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Slope Optimal Designs for Third Degree Kronecker Model Mixture Experiments
Cheruiyot Kipkoech,
Koske Joseph,
Mutiso John
Issue:
Volume 6, Issue 4, July 2017
Pages:
170-175
Received:
13 October 2016
Accepted:
28 October 2016
Published:
1 June 2017
Abstract: Mixture experiments are special type of response surface designs where the factors under study are proportions of the ingredients of a mixture. In response surface designs the main interest of the experimenter may not always be in the response at individual locations, but the differences between the responses at various locations is of great interest. Most of the studies on estimation of slope (rate of change) have concentrated in Central Composite Designs (CCD) yet mixture experiments are intended to show the response for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients at different locations. Slope optimal mixture designs for third degree Kronecker model were studied in order to obtained optimal formulations for all possible ingredients in simplex centroid. Weighted Simplex Centroid Designs (WSCD) and Uniformly Weighted Simplex Centroid Designs (UWSCD) mixture experiments were obtained in order to identify optimal proportions for each of the ingredients formulation. Derivatives of the Kronecker model mixture experiment were used to obtain Slope Information Matrices (SIM) for four ingredients. Maximal parameters of interest for third degree Kronecker model were considered. D-, E-, A-, and T- optimal criteria and their efficiencies for both WSCD and UWSCD third degree Kronecker model were obtained. UWSCD was found to be more efficient than WSCD for almost all the points in the simplex designs, therefore recommended for more optimal results in mixture experiments.
Abstract: Mixture experiments are special type of response surface designs where the factors under study are proportions of the ingredients of a mixture. In response surface designs the main interest of the experimenter may not always be in the response at individual locations, but the differences between the responses at various locations is of great intere...
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Count Regression Models with Application to Caries Experience for Children Attending Lady Northey Dental Clinic in Nairobi
Agnes Njambi Wanjau,
Samuel Musili Mwalili
Issue:
Volume 6, Issue 4, July 2017
Pages:
176-181
Received:
20 May 2017
Accepted:
31 May 2017
Published:
9 June 2017
Abstract: Count regression models were developed to model data with integer outcome variables. These models can be employed to examine occurrence and frequency of occurrence. Four common types of count regression models are applied to caries data among children aged between three and six years attending Lady Northey Dental clinic between September, 2014 and November 2014. These models include Poisson, Negative Binomial (NB), Zero Inflated Poisson (ZIP) and Zero Inflated Negative Binomial (ZINB). The simplest count regression model, Poisson, was fitted first before considering other complex models. However, it did not perform better than its improved counterparts. The NB model proved to be the the simplest model that fits the data well according to Akaike Information Criterion (AIC), and was therefore employed to determine the important predictors of caries experience among the children. Model comparison was performed on the four models by use of AIC. Deviance values for various NB models were compared and the model with the least deviance value was considered to give a subset of best predictors of Early Childhood Caries (ECC). These predictors included age, gender, brushing frequency, feeding habit biscuits, feeding habit jam and highest education of the mother.
Abstract: Count regression models were developed to model data with integer outcome variables. These models can be employed to examine occurrence and frequency of occurrence. Four common types of count regression models are applied to caries data among children aged between three and six years attending Lady Northey Dental clinic between September, 2014 and ...
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Bayesian Joint Modelling of Longitudinal and Survival Data of HIV/AIDS Patients: A Case Study at Bale Robe General Hospital, Ethiopia
Ahmed Hasan Dessiso,
Ayele Taye Goshu
Issue:
Volume 6, Issue 4, July 2017
Pages:
182-190
Received:
14 February 2017
Accepted:
25 February 2017
Published:
23 June 2017
Abstract: Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for AIDS. This study explores application of Bayesian joint modeling of HIV/AIDS data obtained from Bale Robe General Hospital, Ethiopia. The objective is to develop separate and joint statistical models in the Bayesian framework for longitudinal measurements and time to death event data of HIV/AIDS patients. A linear mixed effects model (LMEM), assuming homogenous and heterogeneous CD4 variances, is used for modeling the CD4 counts and a Weibull survival model is used for describing the time to death event. Then, both processes are linked using unobserved random effects through the use of a shared parameter model. The analysis of both the separate and the joint models reveal that the assumption of heterogeneous (patient-specific) CD4 variances brings improvement in the model fit. The Bayesian joint model is found to best fit to the data, and provided more precise estimates of parameters. The shared frailty is significant showing the association between the linear mixed effect (LME) and survival models.
