• Title, Summary, Keyword: goodness-of-t

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Effect of Number of Measurement Points on Accuracy of Muscle T2 Calculations

  • Tawara, Noriyuki;Nishiyama, Atsushi
    • Investigative Magnetic Resonance Imaging
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    • v.20 no.4
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    • pp.207-214
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    • 2016
  • Purpose: The purpose of this study was to investigate the effect of the number of measurement points on the calculation of transverse relaxation time (T2) with a focus on muscle T2. Materials and Methods: This study assumed that muscle T2 was comprised of a single component. Two phantom types were measured, 1 each for long ("phantom") and short T2 ("polyvinyl alcohol gel"). Right calf muscle T2 measurements were conducted in 9 healthy male volunteers using multiple-spin-echo magnetic resonance imaging. For phantoms and muscle (medial gastrocnemius), 5 regions of interests were selected. All region of interest values were expressed as the mean ${\pm}$ standard deviation. The T2 effective signal-ratio characteristics were used as an index to evaluate the magnetic resonance image quality for the calculation of T2 from T2-weighted images. The T2 accuracy was evaluated to determine the T2 reproducibility and the goodness-of-fit from the probability Q. Results: For the phantom and polyvinyl alcohol gel, the standard deviation of the magnetic resonance image signal at each echo time was narrow and mono-exponential, which caused large variations in the muscle T2 decay curves. The T2 effective signal-ratio change varied with T2, with the greatest decreases apparent for a short T2. There were no significant differences in T2 reproducibility when > 3 measurement points were used. There were no significant differences in goodness-of-fit when > 6 measurement points were used. Although the measurement point evaluations were stable when > 3 measurement points were used, calculation of T2 using 4 measurement points had the highest accuracy according to the goodness-of-fit. Even if the number of measurement points was increased, there was little improvement in the probability Q. Conclusion: Four measurement points gave excellent reproducibility and goodness-of-fit when muscle T2 was considered mono-exponential.

Notes on the Goodness-of-Fit Tests for the Ordinal Response Model

  • Jeong, Kwang-Mo;Lee, Hyun-Yung
    • The Korean Journal of Applied Statistics
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    • v.23 no.6
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    • pp.1057-1065
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    • 2010
  • In this paper we discuss some cautionary notes in using the Pearson chi-squared test statistic for the goodness-of-fit of the ordinal response model. If a model includes continuous type explanatory variables, the resulting table from the t of a model is not a regular one in the sense that the cell boundaries are not fixed but randomly determined by some other criteria. The chi-squared statistic from this kind of table does not have a limiting chi-square distribution in general and we need to be very cautious of the use of a chi-squared type goodness-of-t test. We also study the limiting distribution of the chi-squared type statistic for testing the goodness-of-t of cumulative logit models with ordinal responses. The regularity conditions necessary to the limiting distribution will be reformulated in the framework of the cumulative logit model by modifying those of Moore and Spruill (1975). Due to the complex limiting distribution, a parametric bootstrap testing procedure is a good alternative and we explained the suggested method through a practical example of an ordinal response dataset.

GOODNESS-OF-FIT TEST USING LOCAL MAXIMUM LIKELIHOOD POLYNOMIAL ESTIMATOR FOR SPARSE MULTINOMIAL DATA

  • Baek, Jang-Sun
    • Journal of the Korean Statistical Society
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    • v.33 no.3
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    • pp.313-321
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    • 2004
  • We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

Likelihood ratio in estimating Chi-square parameter

  • Rahman, Mezbahur
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.3
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    • pp.587-592
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    • 2009
  • The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

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On a Bayes Criterion for the Goodness-of-Link Test for Binary Response Regression Models : Probit Link versus Logit Link

  • Kim, Hea-Jung
    • Journal of the Korean Statistical Society
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    • v.26 no.2
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    • pp.261-276
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    • 1997
  • In the context of binary response regression, the problem of constructing Bayesian goodness-of-link test for testing logit link versus probit link is considered. Based upon the well known facts that cdf of logistic variate .approx. cdf of $t_{8}$/.634 and, as .nu. .to. .infty., cdf of $t_{\nu}$ approximates to that of N(0,1), Bayes factor is derived as a test criterion. A synthesis of the Gibbs sampling and a marginal likelihood estimation scheme is also proposed to compute the Bayes factor. Performance of the test is investigated via Monte Carlo study. The new test is also illustrated with an empirical data example.e.

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A Nonparametric Goodness-of-Fit Test for Sparse Multinomial Data

  • Baek, Jang-Sun
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.2
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    • pp.303-311
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    • 2003
  • We consider the problem of testing cell probabilities in sparse multinomial data. Aerts, et al.(2000) presented $T_1=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2$ as a test statistic with the local polynomial estimator $(\hat{p}_i$, and showed its asymptotic distribution. When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2/p_i$ instead, and show it follows an asymptotic normal distribution.

