• Proceedings of the Korea Water Resources Association Conference
• /
• 2008.05a
• /
• pp.490-494
• /
• 2008

본 연구에서는 상수도 배수관로의 내 외부적 특성에 따라 개별관로를 정의하는 방법을 연구대상 지역의 배수관로 파손 데이터베이스에 적용하여 비례위험모형을 구축하였다. 연구에 사용된 자료는 연구대상지역의 배수관로의 제원 및 파손시기를 포함하는 관로 파손데이터베이스, 관로매설지역의 급수인구 및 수압범위에 관한 자료를 포함하는 GRID 데이터베이스와 관로매설지역의 토지개발 정도에 관한 자료를 포함한다. 이러한 자료를 이용하여 관로를 순차적 파손경험에 따라 7개의 생존시간군(STG I $\sim$ VII)으로 구분하고 각 생존시간군에 대한 비례위험모형(Model I $\sim$ VII)을 구축하였다. 이러한 모형을 이용하여 관로의 파손횟수가 증가하는 동안 파손에 영향을 미치는 인자의 변화와 그 효과를 파악하였으며, 또한 추정된 공변수의 위험비율을 분석함으로써 관로의 제원 혹은 매설환경, 급수인구 등에 따른 위험률의 상대적인 변화를 분석하였다. 또한 비례 위험모형의 구축과정에서 관로의 파손에 영향을 미치는 공변수의 비례성 가정을 검토하여 시간종속형 공변수를 모형화하였으며, 모형의 이탈잔차(deviance residual)를 분석하여 모형의 적합성을 검토하였다. 본 연구에서 구축된 비례위험모형에 대해 Shoenfeld 잔차를 이용한 스코어 잔차의 변화(score process)를 검토한 결과, Model I 과 Model II 에 대해서는 공변수의 시간종속 효과가 발견되었다. Model I에 대해서는 관로재질과 급수인구의 영향이 시간에 따라 변하며 Model II에서는 급수인구의 영향만이 시간에 따라 변하는 것으로 나타났다. 한편 Model III $\sim$ Model VII 들에 대해서는 공변수의 영향이 시간에 따라 변하지 않는 것으로 나타났다. 각 생존시간군에 대해 관로재질, 토지개발정도, 관로길이 및 급수인구의 변화가 관로의 상대적 누수위험률에 미치는 영향을 상대위험률의 95% 신뢰구간을 고려하여 정량적으로 산정하였고, 시간 종속형 공변수로 모형화된 공변수는 시간에 따른 공변수 영향의 변화를 분석하였다. 순차적 파손사건에 대한 비례위험모형의 구축 결과 생존시간군(STG) I의 기저위험률은 매설 후 대략 450개월까지는 파손 위험률이 '0'에 가까우나 그 이후로 급격히 증가하다가 매설 후 약 700개월에 이르러서는 약간 감소하고 약 850개월 이후에는 다시 급격히 증가한다. STG II의 기저위험률은 첫 번째 파손 후 약 300개월이 되면 위험률이 급격히 증가하는 것으로 나타났다. STG III $\sim$ STG VII의 기저위험률은 이차함수의 형태를 띄며, 특히 STG V, STG VI 및 STG VII의 기저위험률은 욕조형 곡선(bathtub curve)의 형태를 가진다. 각 생존시간군의 기저생존함수의 생존확률 '0.5'에 해당하는 기저중간생존시간에 대한 분석으로부터 파손횟수가 많아질수록 순차적 파손사건 사이의 경과시간은 감소하는 것으로 나타났다. 이러한 기저생존시간에 대한 경향은 관로의 파손횟수가 많아질수록 관로의 일반적은 내구성은 감소하기 때문인 것으로 분석된다.

• Communications for Statistical Applications and Methods
• /
• v.5 no.2
• /
• pp.447-458
• /
• 1998

본 논문에서는 환자의 수명과 치료횟수의 모형화를 위해 관측가능한 공변량을 포함하는 동시에 두 변수에 영향을 미치는 관측불가능한 환경요인을 고려하기 위한 개별환경효과모형을 도입하고자 한다. 개별환경효과를 나타내는 분포를 감마분포로 가정하여 사망시간과 치료횟수의 모형을 개발하고, 모형에 포함된 모수의 추론과정을 논의하며, 개발된 모형을 Autologous Blood and Marrow Transplant Registry(ABMTR)에 등록된 환자의 자료에 적용하여 환경효과를 고려하지 않은 독립모형과 비교하고자 한다.

• The Korean Journal of Ecology
• /
• v.4 no.3_4
• /
• pp.59-67
• /
• 1981

Stomatal resistances of the leaves in Heteromeres arbutifolia and of the stems in Ferocactus acanthodes were studied to estimate active and passive behaviors of the guard cells on a theoretical basis. Active and passive stomatal responses to light and water deficit were observed. When the change rate of existent water due to variation of osmotic potential in the guard cells and the loss rate of transpirational water from the guard cells are $\Delta$wi-$\Delta$wt and leaded to active behaviors for opening and closing stomata. However, when stems of F. acanthodes with stomata closecd under the solar irradiation were covered with black cloth and then taken off, behaviors of the guard cells occurred in the condition of $\Delta$wi<$\Delta$wt and were passive. Under the conditiion of $\Delta$wi<$\Delta$wt due to cutout from stems, passive behaviors of the guard cells in H. arbutifolia and F. acanthodes always occurred in spite of the solar irradiation and darkness, respectively. The transpirational resistance coefficients of the guard cells in stems of F. acanthodes (0.380) and Opuntia bigelovii (0.135) wer emuch higher than in leaves of H. arbutifolia (0.034). Moreover, stomatal opening in stems of F. acanthodes during the daytime could be induced by watering. Those results are interpreted as that since the guard cells in desert Crassulacean acid metabolism (CAM) plants always exist in the state of stomatal opening, nocturnal stomatal opening and daytime stomatal closing are exhibited by passive behaviors of the guard cells in the alternant conditioins of $\Delta$wi>$\Delta$wt and $\Delta$wi<$\Delta$wt, respectively.

