Ordinal Logit and Multilevel Ordinal Logit Models: An Application on Wealth Index MICS-Survey Data

Ordinal logistic regression models are used to predict the dependent variable, when dependent variable is of ordinal type in both the situation for single level and multilevel. The most used model for ordinal regression is the Proportional Odd (PO) model which assumes that the effect of the each predictor remains same for each category of the response variable. To estimate the wealth index of household in the province Punjab the proportional odds model is used. The wealth index is an order categorical dependent variable having five categories. The data MICS (2014), a multiple indicator cluster survey conduct by Punjab bureau of statistics was used in this article. The data was recorded at different level such as individual level (household level), district level and division level. The secondary data MICS contains a sample of 41413 household collected from both rural and urban areas of the province Punjab. In the present study analysis were made for single level (household level) and two levels (division level). After fitting the proportional odds model for the single level the proportionality assumption is tested by the brand test whose results suggest that all the predictors fulfill assumption of proportional odds. The significance value suggests that all the predictors have significant effect on the wealth index. The variation due to division level was estimated by two level ordinal logistic regression equal to 5.842, and the Intra Class Correlation ICC is equal to 0.6397 which show that 63.97% of total variation is due to division level

Comparison of fractional splines with polynomial splines; An Application on under-five year’s child mortality data in Pakistan (1960-2012)

Cubic splines are commonly used for capturing the changes in economic analysis. This is because of the fact that traditional regression including polynomial regression fail to capture the underlying changes in the corresponding response variables. Moreover, these variables do not change monotonically, i.e. there are discontinuities in the trend of these variables over a period of time. The objective of this research is to explain the movement of under-five child mortality in Pakistan over the past few decades through a combination of statistical techniques. While cubic splines explain the movement of under-five child mortality to a large extent, we cannot deny the possibility that splines with fractional powers might better explain the underlying movement. . Hence, we estimated the value of fractional power by nonlinear regression method and used it to develop the fractional splines. Although, the fractional spline model may have the potential to improve upon the cubic spline model, it does not demonstrate a real improvement in results of this case, but, perhaps, with a different data set

Smoking and prevalence of COVID-19: Evidence from studies from January 2020 – May 2020

It is well-known that smoking tobacco harms the respiratory system and can lead to various health problems. Regarding COVID-19, a respiratory illness caused by the novel coronavirus SARS-CoV-2, smoking may have implications for both the risk of infection and the severity of the disease. Several studies have explored the association between smoking and COVID-19. However, findings have been somewhat inconsistent and vary from region to region for sample size. This article aims to study the prevalence of COVID-19 among those affected with their ongoing smoking history by computing pooled estimates of the published research. Fixed effect meta-analysis by following the guidelines of PRISMA has been carried out on 34 studies. The patients with confirmed RT-PCR and CT-scan were included, a total of 13,368; The studies' quality assessment was performed according to the Appraisal Checklist recommended by the Joanna Briggs Institute. The effect sizes of the published research are presented in the form of pooled estimates with their respective confidence intervals. Forest plots are used to represent the effect size graphically. Current smokers' effect sizes are 0.12 (CI = 0.11–0.12); for non-smokers, it is estimated to be 0.88 (CI = 0.88–0.89). The heterogeneity statistic I2 describes 0% of the total variation, meaning no heterogeneity among studies exists. A higher prevalence of COVID-19 among non-smokers is observed than the smokers

Rehabilitation of Acute and Chronic Ankle Sprain for Male Cricketers through Mixedbag (Hydrotherapy and Land-Based) Exercises

Ninety-five amateur cricketers of age, 15-35 years with confirmed acute or chronic ankle sprain, selected from four different cities of the Punjab, Pakistan were evaluated through Star Excursion Balance Test (SEBT), Single Leg Balance test (SLB) and subject to a set of progressively increasing exercises on ground and in water as well known as MixedBag rehab exercises which consisted of Hydro, Isometric, Isotonic and proprioception protocols. Another group of same level cricketer (n = 40) served as control. Comparisons of pre and post-exercise values showed significant increase (p \u3c 0.001) in Lateral direction reach and Posteromedial direction while the rest of the six directions showed non-significant results. MixedBag Rehab Group showed an overall improvement of 14.3 % and 9.2 % with an increase (cm) of 9.6 and 6.3 for the non-injured and injured leg respectively. However, the range of improvement in percentage for all eight directions lies between 5.5-6.3 and 7.7-11.8 for the non-injured and injured leg, respectively. Similarly, the difference between pre and post-exercise difference of two positions of non-injured leg and injured leg in seconds were 2.9, 12.1 and 4.1, 27.7. The results indicated that MixedBag exercises improved isometric and isotonic muscular strength, proprioception and stability that ultimately helped to recover, regaining strength and reinstall proprioception. After completing the MixedBag Rehab plan, the subjects were followed for four months to check the recurrence and it was found that the recurrence of Control Injured Group and MixedBag Rehab Group was 17.5 % and 7.5 %, respectively

Selecting and Estimating Rank Score Functions Based on Residuals for Linear Mixed Models