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The Influence of Child-Mother's Goodness of Fit on Children's Child Care Center Adjustment (유아-어머니의 조화적합성이 어린이집 적응에 미치는 영향)

  • Yoo, Mina;Hwan, Hae Shin
    • Korean Journal of Childcare and Education
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    • v.13 no.1
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    • pp.43-63
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    • 2017
  • Objective: The goal of this study was to clarify the differences in children's child care center adjustment depending on child-mother's goodness of fit. Methods: A total of 478 subjects, 239 dyads of 3 and 4 year old children and their mothers and 16 teachers participated in this study. The instruments used in this study were the DOTS-R, EAS Scale and PAQ. The collected data were analyzed using a t-test, Anova, and regression with the SPSS. Results: First, mother's demand was significantly different only with regard to the income level. Second, mother's temperament and mother's demand were positively correlated and the mother's demand was influenced by the mother's temperament. Third, mother's demand according to children's gender was indicated to differ significantly. Fourth, children's temperament and mother's demand were positively correlated and mother's demand was influenced by children's temperament. Finally, ego strength according to active and adoptive temperaments in child-mother's goodness of fit had significant differences. In addition, prosocial behavior according to regular temperament of child-mother's goodness of fit was indicated to have a significant difference. Conclusion/Implications: This study suggests that it is important for mothers to understand and appropriately demand the temperament of the children in the adaptation of the child care center.

On scaled cumulative residual Kullback-Leibler information

  • Hwang, Insung;Park, Sangun
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1497-1501
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    • 2013
  • Cumulative residual Kullback-Leibler (CRKL) information is well defined on the empirical distribution function (EDF) and allows us to construct a EDF-based goodness of t test statistic. However, we need to consider a scaled CRKL because CRKL is not scale invariant. In this paper, we consider several criterions for estimating the scale parameter in the scale CRKL and compare the performances of the estimated CRKL in terms of both power and unbiasedness.

Effects of a Maternal Education Program Based on the Temperament Theory on the Temperamental Goodness-of-Fit between Mother and Child (기질이론에 근거한 어머니교육 프로그램이 모아기질조화에 미치는 효과)

  • Ahn, Min Soon
    • Journal of Korean Academy of Nursing
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    • v.35 no.6
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    • pp.1044-1053
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    • 2005
  • Purpose: This study was aimed to evaluate the effects of a maternal education program based on the temperament theory on the temperamental goodness-of-fit between mother and child. Method: The research method was a nonequivalent, control group, non-synchronized design and the experimental period was from May 10, 2004 to July 24, 2004. The subjects were mothers who had children 3-4 years old who registered in eight kindergartens or infant schools in M city. Among the total 94 subjects, 47 were allocated as an experimental group and 47 were a control group. Using the SPSS/WIN 10.0 program, the data was analyzed by a Chi-square test, and t-test. Result: 1. After treatment with a maternal education program based on the temperament theory, the experimental group significantly decreased in scores for perceived children's behavior problems in comparison to the control group(t=-4.01, p<.001). 2. After treatment with a maternal education program based on the temperament theory, the experimental group did not significantly decrease in scores for parenting stress in comparison to the control group(t=-.85, p=.40). 3. After treatment with a maternal education program based on the temperament theory, the experimental group did not significantly decrease in scores for rejective parenting behaviors in comparison to the control group(t=-1.32, p=.19). Conclusion: A maternal education program based on the temperament theory is a useful intervention to decrease perceived children's behavior problems.

Studies on Relations between Goodness of Fit in Mother-children Temperament Interaction and Problem Behaviors of Children (모-자녀 기질 적합성과 자녀의 문제행동간의 관련성 연구)

  • Ha, Hyun-Yee;Jung, HaeRee;Lee, Soo Jin;Chae, Han
    • The Journal of Pediatrics of Korean Medicine
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    • v.27 no.2
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    • pp.11-19
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    • 2013
  • Objectives The purpose of this study was to identify the importance of goodness of fit in mother-child temperamental interaction (MCTI) and the child problem behaviors. Methods The behavior problem of 180 child outpatients from traditional Korean medical clinic was measured with Korean version of Child Behavior Checklists, and the temperament of child and their mother was measured with Junior Temperament and Character Inventory and Temperament and Character Inventory-Revised-Short. The MCTI was calculated as the difference of the temperament score between mother and child. The correlation and linear regression analysis was performed to examine the effects of temperament on Child Behavior Checklists. Results The MCTI on Harm-Avoidance was the significant factor for explaining the internalizing problem (B=-.154, t=-10.130, p<.001), externalizing problem (B=-.045, t=-3.340, p=.001) and total problem (B=-.298, t=-7.574, p<.001). We also confirmed that the temperament of mother and child significantly correlated with the child behavior problems as provided previously. Conclusions These results showed that the temperament interaction between mother and child is an important factor for predicting problem behaviors in child clinical sample. The goodness of fit in MCTI and problem behavior should be considered as pivotal element in traditional Korean pediatrics.