Robust regression analysis: a useful two stage procedure

이 연구에서는 사례연구를 통해 중등 초임 과학영재교육 담당교사의 코티칭 과정에서 나타나는 과학수업 반성의 특징을 조사했다. 중등 과학영재교육 경력이 5년 미만인 초임 교사 2인을 선정하여 총 3회에 걸친 9차시의 과학영재수업을 공동으로 계획, 진행, 평가하도록 했다. 두 교사의 모든 코티칭 과학영재수업을 참관했고, 반성대화 전사본과 반성일지를 Davis(2006)가 제안한 '생산적 반성'의 관점에서 분석했다. 연구 결과, 자료의 종류 및 수업 차수에 관계없이 두 교사의 수업 반성 과정에서 모두 '과학영재 교수전략 및 지도'와 '과학영재학생' 측면이 비교적 많았다. 두 측면보다 적긴 했지만 '과학영재 교육과정' 측면에 대한 반성의 빈도도 낮지 않았다. 그러나 '과학내용지식'과 '과학영재교육 평가' 측면에 대한 반성은 매우 적었다. 통합 수준에 대한 결과에서는 두 교사의 반성 과정에서 과학영재수업의 5가지 측면 중 2~4가지 측면이 다양한 형태로 통합되어 있었다. 특히 '과학영재 교수전략 및 지도'나 '과학영재학생' 측면과 다른 측면이 통합된 경우가 많았다. 이런 경향은 과학영재교육 경험이 더 많은 교사에게서 강하게 나타났으며, 이 교사의 경우에는 '과학내용지식'과 다른 측면이 통합된 경우도 적지 않게 나타났다. This study investigated secondary beginning science-gifted education teachers' reflection on their science teaching through coteaching with the case study. We selected two beginning teachers whose teaching careers in secondary science-gifted education were less than five years. The teachers planned, performed, and reflected together their science teaching for science-gifted students during nine class hours over three times. We observed their science classes through coteaching, and analyzed the transcripts for reflective discussions between them and their reflective journals in terms of 'productive reflection,' a concept suggested by Davis (2006). The results revealed that the aspects of 'instructional strategies and instruction for science-gifted education' and 'science-gifted students' were most frequently included in their reflection processes on science teaching, regardless of the type of data and the class time. 'Curriculum for science-gifted education' were also frequently included although fewer than two previous aspects. However, 'subject matter knowledge' and 'assessment' was hardly included. Two to four aspects among five aspects of the science teaching for science-gifted students were variously integrated in their reflection processes. Especially, the integrations between 'instructional strategies and instruction for science-gifted education' or 'sciencegifted students' and the other aspects were most frequent, and this tendency was stronger in more experienced teacher in science-gifted education. The integrations between 'subject matter knowledge' and the other aspects were often included in the more experienced teacher's reflection processes.

Unemployment is one of the most important issues in macro economics. Unemployment creates many economic and social problems in the economy. The condition and qualification of labor force in a country show economical developments. In the light of these facts, a developing country should overcome the problem of unemployment. In this study, the performance of robust biased Robust Ridge Regression (RRR), Robust Principal Component Regression (RPCR) and RSIMPLS methods are compared with each other and their classical versions known as Ridge Regression (RR), Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR) in terms of predictive ability by using trimmed Root Mean Squared Error (TRMSE) statistic in case of both of multicollinearity and outliers existence in an unemployment data set of Turkey. Analysis results show that RRR model is chosen as the best model for determining unemployment rate in Turkey for the period of 1985-2012. Robust biased RRR method showed that the most important independent variable effecting the unemployment rate is Purchasing Power Parities (PPP). The least important variables effecting the unemployment rate are Import Growth Rate (IMP) and Export Growth Rate (EXP). Hence, any increment in PPP cause an important increment in unemployment rate, however, any increment in IMP causes an unimportant increase in unemployment rate. Any increment in EXP causes an unimportant decrease in unemployment rate.

An examination of preschool prospective teachers' subject matter knowledge and pedagogical content knowledge on basic geometric shapes in Turkey

Relations between teachers’ subject matter knowledge, teaching experience and their mental models of children’s minds and learning

