Sanizah Ahmad

Outlier detection in logistic regression and its application in medical data analysis

The application of logistic regression is widely used in medical research. The detection of outliers has become an essential part of logistic regression. It is often observed outliers have a considerable influence on the analysis results, which may lead the study to the wrong conclusions. Many procedures for the identification of outliers in logistic regression are available in the literature. In this paper, four methods for outlier detection have been investigated and compared through numerical examples.

Estimating Optimal Parameter of Box-Cox Transformation in Multiple Regression with Non-normal Data

Normally distributed data are needed in many statistical analyses including multiple regression (MR). When data is not normally distributed, remedial actions in making the data normal are necessary. In this study, the violation of this assumption is overcome by using the Box-Cox transformation (BCT). An investigation using simulation designs with data generated from three skewed sample data of non-normal distributions namely Exponential, Gamma and Beta Distributions based on the various sample sizes (100, 500 and 1000) are carried out. Hence, the simulation studies are implemented to estimate optimal lambda in the BCT based on two scenarios: (i) response variable (Y) follows several non-normal distributions and (ii) errors from several non-normal distributions. The results show that lambda = 0.30, 0.40 and 0.50 are the optimal lambdas produced for Exponential, Gamma and Beta Distributions. Therefore, BCT with optimal lambda value improves analyses in MRs when data are not normal. The performance of BCT method is also illustrated using the real-life data.

Box-Cox Optimal Parameter Estimation for Multiple Regressions with Homoscedasticity

Many real data do not conform to the assumption of homoscedasticity. In multiple regressions, the violation of the homoscedasticity assumption can be a complicating factor in estimating parameters, hypothesis testing and model selection. In this study, the violation of this assumption can be overcome by using the Box-Cox transformation. An investigation using simulation designs with data generated from three skewed sample data of non-normal distributions namely Exponential, Gamma and Beta distributions based on the various sample sizes (n = 100, 500 and 1000) are carried out. Hence, the simulation studies are implemented to estimate optimal lambda in the Box-Cox transformation based on data sets with different variances with errors that follow a normal distribution with a mean (µ = 0) and different variances (σ2 = 50, 100). Results show that lambda = 0.30* and lambda = 0.40* are the most often optimal lambda produced for these three distributions. As such, Box-Cox transformation with optimal lambda value improves analyses in multiple regressions particularly in the presence of homoscedasticity.

Diagnosis of students’ ability in a statistical course based on Rasch probabilistic outcome

Measuring students’ ability and performance are important in assessing how well students have learned and mastered the statistical courses. Any improvement in learning will depend on the student’s approaches to learning, which are relevant to some factors of learning, namely assessment methods carrying out tasks consisting of quizzes, tests, assignment and final examination. This study has attempted an alternative approach to measure students’ ability in an undergraduate statistical course based on the Rasch probabilistic model. Firstly, this study aims to explore the learning outcome patterns of students in a statistics course (Applied Probability and Statistics) based on an Entrance-Exit survey. This is followed by investigating students’ perceived learning ability based on four Course Learning Outcomes (CLOs) and students’ actual learning ability based on their final examination scores. Rasch analysis revealed that students perceived themselves as lacking the ability to understand about 95% of the stat...

A comparison of model-based imputation methods for handling missing predictor values in a linear regression model: A simulation study

In regression analysis, missing covariate data has been a common problem. Many researchers use ad hoc methods to overcome this problem due to the ease of implementation. However, these methods require assumptions about the data that rarely hold in practice. Model-based methods such as Maximum Likelihood (ML) using the expectation maximization (EM) algorithm and Multiple Imputation (MI) are more promising when dealing with difficulties caused by missing data. Then again, inappropriate methods of missing value imputation can lead to serious bias that severely affects the parameter estimates. The main objective of this study is to provide a better understanding regarding missing data concept that can assist the researcher to select the appropriate missing data imputation methods. A simulation study was performed to assess the effects of different missing data techniques on the performance of a regression model. The covariate data were generated using an underlying multivariate normal distribution and the dep...

The refinement of partial robust M-regression model using winsorized mean and Hampel weight function

Partial Robust M-Regression (PRM) is a robust Partial Least Squares (PLS) method using M-estimator, with multivariate L1 median and a monotonous weight function, known as Fair function in its algorithm. In many studies, the use of re-descending weight functions were much preferred to monotonous weight function due to the fact that the latter often failed to assign proper weights to outliers according to their severity. With the intention of improving the performance of PRM, this study suggested slight modifications to PRM by using winsorized mean and Hampel function, which comes from the family of re-descending weight functions. The proposed method was applied to a real high dimensional dataset which then modified to contain residual outliers as well as bad leverage points. The performance of PLS, PRM and modified PRM was assessed by means of their standard error of prediction (SEP) values. Compared to classical PLS and PRM, an improved performance was observed from the proposed method.

Enhancement of partial robust M-regression (PRM) performance using Bisquare weight function

Partial Least Squares (PLS) regression is a popular regression technique for handling multicollinearity in low and high dimensional data which fits a linear relationship between sets of explanatory and response variables. Several robust PLS methods are proposed to accommodate the classical PLS algorithms which are easily affected with the presence of outliers. The recent one was called partial robust M-regression (PRM). Unfortunately, the use of monotonous weighting function in the PRM algorithm fails to assign appropriate and proper weights to large outliers according to their severity. Thus, in this paper, a modified partial robust M-regression is introduced to enhance the performance of the original PRM. A re-descending weight function, known as Bisquare weight function is recommended to replace the fair function in the PRM. A simulation study is done to assess the performance of the modified PRM and its efficiency is also tested in both contaminated and uncontaminated simulated data under various perc...