Abstract: Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for AIDS. This study explores application of Bayesian joint modeling of HIV/AIDS data obtained from Bale Robe General Hospital, Ethiopia. The objective is to develop separate and joint statistical models in the Bayesian framework for l...
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Identification and Modeling of Outliers in a Discrete - Time Stochastic Series
Imoh Udo Moffat,
Emmanuel Alphonsus Akpan
Issue:
Volume 6, Issue 4, July 2017
Pages:
191-197
Received:
27 February 2017
Accepted:
8 April 2017
Published:
5 July 2017
Abstract: This study was prompted by the fact that the presence of outliers in discrete-time stochastic series may result in model misspecification, biases in parameter estimation and in addition, it is difficult to identify some outliers due to masking effects. However, the iterative approach which involves joint estimation of outliers effects and model parameters appears to be a panacea for masking effects. Considering the dataset on credit to private sector in Nigeria from 1981 to 2014, we found that ARIMA (1, 1, 1) model fitted well to the series without considering the presence of outliers. Using the iterative procedure method to reduce masking effects, the following outliers, IO (t = 24), AO (t = 33) and TC (t = 22) were identified. Adjusting the series for outliers and iterating further, ARIMA (2, 0, 1) model alongside AO (t = 33) and TC (t = 22) outliers was found to fit the series better than ARIMA (1, 1, 1) model. The implication is that in the presence of outliers, ARIMA (1, 1, 1) model was misspecified, the order of integration was wrong and by extension, autocorrelation and partial autocorrelation functions were misleading, and the estimated parameters were biased.
Abstract: This study was prompted by the fact that the presence of outliers in discrete-time stochastic series may result in model misspecification, biases in parameter estimation and in addition, it is difficult to identify some outliers due to masking effects. However, the iterative approach which involves joint estimation of outliers effects and model par...
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Determinant of Under-Five Child Mortality in Ethiopia
Issue:
Volume 6, Issue 4, July 2017
Pages:
198-204
Received:
1 March 2017
Accepted:
27 March 2017
Published:
7 July 2017
Abstract: Many countries are not on track to complete UNICEF’s Millennium Development Goals (MDGs) target of a two-thirds reduction in the rate of child mortality by 2015. This paper examines determinants of under-five mortality in Ethiopia. The study utilizes the data extracted from the 2011 Ethiopia demographic and health survey. Multivariate logistic analysis reflects that sex of the child, family size, education level of mother, age at first birth of mother, breast-feeding; using contraceptive method and region of child have significant influence on under-five child mortality in Ethiopia. The proximate determinants are found to have stronger influence on under-five mortality than the socioeconomic factors considered in the study do.
Abstract: Many countries are not on track to complete UNICEF’s Millennium Development Goals (MDGs) target of a two-thirds reduction in the rate of child mortality by 2015. This paper examines determinants of under-five mortality in Ethiopia. The study utilizes the data extracted from the 2011 Ethiopia demographic and health survey. Multivariate logistic anal...