Ochroma pyramidale (Cav. ex. Lam.) Urb. (balsa-tree) is a commercially important tree species that ranges from Mexico to northern Brazil. Due to its low weight and mechanical endurance, the wood is particularly well-suited for wind turbine blades, sporting equipment, boats and aircrafts; as such, it is in high market demand and plays an important role in many regional economies. This tree species is also well-known to exhibit a high degree of variation in growth. Researchers interested in modeling the height–diameter relationship typically resort to using ordinary least squares (OLS) to fit linear models; however, this method is known to suffer from sensitivity to outliers. Given the latter, the application of these models may yield potentially biased tree height estimates. The use of robust regression with iteratively reweighted least squares (IRLS) has been proposed as an alternative to mitigate the influence of outliers. This study aims to improve the modeling of height–diameter relationships of tree species with high growth variation, by using robust regressions with IRLS for data-sets stratified by site-index and age-classes. We implement a split sample approach to assess the model performance using data from Ecuador’s continuous forest inventory (n = 32,279 trees). A sensitivity analysis of six outlier scenarios is also conducted using a subsample of the former (n = 26). Our results indicate that IRLS regression methods can give unbiased height predictions. At face value, the sensitivity analysis indicates that OLS performs better in terms of standard error of estimate. However, we found that OLS suffers from skewed residual distributions (i.e., unreliable estimations); conversely, IRLS seems to be less affected by this source of bias and the fitted parameters indicate lower standard errors. Overall, we recommend using robust regression methods with IRLS to produce consistent height predictions for O. pyramidale and other tree species showing high growth variation.

The prime aim of the study was to investigate and understand first-year pre-engineering students’ perceptions about mathematics teachers’ knowledge and instruction. A case study method was employed as a mode of inquiry and a Likert-type survey for data collection. Participants included 158 first-year pre-engineering students and five mathematics teachers from Assosa University, Ethiopia. IBM SPSS statistics 20 was used to analyze the quantitative survey data, and open-ended qualitative questions were analyzed by creating common themes. The mean score for each category of teachers’ knowledge was computed. Accordingly, the higher mean was obtained for subject matter knowledge, and the lower mean was obtained for instructional representation and strategies category. The study revealed that students believe their teachers’ subject matter knowledge is constructive. Students have confidence in their teachers’ subject matter knowledge. However, students also believe that their teachers’ teaching methods and overall instructional strategy should be improved. Finally, we proposed that students’ evaluation of their teachers’ knowledge can develop higher education teachers’ professional growth to improve engineering students’ mathematics teaching and learning.

Problem statement: High leverage points are extreme outliers in the X-direction. In regression analysis, the detection of these leverage points becomes important due to their arbitrary large effects on the estimations as well as multicollinearity problems. Mahalanobis Distance (MD) has been used as a diagnostic tool for identification of outliers in multivariate analysis where it finds the distance between normal and abnormal groups of the data. Since the computation of MD relies on non-robust classical estimations, the classical MD can hardly detect outliers accurately. As an alternative, Robust MD (RMD) methods such as Minimum Covariance Determinant (MCD) and Minimum Volume Ellipsoid (MVE) estimators had been used to identify the existence of high leverage points in the data set. However, these methods tended to swamp some low leverage points even though they can identify high leverage points correctly. Since, the detection of leverage points is one of the most important issues in regression analysis, it is imperative to introduce a novel detection method of high leverage points. Approach: In this study, we proposed a relatively new two-step method for detection of high leverage points by utilizing the RMD (MVE) and RMD (MCD) in the first step to identify the suspected outlier points. Then, in the second step the MD was used based on the mean and covariance of the clean data set. We called this method two-step Robust Diagnostic Mahalanobis Distance (RDMDTS) which could identify high leverage points correctly and also swamps less low leverage points. Results: The merit of the newly proposed method was investigated extensively by real data sets and Monte Carlo Simulations study. The results of this study indicated that, for small sample sizes, the best detection method is (RDMDTS) (MVE)-mad while there was not much difference between (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad for large sample sizes. Conclusion/Recommendations: In order to swamp less low leverage as high leverage point, the proposed robust diagnostic methods, (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad were recommended.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

The performance of teachers at the higher secondary level is influenced by various factors that directly affect educational outcomes. This mixed-methods study explores the impact of the key factor of Subject Matter Knowledge on the performance of teachers in District Mirpurkhas through national professional standards for teachers in Pakistan. The research utilized questionnaires for the collection of quantitative data from teachers and interviews to gather qualitative data from Principals across public schools in the district. The sample size of questionnaire was 79 teachers and the sample for the interview was 10 principals from rural and urban area schools. The quantitative data was analyzed through SPSS software while the qualitative data was analyzed thematically. Findings reveal that subject matter knowledge significantly enhances teachers' performance and also play a crucial role in the quality education. This study provides actionable insights for policymakers and educational leaders to design programs that enhance teachers’ subject matter knowledge and ultimately their performance at the higher secondary level. Further research is recommended to evaluate the long-term impact of these interventions on overall student outcomes.