The rank-based method is a well-known robust estimation technique in analyzing linear models, it serves as an alternative to Restricted Maximum Likelihood Estimation (REML) for non-normal error distribution. It is based on minimizing a pseudo-norm and can be upgraded by selecting a suitable score function according to the probability distribution of the error term. Some generic score functions are recommended in the literature for specific shapes of the error distributions in linear models. In this study, the efficiency of score functions is examined through simulations for various level-1 and level-2 sample sizes applied on a random intercept multilevel model for symmetric, asymmetric, and light-tailed to heavy-tailed error distributions. Score functions like wscores, nscores, Bentscores1, and Bentscores4 show minimum SE only when the level-2 sample size is 10 or more. Bentscores1 and Bentscores3 are more suitable than other score functions even for the smallest sample size and their magnitudes reduce as sample size increases for right-skewed and left-skewed error distributions, respectively. Another selection criterion based on Hogg type adaptive scheme is also applied for the same class of error distribution. The efficiency rank-based fit with the selected score function is compared with the Wilcoxon score based on minimum standard error (SE).For the case of right-skewed, moderately heavy-tailed and light-tailed distribution, selected fit from the adaptive scheme is more precise than Wilcoxon fit. For contaminated normal distribution selected fit is more precise in small sample sizes only. In group size 30 or more, the selection of score function does not make a significant change in SE

Ordinal Logit and Multilevel Ordinal Logit Models: An Application on Wealth Index MICS-Survey Data

Ordinal logistic regression models are used to predict the dependent variable, when dependent variable is of ordinal type in both the situation for single level and multilevel. The most used model for ordinal regression is the Proportional Odd (PO) model which assumes that the effect of the each predictor remains same for each category of the response variable. To estimate the wealth index of household in the province Punjab the proportional odds model is used. The wealth index is an order categorical dependent variable having five categories. The data MICS (2014), a multiple indicator cluster survey conduct by Punjab bureau of statistics was used in this article. The data was recorded at different level such as individual level (household level), district level and division level. The secondary data MICS contains a sample of 41413 household collected from both rural and urban areas of the province Punjab. In the present study analysis were made for single level (household level) and two levels (division level). After fitting the proportional odds model for the single level the proportionality assumption is tested by the brand test whose results suggest that all the predictors fulfill assumption of proportional odds. The significance value suggests that all the predictors have significant effect on the wealth index. The variation due to division level was estimated by two level ordinal logistic regression equal to 5.842, and the Intra Class Correlation ICC is equal to 0.6397 which show that 63.97% of total variation is due to division level

Efficient Rank-Based Analysis of Multilevel Models for the Family of Skew-t Errors

Rank-based analysis of linear models is based on selecting an appropriate score function. The information about the shape of the underlying distribution is necessary for the optimal selection; leading towards asymptotically efficient analysis. In this study, we analyzed the multilevel model with cluster-correlated error terms following a family of skew-t distribution with the rank-based approach based on score function derived for the class of skew-normal distribution. The rank fit is compared with the Restricted Maximum Likelihood (REML) estimation in terms of validity and efficiency for different sample sizes. A Monte Carlo simulation study is carried out over skewed-t and contaminated-t distribution with a range of skewness parameters from moderately to highly skewed. The standard error of regression coefficients is significantly reduced in the rank-based approach and further reduces for a large sample size. Rank-based fit appeared asymptotically efficient than REML for each shape parameter of skewness in skew-t and contaminated-t distribution computed through a calculation of precision. The empirical validity of fixed effects is obtained up to the nominal level 0.95 in REML but not rank-based with skew-normal score function

Enhanced performance of mixed HWMA-CUSUM charts using auxiliary information.

Quality control (QC) is a systematic approach to ensuring that products and services meet customer requirements. It is an essential part of manufacturing and industry, as it helps to improve product quality, customer satisfaction, and profitability. Quality practitioners generally apply control charts to monitor the industrial process, among many other statistical process control tools, and to detect changes. New developments in control charting schemes for high-quality monitoring are the need of the hour. In this paper, we have enhanced the performance of the mixed homogeneously weighted moving average (HWMA)-cumulative sum (CUSUM) control chart by using the auxiliary information-based (AIB) regression estimator and named it MHCAIB. The proposed MHCAIB chart provided an unbiased and more efficient estimator of the process location. The various measures of the run length are used to judge the performance of the proposed MHCAIB and to compare it with existing AIB charts like CUSUMAIB, EWMAAIB, MECAIB (mixed AIB EWMA-CUSUM), and HWMAAIB. The Run length (RL) based performance comparisons indicate that the MHCAIB chart performs relatively better in monitoring small to moderate shifts over its competitor's charts. It is shown that the chart's performance improves with the increase in correlation between the study variable and the auxiliary variable. An illustrative application of the proposed MHCAIB chart is also provided to show its implementation in practical situations

Relations for Moments of Generalized Order Statistics for Transmuted Exponential Distribution and Characterization

The relations for moments of generalized order statistics (gos) for transmuted exponential distribution are obtained. These include relations for single, inverse, product and ratio moments. These relations are useful in for recursive computation of moments of gos for transmuted exponential distribution. Some characterizations of the distribution, based on single and product moments of gos, are also obtained

New Diagnosis Test under the Neutrosophic Statistics: An Application to Diabetic Patients

The diagnosis tests (DT) under classical statistics are applied under the assumption that all observations in the data are determined. Therefore, these DT cannot be applied for the analysis of the data when some or all observations are not determined. The neutrosophic statistics (NS) which is the extension of classical statistics can be applied for the data having uncertain, unclear, and fuzzy observations. In this paper, we will present the DT, and gold-standard tests under NS are called neutrosophic diagnosis tests (NDT). Therefore, the proposed NDT is the generalization of the existing DT and can be applied under the uncertainty environment. We will present the NDT table and present a real example from the medical field. The use of the proposed method will be more effective and adequate to be used in medical science, biostatistics, decision, and classification analysis