (livebirth), while medical service availability, marital status age, antenatal and previous cesareans reduce the likelihood/chance of having stillbirth. Conclusion/Recommendations: The odds of being in either of these categories i.e., livebirth or stillbirth showed that women with baby’s weight less than 2.5 kg are 18.4 times more likely to have had a livebirth than are women with history of babies 2.5 kg. Age (older age and middle aged) women are one halve (1.5) more likely to occur than lower aged women, likewise is antenatal, (high parity and low parity) are more likely to occur 1.5 times than nullipara.
Robustness of simultaneous estimation methods to varying degrees of correlation between pairs of random deviates
(International Research Publication House, 2010) Oyamakin, O.; Adepoju, A.A.
This study examined how six estimation methods of a simultaneous equation model cope with varying degrees of correlation between pairs of random deviates using the Variance and Total Absolute Bias (TAB). A two-equation simultaneous system was considered with assumed covariance matrix. The model was structured to have a mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The correlation between the pairs of normal deviates were generated using three scenarios of r = 0.0, 0.3 and 0.5. The performances of various estimators considered were examined at various sample sizes, correlation levels and 50 replications. The sample size, N = 20,25,30 each replicated 50 times was considered. OLS is performed best when the variance is used to study the finite sample properties of the estimators in that it produces the least variances in all the cases considered and at all sample sizes. All the estimators revealed an asymptotic pattern under CASE I.
Sensitivity of estimators to three levels of correlation between error terms
(2010-05) Adepoju, A.A; Iyaniwura, J.O.
A Monte Carlo simulation is employed to investigate the sensitivity of simultaneous equation different levels of correlation between random deviates. Three arbitrary levels of correlation between pairs random deviates were assumed. Three small sample sizes were used in this experiment, N = 15, N=25 and N 40 each replicated 100 times. A number of factors should be taken into account in choosing an method Although system methods are asymptotically most efficient in the absence of violation of independence of random errors, system methods are more sensitive to any kind of error than single equation methods. In practice, models are never perfectly specified nor are they completely free of correlated random deviates. It is a matter of judgment whether the correlation is strong enough to warrant avoidance of system methods. As sample size increases, the TAB for all the estimators decreased consistently except for FIML. OLS, 2SLS, LIML and FIML are remarkably insensitive to the choice of triangular matrices (P1 and P2) when using TAB to judge their performances. Best RSS estimates of 2SLS, LIML, and 3SLS found in the feebly correlated region
Alternative goodness-of-fit test in logistic regression models
(Medwell Journals, 2011) Nja, M. E.; Enang, E. I.; Chukwu, A. U.; Udomboso, C. G.
The Deviance and the Pearson chi-square are two traditional goodness-of-fit tests in generalized linear models for which the logistic model is a special case. The effort involved in the computation of either the Deviance or Pearson chi-square statistic is enormous and this provides a reason for prospecting an alternative goodness-of-fit test in logistic regression models with discrete predictor variables. The Deviance is based on the log likelihood function while the Pearson chi-square derives from the discrepancies between observed and predicted counts. Replacing observed and predicted counts with observed proportions and predicted probabilities, respectively in a cross-classification data arrangement, the standard error of estimate is proposed as an alternative goodness-of-fit test in logistic regression models. The illustrative example returns favourable comparisons with Deviance and the Pearson chi-square statistics.
Comparative analysis of rainfall prediction using statistical neural network and classical linear regression model
(Medwell Journals, 2011) Udomboso, C. G.; Amahia., G. N.
Different types of models have been used in modeling rainfall. Since 1990s however, interest has shifted from traditional models to ANN in rainfall modeling. Many researchers found out that the ANN performed better than such traditional models. In this study, we compared a traditional linear model and ANN in the modeling of rainfall in Ibadan, Nigeria. Ibadan is a city in West Africa, located in the tropical rainforest zone, using the data obtained from the Nigeria Meteorological (NIMET) station. Three variables were considered in this study rainfall, temperature and humidity. In selecting between the two models, we concentrated on the choice of adjusted R2 (R-2 ), Akaike Information Criterion (AIC) and Schwarz Information Criterion (SIC). Though, the MSE and R2 were also used, it was concluded from results that MSE is not a good choice for model selection. This is due to the nature of the rainfall data (which has wide variations). It was found that the Statistical Neural Network (SNN), generally performed better than the traditional (OLS).