Ordinary Least Squares (OLS) is one method of parameter estimation in regression analysis. However, the presence of outliers can cause estimation of regression coefficients obtained are not exact. Act of throwing away an outlier is not a wise move, because sometimes outliers provide significant information. Therefore, robust regression methods are needed to data contain outliers. This paper will use robust regression estimation method by M-estimation. This estimation use Iteratively Reweighted Least Squares (IRLS) method with weighting function by Huber and Tukey Bisquare. IRLS is applied to the case of food security in Central Java in 2007 that is influenced by the stock of rice, harvested area, average production, price of rice and the amount of consumption. The purpose of this writing is to compare goodness of M-estimation IRLS using Huber and Tukey Bisquare function in estimating the model parameters of food security in Central Java in 2007. Based on the research results can be concluded that the M-estimation by the Tukey Bisquare is better recommended than Huber function. This can be seen by value results of Mean Square Error and determination coefficient

Several robust regression methods, including a new proposal, are described and their properties discussed. Resistance to various types of outliers and non‐normality is demonstrated. The techniques are applied to non‐linear regression models from chemical kinetics and calibration. Optimization of the types of objective functions encountered when applying robust regression is considered.

The use of laser technology to scan hardwood log surfaces for defects holds great promise for improving processing efficiency and the value and volume of lumber produced. External and internal defect detection to optimize hardwood log and lumber processing is one of the top four technological needs in the nation’s hardwood industry. The location, type, and severity of defects on hardwood logs are the key indicators of log quality and value. These visual cues provide information about internal log characteristics and products for which the log is suitable. We scanned 162 logs with a high-resolution industrial four-head laser surface scanner. The resulting data sets contain hundreds of thousands of three-dimensional coordinate points. The size of the data and noise presented special problems during processing. Robust regression models were used to fit geometric shapes to the data. The estimated orthogonal distances between the fitted model and the log surface are converted to a two-dimensional image to facilitate defect detection. Using robust regression methods and standard image processing tools we have demonstrated that severe surface defects on hardwood logs can be detected using height and contour analyses of three-dimensional laser scan data.

We conducted a short subject matter knowledge-based intervention in a quasi-experimental design and explored whether providing health-related subject matter knowledge affects university students’ risk perception and their behavioural intentions. We chose the everyday context of using antiperspirants that contain aluminium and focused on the presumption that antiperspirants facilitate Alzheimer’s disease development. This study was devoted to a risk perception gap caused by the epistemic and ontological uncertainty involved in the contextual background of using antiperspirants and developing Alzheimer’s disease . By computing repeated measures ANOVA, we found that imparting subject matter knowledge as system, action-related and effectiveness health knowledge increased students’ cognitive and affective risk perception. Path analyses revealed that cognitive and affective risk perception had an indirect, negative effect on behavioural intentions towards using antiperspirants. Attitudes and perceived behavioural control fully mediated the relationship between risk perception and intention. The mediation effect differed between students who received subject matter knowledge and students who did not. We discuss the findings from our study related to the role of subject matter knowledge for understanding risk perception, the ambiguity of overcoming and creating a risk perception gap when uncertainty holds and how risk perception relates to attitudes and behavioural intention.

Mathematics achievement in senior high schools (SHS) in Ghana is not encouraging and this has become a concern for major stakeholders. Several studies have been conducted to provide information to understand the issue of poor mathematics achievement. Of all the studies, areas regarding the joint influence of experience, pedagogical content knowledge (PCK) and subject matter knowledge (SMK) have been less explored in Ghana. In this study, the interplay among these variables is examined in an attempt to explain the variances in students’ mathematics achievement. To achieve this purpose, 210 SHS teachers and 8,400 students in SHS across the country were surveyed and subsequently administered tasks on algebra taking into consideration the variables of interest. The study revealed that teacher knowledge and teaching experience significantly influenced students’ mathematics achievement. It was discovered that PCK had a significant indirect effect on students’ mathematics achievement through teachers’ SMK. The findings also showed that experience did not significantly moderate the relationship between teachers’ SMK and students’ mathematics achievement. The study, based on the outcome, made conclusions and recommendations for practice. Suggestions for the implementation of future studies were also highlighted.

INTRODUCTION. The article questions a basic problem of didactics: the relevance of subject matter knowledge as a quality requirement in teacher training. Subject matter knowledge is assumed to be necessary to facilitate student learning and education. Specifically, it is understood as a requirement for teachers to be able to carry out didactic designs and developments that facilitate meaningful learning experiences and strengthen the conceptual structure of students. The objective of the research is to know if future Primary Education teachers and preservice Primary Education teachers have an adequate knowledge of subject matter knowledge. METHOD. To answer the objective, the type and organization of their knowledge is examined through concept maps, evaluating the productions with validated structural and semantic rubrics. RESULTS. The results show that, in general, teachers have a very poor organization of subject matter knowledge, with a weak didactic potential. DISCUSSION. Likewise, the data indicate that there are insignificant differences between the concept maps of teachers in training and those made by practicing teachers, which reflects a similar andcyclical knowledge structure. The conclusions point to the low and limited impact of teacher education programs on pre-service teachers’ acquisition of subject matter knowledge, even though it is understood as a general didactic requirement for teacher education and, for the development of quality teaching.