The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.
Two-parameter ridge regression is a widely used method in the last two decades to circumvent the problem of multicollinearity. Ridge parameter k plays an important role in such situations. Several methods are available in the literature for the estimation of ridge parameter. For high multicollinearity, the available methods do not perform well in terms of mean square error. In this article, we propose some new estimators for the ridge parameter. Based on simulation study, our new estimators generally perform better than ordinary least squares estimator, ridge regression estimator and two-parameter ridge regression estimator in many considered scenarios especially for high multicollinearity. In addition, the new estimators also perform well for some non-normal error distributions. Finally, two real-life examples are used to illustrate the application of the proposed estimator.
Aim: To determine the factors that influence the stunting level of children under the age of five years in Pakistan. Methods: This study was conducted using Pakistan Demographic and Health Survey (PDHS) 2017-2018 during 2020-2021.The response variable comprised two categories: stunted and not stunted. In this study the demographic and socioeconomic factors affecting stunting are region, birthplace, preceding birth interval, women's education level, husband\partner`s education level, women's age, breast feeding, size of child at birth, total child ever born, type of place of residence, frequency of listening to the radio, sources of drinking facilities, and antenatal visits. A binary logistic regression model was applied to access the relationship between stunting with potential demographic and socioeconomic factors. Results: The binary logistic regression model identified that the significant factors for stunting of children in the regions of Pakistan are: Punjab (OR=.311, CI; 0.104, 0.934),KPK(OR=0.278,CI; 0.091,0.853), mother education(secondary OR=2.671,CI; 1.025,6.959),father education (Secondary OR=0.370, CI;0.146, 0.938),breastfeeding (1-year OR=0.197, CI; 0.056,0.689), child size (larger than average OR=0.113, CI; 0.020,0.646) and (average OR=0.212, CI;0.047,0.962). Practical implication: Identifying the determinants of stunting can lead to improved health outcomes for children, including reduced mortality rates, better cognitive development, and improved physical growth. Conclusion: This study discovered that stunting in Pakistan can be reduced by improving the education level of parents, proper breastfeeding, and proper diet during pregnancy duration. Keywords: Stunting, Binary logistic model, children, parent’s education
Background: South Asia is the world's most populous region, and it also has the highest rate of pregnancy loss. It is necessary to understand the risk factors for pregnancy loss in South Asian countries like Pakistan for reducing the global burden of pregnancy loss. Aim: To determine the potential clinical factors affecting pregnancy outcomes of Pakistani women aged 15-49 years during 2016-2019. Study design: This study was conducted using Pakistan Maternal Mortality Survey (PMMS 2019) during 2020-2021. All eligible ever-married women (n=7096) aged 15-49 were selected for this study. In this study, the clinical risk factors considered are fever, unconsciousness, high blood pressure, diabetes, vaginal bleeding, problems associated with the placenta, problems associated with the position of the baby, and preeclampsia. The response variable was pregnancy outcome comprising four categories that are live-birth, stillbirth, miscarriage, and abortion. A multinomial logistic regression model was applied to test the relationship between the dependent variable and each of the eight risk factors. Results: Multinomial logistic regression model identified that fever (OR=0.723), vaginal bleeding(OR=1.614), high blood pressure (OR=1.473), and problems associated with the position of the baby (OR=0.396)are significantly associated with a stillbirth at a 10% level of significance. Additionally, unconsciousness (OR=1.019) appears as a potential risk factor for abortion. Practical implication: Understanding the most significant risk factors that contribute to negative pregnancy outcomes, it can prioritize resources to improve maternal health. Also, assistance to healthcare providers and policymakers in making informed decisions regarding maternal health in Pakistan can be provided. Conclusion: Fever, vaginal bleeding, high blood pressure, problems associated with the position of the baby are significant risk factors of stillbirth. However, unconsciousness identified a risk factor of abortion. It is concluded that in Pakistan pregnancy loss can be reduced by controlling the prevalence of diseases during pregnancy. Keywords: Abortion, Clinical risk factors, Miscarriage, Multinomial logistic model, Pregnancy loss, Stillbirth
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