An Extract Test for Comparison of Correlation Coefficients from Two or More Groups in a Regression Situation

Rheem, Sungsue 高麗大學校統計硏究所 2001 應用統計 Vol.16 No.-

본고는 회귀 상황에서의 두 개 이상의 집단들로부터의 상관계수들을 비교하기 위한 정확한 검정을 제안한다. 이 검정의 실행 방법을 예시하는 SAS 프로그램도 제공한다. This article proposes an exact test for comparison of correlation coefficients from two or more groups in a regression situation. A SAS program is provided for illustration of how to implement this test.

Response Surface Methodology Using a Fullest Balanced Model: A Re-Analysis of a Dataset in the Korean Journal for Food Science of Animal Resources

Sungsue Rheem,Insoo Rheem,Sejong Oh 한국축산식품학회 2017 한국축산식품학회지 Vol.37 No.1

Response surface methodology (RSM) is a useful set of statistical techniques for modeling and optimizing responses in research studies of food science. In the analysis of response surface data, a second-order polynomial regression model is usually used. However, sometimes we encounter situations where the fit of the second-order model is poor. If the model fitted to the data has a poor fit including a lack of fit, the modeling and optimization results might not be accurate. In such a case, using a fullest balanced model, which has no lack of fit, can fix such problem, enhancing the accuracy of the response surface modeling and optimization. This article presents how to develop and use such a model for the better modeling and optimizing of the response through an illustrative re-analysis of a dataset in Park et al. (2014) published in the Korean Journal for Food Science of Animal Resources.

Using REG and RSREG Procedures of the SAS System to Analyze a Response Surface with a Subset Second-Order Polynomial Regression Model

Sungsue Rheem 고려대학교 통계연구소 1996 應用統計 Vol.11 No.-

Improving the Quality of Response Surface Analysis of an Experiment for Coffee-supplemented Milk Beverage: II. Heterogeneous Third-order Models and Multi-response Optimization

Sungsue Rheem,Insoo Rheem,Sejong Oh 한국축산식품학회 2019 한국축산식품학회지 Vol.39 No.2

This research was motivated by our encounter with the situation where an optimization was done based on statistically non-significant models having poor fits. Such a situation took place in a research to optimize manufacturing conditions for improving storage stability of coffee-supplemented milk beverage by using response surface methodology, where two responses are Y1=particle size and Y2=zeta-potential, two factors are F1=speed of primary homogenization (rpm) and F2=concentration of emulsifier (%), and the optimization objective is to simultaneously minimize Y1 and maximize Y2. For response surface analysis, practically, the second-order polynomial model is almost solely used. But, there exists the cases in which the second-order model fails to provide a good fit, to which remedies are seldom known to researchers. Thus, as an alternative to a failed second-order model, we present the heterogeneous third-order model, which can be used when the experimental plan is a two-factor central composite design having -1, 0, and 1 as the coded levels of factors. And, for multi-response optimization, we suggest a modified desirability function technique. Using these two methods, we have obtained statistical models with improved fits and multi-response optimization results with the predictions better than those in the previous research. Our predicted optimum combination of conditions is (F1, F2)=(5,000, 0.295), which is different from the previous combination. This research is expected to help improve the quality of response surface analysis in experimental sciences including food science of animal resources.

Using REG and RSREG Procedures of the SAS System to Analyze a Response Surface with a Subset Second-Order Polynomial Regression Model

Rheem,Sungsue 高麗大學校統計硏究所 1996 應用統計 Vol.11 No.-

SAS 씨스템의 RSREG 절차는 완전 2차 다항회귀모형(a full second-order polynomial regression model)에 의거하여 반응표면분석을 실시하다. 본고에서는 부분집합 2차 다항회귀모형(a subset second-order polynomial regression model)에 의거한 반응표면분석의 실시를 위하여 SAS 씨스템의 REG 절차와 RSREG 절차를 이용하는 방법을 제안한다. The RSREG procedure of the SAS system performs response surface analysis with a full second-order polynomial regression model. This article presents how to use REG and RSREG procedures of the SAS system for implementation of analysis of a response surface with a subset second-order polynomial regression model.

