Archive of "Mathematics and Computer Sciences Journal (MCSJ)"
Volume 2, Issue 3
Mar 2017

Longitudinal Data with Nonignorable Dropout

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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We investigate marginal inference for longitudinal data subject to nonignorable dropout.The proposed marginalised model directly specifies marginal associations between longitudinal responses and covariates while leaving the within-subject dependence unspecified. It incorporates nonignorable dropout events, which marginally follow a semiparametric transformation model, through a flexible conditional mean model. We develop an estimation procedure based on a series of asymptotically unbiased estimating equations. The resulting estimators for the marginal regression parameters are consistent and asymptotically normal, with a sandwich-type variance-covariance matrix that can be consistently estimated by the usual plug-in rule. The proposed approach is evaluated by simulations and illustrated by a real data application.

Author(s): Mengling Liu

A Century of Nonparametrics

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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In this talk the author discusses the developments of nonparametric statistics from its infancy to modern methods through eyes of the text books that came about through the century. Some key mathe- matical techniques will be discussed enriching the adhoc methods. This discussion will help the new comers to see that simple ideas may lead to profound developments of modern times. Books are of historic value to the development of a subject.

Author(s): A. K. Md. Ehsanes Saleh

Wave Approach in Dynamical Discrete-Continuous Systems

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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The paper deals with the dynamics of discrete-continuous systems consisting of elastic elements connected by means of rigid bodies. They belong to a certain class of discrete-continuous systems, namely to those where the motion of elastic elements with a constant cross-section is described by means of the classical wave equation, [1-3]. The discussed systems can be longitudinally or torsionally deformed. In the discussion a wave method using the solution of the dAlembert type is applied, what leads to solving equations with a retarded argument. After a short description of the approach applied, detailed considerations are done for two nonlinear discrete-continuous systems. The first one consists of three noncoaxial rods longitudinally deformed, two rigid bodies and a local nonlinearity having characteristics of a hard type as well as of a soft type. In systems with a hard type characteristic amplitudes jumps are observed while in systems with a soft type characteristic solutions amplitudes can diverge to infinity. The second one is a multi-mass system torsionally deformed with rigid bodies having variable mass moments of inertia. Local nonlinearities and variable inertia in such systems are justified by engineering solutions in many machines and mechanisms. Moreover, it is shown that in linear cases analytical solutions can be derived in the form of series consisting of exponential functions and polynomials.

Author(s): Amalia Pielorz

Plurality of Methods for the Categorical Variables: Empirics of Microfinance Impacts on Happiness in Thailand and Brazil

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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This paper aims to explore and compare different types of econometric models for capturing impacts of microfinance on the level of self-reported happiness and subjective wellbeing indicators such as life domain satisfaction, positive and negative affects. Using a comparison of microfinance case studies from Thailand (The village fund programme and the savings group fund) and Brazil (Social bank programme), this research examines the impact of small loans for the poor on their happiness and subjective wellbeing indicators. The data is from household surveys and in-depth interviews, collected by the author in 2008-2009 in rural areas of both countries. When measuring the impact of microfinance on happiness and other related subjective indicators, the issues of discrete choice problems involving binary, ordered or multinomial discrete alternatives cannot be avoided. In this study, for example, self-reported happiness can be measured in a categorical variable (1 = not too happy, 2 = fairly happy, and 3 = very happy). A large body of previous literature acknowledges the inappropriateness of using linear regression when the dependent variable is categorical. By using different types of model, including ordinary least square, ordered probit and ordered logit models, multinomial logit model, binary choice model, and Heckman selection model, results have been generated showing differences and similarities among those methods which can assist in selecting the optimal model.

Author(s): Thanawit Bunsit

Multiple Confounded and Orthogonal Replicated Full Factorial BIB Designs

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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The sn factorial design, where s is a prime number like 2, 3, 5, etc., generally confounds a set of diferent orthogonal factorial efects with sr blocks (n > r > 1) under one replicate. Thus there will be a complete set of orthogonal replicates of different group of orthogonal factorial efects for constructing a partially confounded sn factorial design in sr blocks. The factorial design, in general, when it partially confounds different orthogonal sets of diferent groups of orthogonal factorial efects under the complete set of different orthogonal replicates constitutes a BIB design having their individual properties, same result and detailed information of all factorial efects. The procedure is illustrated with some examples and one practical application.

Author(s): M. Shamsuddin, M. Albassam

Sequential test for censored data with linear transformation models

Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Mar 2017

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In this talk, we will present a sequential test for censored data with linear transformation models which include Cox proportional hazards model and proportional odds model. The approach is based on a score process motivated by Chen, Jin and Yings (2002) estimation procedure. We show that for given interim analyses time points, the score process is approximated by a mean 0 multivariate normal distribution and the covariance matrix can be consistently estimated. Then with the boundaries procedure proposed by Slud andWei (1982), a repeated significant test can be conducted. Numerical studies will also be presented.

Author(s): Lin Huang and Zhezhen Jin