Siti Meriam Zahari

Weighted ridge M-estimator in the presence of multicollinearity

This study is about a development of weighted ridge M-estimator (WRM) which is believed to be a potential estimator in remedying the problems of multicollinearity under both assumptions of normality and non-normality error distributions. The proposed method has been compared with several existing estimators, namely ordinary least squares (OLS), ridge regression (RIDGE), weighted ridge (WRID) and ridge MM-estimator (RMM) using two criteria; bias and root mean square error (RMSE). In addition, the efficiency of the proposed method to the alternatives has been examined using simulation. In general, it has been found that the proposed estimator scores efficiently against the four existing estimators, particularly in the presence of high multicollinearity and under the non-normality error distribution.

The comparison between several robust ridge regression estimators in the presence of multicollinearity and multiple outliers

In the presence of multicollinearity and multiple outliers, statistical inference of linear regression model using ordinary least squares (OLS) estimators would be severely affected and produces misleading results. To overcome this, many approaches have been investigated. These include robust methods which were reported to be less sensitive to the presence of outliers. In addition, ridge regression technique was employed to tackle multicollinearity problem. In order to mitigate both problems, a combination of ridge regression and robust methods was discussed in this study. The superiority of this approach was examined when simultaneous presence of multicollinearity and multiple outliers occurred in multiple linear regression. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Results of the study showed that in the presence of simultaneous multicollinearity and multiple outliers (in both x and y-direction), the RMM and RIDGE are more or less similar in terms of superiority over the other estimators, regardless of the number of observation, level of collinearity and percentage of outliers used. However, when outliers occurred in only single direction (y-direction), the WRMM estimator is the most superior among the robust ridge regression estimators, by producing the least variance. In conclusion, the robust ridge regression is the best alternative as compared to robust and conventional least squares estimators when dealing with simultaneous presence of multicollinearity and outliers.

Comparing Methods for Lee–Carter Parameter’s Estimation for Predicting Hospital Admission Rates

The government hospital in Malaysia is prominent for the low cost of health care and medical treatment, and it had been reported that the hospital admission is increasing annually. This has led to the widespread problem of overcrowding. In order to assist the government to plan and manage demands for health services and health care needs, the prediction for future admission is outlined. The model is fitted to the matrix of admission rates, spanning the period of historical data from 2001 to 2011 for estimation. In particular, there are three types of estimation approaches used to generate the parameters of the Lee-Carter model which are singular value decomposition (SVD), iterative Newton–Raphson method (NR) and Poisson maximum likelihood estimation (PMLE). The resulting estimation generated by these three estimation approaches is then being compared and evaluated by two types of error measures which are mean squared error (MSE) and mean absolute percentage error (MAPE). The smallest values of MSE and MAPE indicate the better performance of the estimated parameters. The best estimation approach is subsequently used to forecast the admission rates of HRPZ II, Kota Bharu, for ten years ahead; using the out samples data from period 2012–2015. At the end of the study, it can be generally concluded that the occurrence of admission to HRPZ II, Kota Bharu, for both genders in each of the all broad age groups will slowly decrease along with the increment of years (2016–2025).

Predicting the “graduate on time (GOT)” of PhD students using binary logistics regression model

Malaysian government has recently set a new goal to produce 60,000 Malaysian PhD holders by the year 2023. As a Malaysia’s largest institution of higher learning in terms of size and population which offers more than 500 academic programmes in a conducive and vibrant environment, UiTM has taken several initiatives to fill up the gap. Strategies to increase the numbers of graduates with PhD are a process that is challenging. In many occasions, many have already identified that the struggle to get into the target set is even more daunting, and that implementation is far too ideal. This has further being progressing slowly as the attrition rate increases. This study aims to apply the proposed models that incorporates several factors in predicting the number PhD students that will complete their PhD studies on time. Binary Logistic Regression model is proposed and used on the set of data to determine the number. The results show that only 6.8% of the 2014 PhD students are predicted to graduate on time and the results are compared wih the actual number for validation purpose.

Optimization of location routing inventory problem with transshipment

Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.