A Response Surface Analysis in the Presence of Lack of Fit of a Second-order Model : A Case Study in Microbiology 미생물학에서의 사례연구

Rheem, Sungsue 高麗大學校統計硏究所 1994 應用統計 Vol.9 No.-

이 연구는 미생물학분야에서의 한 사례연구를 통하여 2차모형의 적합결여가 유의할 때의 반응표면분석을 위한 통계적 방법들을 제시하고 있다. 유산균배양의 최적조건을 찾기 위하여 한 실험이 수행되었다. 이 실험에서 설명요인은 다섯 개이고 반응변수는 한 개이다. 다섯 개의 요인들 중 네 개는 유산균 배양기의 성분들이고, 나머지 하나는 배양시의 온도이다. 반응변수는 유산균의 배양 양을 나타내는 ??(유산균 세포 수)이다. 이 실험의 목적은 반응변수를 최대화하는 요인들의 최적수준값들을 찾고 요인들의 효과들을 평가하는 것이다. 처리조합들을 할당하는 실험계획으로는 중심합성계획이 사용되었다. 분석모형으로는 처음에 2차다항모형이 고려되었으나 적합결여가 유의하였으므로, 회귀분석에서의 변수선택기법들을 사용하여 3차항, 4차항 등을 모형에 포함시켰다. 요인들의 최적수준값들은 요인들의 많은 수준값들로 이루어진 격자(grid)상에서 모형으로부터 나올 수 있는 최대반응치에 대응되는 수준값들을 찾는 방식으로 찾아졌다. 요인들의 효과들을 평가하기 위한 하나의 방법으로 각 요인의 편효과(partial effect)를 시각적으로 비교할 수 있는 편호과그림을 제안하였다. 두 요인들의 효과들을 나타내는 3차원그림들도 그려졌다. 최종적으로 확인실험을 통하여 우리가 찾아낸 최적요인수준값들의 조합(combination of optimum factor levels)이 기존에 사용되던 수준값들의 조합에 비해 향상된 생산성을 갖고 있음을 확인하였다. This article describes, through a case study in microbiology, some statistical methods used to analyze a response surface experiment when lack of fit of a second-order model is significant. An experiment was conducted to make a search for optimum conditions of lactobacilli cultivation. This experiment had five factors and one response. Five factors are four components of a growth medium and incubaion temperature. The response is ??(the number of viable lactobacilli cells) that represents the amount of lactobacilli growth. Objectives of this experiment are to find the optimum point of the factors for which the response is maximizd and to assess the effects of the factors. A central composite design was used for allocation of treatment combinations. A second-order polynomical regression model, which was at first fitted to the data, had a significant lack of fit, so, cubic and quartic terms were incorporated into the regression model through variable selection. The optimum point of the factors was found through search for the maximum on a grid of many values of the factors. The partial effects plot was proposed to assess the partial effect of each factor. Three-dimensional plots were drawn that depicts response surfaces for the effects of two factors with the other factors being fixed at their optimum levels. A validation experiment ascertained an improved productivity at out chosen optimum point.

An Extract Test for Comparison of Correlation Coefficients from Two or More Groups in a Regression Situation

Sungsue Rheem 고려대학교 통계연구소 2001 應用統計 Vol.16 No.-

Improving the Quality of Response Surface Analysis of an Experiment for Coffee-Supplemented Milk Beverage: Ⅰ. Data Screening at the Center Point and Maximum Possible R-Square