• Journal of Korean Society of Forest Science
• /
• v.80 no.4
• /
• pp.360-368
• /
• 1991

Utilizing chi-square test statistics, inter-species association and covariation were analyzed for the 37 woody plant species in a deciduous forest dominated by Quercus mongolica and Q. variabilis. within 50 temporarily established $20m{\times}20m$ square quadrats, the association for each pair of species was presented based on the presence-absence parameters. Acer palmatum had significant positive association with Acer mono and Kalopanax pictus, but negative association with Pinus densiflora. Other positively associated species pairs were Prunus sargentii-Macckia amurensis, Quercus serrata-Kalopanax pictus, Symplocos chinensis var. pilosa-Euonymus oxyphyllus, and Ulmus davidiana var. japonica-Lindera obtusiloba. The covariation far each pair of species was evaluated based on the quantitative measures, density and basal area. Overall results showed that the association and covariation values among species generally agreed with each other. Because covariation was calculated by density and basal area of the tallied species in the sample plots, the number of species pairs of covariation tended to be greater than those of association. Especially, Pinus densiflora, considered to be pioneer species in the successional stage, had negative covariation with most of climax species. These ecological information could be applied to silvicultural practices, such as ecosystem classification, establishment of mixed hardwood forest, and tending operations for marking crop trees and desirable species.

• The Korean Journal of Applied Statistics
• /
• v.29 no.7
• /
• pp.1347-1359
• /
• 2016

Finite mixtures of regression models provide an effective tool to explore a hidden functional relationship between a response variable and covariates. However, it is common in practice that data are not fully observed due to several reasons. In this paper, we derived an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimator when some covariates are missing at random in the finite mixture of regression models. We conduct some simulation studies and we also provide some real data examples to show the validity of the derived EM algorithm.

• School Mathematics
• /
• v.18 no.1
• /
• pp.43-59
• /
• 2016

The purpose of this qualitative case study is to investigate differences among two gifted middle school students emerging through the process of algebra word problem solving from the covariational perspective. We collected the data from four middle school students participating in the mentorship program for gifted students of mathematics and found out differences between Junghee and Donghee in solving problems involving varying rates of change. This study focuses on their actions to solve and to generalize the problems situations involving constant and varying rates of change. The results indicate that their covariational reasoning played a significant role in their algebra word problem solving.

• The Korean Journal of Applied Statistics
• /
• v.26 no.5
• /
• pp.697-712
• /
• 2013

When analyzing repeated binary data, the generalized estimating equations(GEE) approach produces consistent estimates for regression parameters even if an incorrect working correlation matrix is used. However, time-varying covariates experience larger changes in coefficients than time-invariant covariates across various working correlation structures for finite samples. In addition, the GEE approach may give biased estimates under missing at random(MAR). Weighted estimating equations and multiple imputation methods have been proposed to reduce biases in parameter estimates under MAR. This article studies if the two methods produce robust estimates across various working correlation structures for longitudinal binary data with time-varying covariates under different missing mechanisms. Through simulation, we observe that time-varying covariates have greater differences in parameter estimates across different working correlation structures than time-invariant covariates. The multiple imputation method produces more robust estimates under any working correlation structure and smaller biases compared to the other two methods.

• Journal of Educational Research in Mathematics
• /
• v.27 no.1
• /
• pp.23-49
• /
• 2017

This study examined two current learning models for covariational reasoning(Carlson et al.(2002), Thompson, & Carlson(2017)), applied the models to teaching two $9^{th}$ grade students, and analyzed the results according to the types of graphs(a quantitative graph or qualitative graph). Results showed that the model of Thompson and Carlson(2017) was more useful than that of Carlson et al.(2002) in figuring out the students' levels in their quantitative graphing activities. Applying Carlson et al.(2002)'s model made it possible to classify levels of the students in their qualitative graphs. The results of this study suggest that not only quantitative understanding but also qualitative understanding is important in investigating students' covariational reasoning levels. The model of Thompson and Carlson(2017) reveals more various aspects in exploring students' levels of quantitative understanding, and the model of Carlson et al.(2002) revealing more of qualitative understanding.

• The Korean Journal of Applied Statistics
• /
• v.29 no.5
• /
• pp.849-858
• /
• 2016

It is important to control confounding bias when estimating the causal effect of treatment in an observational study. We illustrated that the covariate selection in the causal inference is different from the variable selection in the ANCOVA model. We then investigated the three criteria of covariate selection for controlling confounding bias, which can be used when we have inadequate information to draw a complete causal graph. VanderWeele and Shpitser (2011) proposed one of them and claimed it was better than the other two. We show by example that their criterion also has limitations and some disadvantages. There is no clear winner; however, their criterion is better (if some correction is made on its condition) than the other two because it can remove the confounding bias.

• Communications of Mathematical Education
• /
• v.35 no.3
• /
• pp.323-340
• /
• 2021

The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.