Objectives Forecasting epidemics like COVID-19 is of crucial importance, it will not only help the governments but also, the medical practitioners to know the future trajectory of the spread, which might help them with the best possible treatments, precautionary measures and protections. In this study, the popular autoregressive integrated moving average (ARIMA) will be used to forecast the cumulative number of confirmed, recovered cases, and the number of deaths in Pakistan from COVID-19 spanning June 25, 2020 to July 04, 2020 (10 days ahead forecast). Methods To meet the desire objectives, data for this study have been taken from the Ministry of National Health Service of Pakistan’s website from February 27, 2020 to June 24, 2020. Two different ARIMA models will be used to obtain the next 10 days ahead point and 95% interval forecast of the cumulative confirmed cases, recovered cases, and deaths. Statistical software, RStudio, with “forecast”, “ggplot2”, “tseries”, and “seasonal” packages have been used for data analysis. Results The forecasted cumulative confirmed cases, recovered, and the number of deaths up to July 04, 2020 are 231239 with a 95% prediction interval of (219648, 242832), 111616 with a prediction interval of (101063, 122168), and 5043 with a 95% prediction interval of (4791, 5295) respectively. Statistical measures i.e. root mean square error (RMSE) and mean absolute error (MAE) are used for model accuracy. It is evident from the analysis results that the ARIMA and seasonal ARIMA model is better than the other time series models in terms of forecasting accuracy and hence recommended to be used for forecasting epidemics like COVID-19. Conclusion It is concluded from this study that the forecasting accuracy of ARIMA models in terms of RMSE, and MAE are better than the other time series models, and therefore could be considered a good forecasting tool in forecasting the spread, recoveries, and deaths from the current outbreak of COVID-19. Besides, this study can also help the decision-makers in developing short-term strategies with regards to the current number of disease occurrences until an appropriate medication is developed.
Educational researchers, psychologists, social, epidemiological and medical scientists are often dealing with multilevel data. Sometimes, the response variable in multilevel data is categorical in nature and needs to be analyzed through Multilevel Logistic Regression Models. The main theme of this paper is to provide guidelines for the analysts to select an appropriate sample size while fitting multilevel logistic regression models for different threshold parameters and different estimation methods. Simulation studies have been performed to obtain optimum sample size for Penalized Quasi-likelihood (PQL) and Maximum Likelihood (ML) Methods of estimation. Our results suggest that Maximum Likelihood Method performs better than Penalized Quasi-likelihood Method and requires relatively small sample under chosen conditions. To achieve sufficient accuracy of fixed and random effects under ML method, we established ''50/50" and ''120/50" rule respectively. On the basis our findings, a ''50/60" and ''120/70" rules under PQL method of estimation have also been recommended.
Datasets produced in modern research, such as biomedical science, pose a number of challenges for machine learning techniques used in binary classification due to high dimensionality. Feature selection is one of the most important statistical techniques used for dimensionality reduction of the datasets. Therefore, techniques are needed to find an optimal number of features to obtain more desirable learning performance. In the machine learning context, gene selection is treated as a feature selection problem, the objective of which is to find a small subset of the most discriminative features for the target class. In this paper, a gene selection method is proposed that identifies the most discriminative genes in two stages. Genes that unambiguously assign the maximum number of samples to their respective classes using a greedy approach are selected in the first stage. The remaining genes are divided into a certain number of clusters. From each cluster, the most informative genes are selected via the lasso method and combined with genes selected in the first stage. The performance of the proposed method is assessed through comparison with other stateof-the-art feature selection methods using gene expression datasets. This is done by applying two classifiers i.e., random forest and support vector machine, on datasets with selected genes and training samples and calculating their classification accuracy, sensitivity, and Brier score on samples in the testing part. Boxplots based on the results and correlation matrices of the selected genes are thenceforth constructed. The results show that the proposed method outperforms the other methods. INDEX TERMS Clustering, classification, feature selection, high dimensional data, microarray gene expression data.
This research provides the instructional exploration of analytic geometry pattern based on van Hiele thinking pattern, and the potential of GeoGebra effect on experimental group along with its nested group (high and low achievers) in comparison with control group in analytic geometry. To investigate the significant effect of GeoGebra, the two match groups were constructed on their previous grade-11 mathematics records with almost equal statistical background and with the same compatibility in the biological age. Further, six-week experiments of 22 lessons were prepared and two teaching methods (tradition vs DGS aided instructions) were tested. Three hypotheses were carried out i.e. Treatment does not significantly affect, the two groups in mathematical achievement mean scores and, the higher and low achievers of the two groups in mathematical achievement mean scores. To measure the treatment effect, t-test was used by SPSS. Analyses of the research revealed that experimental group performed well, while; GeoGebra was influential in favor of low achievers in comparison to control low achievers.
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