Sungsue Rheem,Sejong Oh 한국축산식품학회 2019 한국축산식품학회지 Vol.39 No.1

Response surface methodology (RSM) is a useful set of statistical techniques for modeling and optimizing responses in research studies of food science. As a design for a response surface experiment, a central composite design (CCD) with multiple runs at the center point is frequently used. However, sometimes there exist situations where some among the responses at the center point are outliers and these outliers are overlooked. Since the responses from center runs are those from the same experimental conditions, there should be no outliers at the center point. Outliers at the center point ruin statistical analysis. Thus, the responses at the center point need to be looked at, and if outliers are observed, they have to be examined. If the reasons for the outliers are not errors in measuring or typing, such outliers need to be deleted. If the outliers are due to such errors, they have to be corrected. Through a re-analysis of a dataset published in the Korean Journal for Food Science of Animal Resources, we have shown that outlier elimination resulted in the increase of the maximum possible R-square that the modeling of the data can obtain, which enables us to improve the quality of response surface analysis.

Steepest Ascent in the Presence of Significant Interactions in Response Surface Analysis

Rheem,Sungsue 高麗大學校産業開發硏究所 1997 産業開發硏究 Vol.5 No.-

We presented a method of steepest ascent in the presence of significant interactions and provided a SAS program that illustrates how to implement our method. As a plot i aid of effect selection, the scree plot of absolute effects was proposed that can be used in conjunction of the normal plot of effects.

구형 중심합성설계 실험자료에 대한 반응표면분석에서의 균형고차모형의 활용

임성수(Sungsue Rheem),임인수(Insoo Rheem) 한국자료분석학회 2020 Journal of the Korean Data Analysis Society Vol.22 No.1

반응표면방법론에서는 실험설계로는 중심합성설계, 분석모형으로는 완전 2차 다항회귀모형이 자주 사용된다. 그런데, 2차 다항회귀모형이 유의하지 못하거나 적합결여가 유의할 경우에는, 3차 이상의 모형을 고차 모형이라고 할 때, 고차 모형을 활용함으로써 이러한 문제를 해결할 수 있다. 중심합성 설계가 구형(spherical)일 때는, 각 요인변수의 세제곱 항들이 완전 2차 모형에 추가된 3차 모형의 사용이 가능하다. 그런데, 현실에서는 구형 중심합성설계 실험자료에 대한 분석에서 이러한 3차 모형에서도 적합결여가 유의한 상황이 존재할 수 있다. 이러한 경우에 모형 항을 더 늘리게 되면, 결국 모형은 포화모형이 되는데, 포화모형은 허용되는 가장 많은 수의 항들을 갖는 모형이다. 최적 요인수준 조합을 찾기 위한 반응표면분석은 원래 완전 2차 모형에서 출발하는데, 완전 2차 모형은 위계(hierarchy) 구조로 되어 있어 각 요인변수의 차수 합이 일정한 균형성을 가지고 있다. 본 연구는, 이러한 위계구조와 균형성은 고차 모형을 구축할 때에도 지켜져야 하는 성질이어서, 반응표면분석을 위한 고차모형은 균형고차모형이어야 하고 모형 항의 선택 시에도 이러한 위계구조와 균형성은 유지되어야 한다고 제언하고, 균형포화모형을 포함하는 균형고차모형의 구축 방법과 모형 항의 선택 방법에 관하여 논한다. 축산학에서의 실험자료들을 이용한 두 개의 사례분석을 통하여 이 논문에서 제안하는 방법들을 예시한다. In response surface analysis, the model significance test and the lack-of-fit test are used as the means to assess the appropriateness of the model. The central composite designs, which are frequently used in response surface analysis, have levels -alpha, -1, 0, 1, alpha for each factor. When alpha is not 1, the number of levels for each factor being 5, if the second-order model has no significance or a significant lack of fit, it is possible to use a third-order model. But, this third-order model can also have no significance or a significant lack of fit. This research suggests the use of the balanced higher-order models including balanced saturated model for the experimental data from a spherical central composite design when the second- and third-order models have no significance or the lack of fit, and how to conduct the selection of the model terms, maintaining the principles of hierarchy and balance. Based on the chosen model, the optimum is found out through the search on the grid points in the experimental region by the use of a computer program. These methods are illustrated using two experimental datasets in food science of animal resources.