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Modified Exact Single-Value Criteria for Partial Replications of the Central Composite Design
Eugene C. Ukaegbu,
Polycarp E. Chigbu
Issue:
Volume 6, Issue 4, July 2017
Pages:
205-208
Received:
18 October 2016
Accepted:
3 February 2017
Published:
10 July 2017
Abstract: Replication of the factorial (cube) and/or axial (star) portions of the central composite design (CCD in response surface exploration has gained great attention recently. Some well known metrics (called single-value functions or criteria) and graphical methods are utilized in evaluating the regression based response surface design. The single-value functions considered here are the A-efficiency, 
and the D-efficiency, 
, where 
, k is number of factors, 
is the kth design measure, 
is the design’s information matrix, 
is its inverse and N is the total number of experimental runs. These two functions are very popular in parameter estimation in response surface methodology. The exact measures of these two design criteria will be developed analytically in this work to account for partial replication of the cube and/or star components of the CCD. This will alleviate the burden of manual computation of these metrics when there are partial replications and reduce over reliance on software values which, often, are approximate values and maybe inaccurate.
Abstract: Replication of the factorial (cube) and/or axial (star) portions of the central composite design (CCD in response surface exploration has gained great attention recently. Some well known metrics (called single-value functions or criteria) and graphical methods are utilized in evaluating the regression based response surface design. The single-value...
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Geostatistics Analysis of Infant Mortality Rate in Ethiopia
Montasir Ahmed Osman Mohamed
Issue:
Volume 6, Issue 4, July 2017
Pages:
209-213
Received:
17 May 2017
Accepted:
24 May 2017
Published:
10 July 2017
Abstract: In this paper, spatial statistical analysis of infant mortality rate in Ethiopia is addressed. The analysis investigated of a significance spatial autocorrelation attendance as well as an adapting of a generalized linear mixed model with spatial covariance structure. The results showed the distribution is much spatially associated. Some geographical, economical and healthy variables are used to estimate the model. Several examined variables have a significant effect in the model contrast to other have an insignificant impact. The results highlight the role of improving education to decline the risk of infant mortality rate. Male and children with extra weight are higher exposed and the risk is highly different from one zone to another.
Abstract: In this paper, spatial statistical analysis of infant mortality rate in Ethiopia is addressed. The analysis investigated of a significance spatial autocorrelation attendance as well as an adapting of a generalized linear mixed model with spatial covariance structure. The results showed the distribution is much spatially associated. Some geographica...
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Determining Solvency and Insolvency of Commercial Banks in Nigeria
Yahaya Haruna U.,
Abdulkarim Muhammad
Issue:
Volume 6, Issue 4, July 2017
Pages:
214-220
Received:
12 April 2017
Accepted:
26 April 2017
Published:
26 July 2017
Abstract: This paper presents the application of artificial intelligence technique to develop aMulti-Layer Perceptron neural network model for determining the status (solvent or insolvent) of commercial banks in Nigeria. The common traditional classification techniques based on statistical parametric methods are constraint to fulfill certain assumptions. When those assumptions fail, the techniques do not often give sufficient descriptive accuracy in classifying the status of the banks. However, a class of feed-forward architecture of neural network known as Multi-Layer Perceptron (MLP) is not constraint by those parametric assumptions and offers good classification technique that competes well with the traditional statistical parametric techniques. In this study, data were sourced from the central bank of Nigeria and financial reports of the commercial banks in Nigeria. The banks specific variable of age, history of merger, time, total assets and total revenue are used as the input variables to the neural network. The solvency or insolvency as status are the two possible outputs of the neural network for each commercial bank in the period of 1994-2015. The developed MLP neural network model has 5 input neurons, 3 hidden neurons and 1 output neuron. Sigmoid activation function for the hidden neurons and “purelin” transfer function for the output neurons were utilized in training the MLP neural network. The results demonstrate that MLP neural networks are a viable technique for status classification of commercial banks in Nigeria.
Abstract: This paper presents the application of artificial intelligence technique to develop aMulti-Layer Perceptron neural network model for determining the status (solvent or insolvent) of commercial banks in Nigeria. The common traditional classification techniques based on statistical parametric methods are constraint to fulfill certain assumptions. Whe...
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