• 응용통계연구
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• 제23권6호
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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.

• Journal of the Korean Data and Information Science Society
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• 제20권3호
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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.

• Journal of the Korean Statistical Society
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• 제26권2호
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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.

• Journal of the Korean Statistical Society
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• 제33권3호
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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.

• Journal of the Korean Data and Information Science Society
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• 제14권2호
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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.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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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.

• International Journal of Reliability and Applications
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• 제7권1호
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• pp.1-11
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• 2006

The better mean residual life at $t_0\;(BMRL-t_0)$ class of life distribution is introduced by Kulasekara and Park (1987). They proved that the $BMRL-t_0$ class contains the DMRL class, but it is a proper subclass of the NBUE class. In this paper we develop a new family of tests for testing exponentiality against the $BMRL-t_0\;(WMRL-t_0)$ alternatives based on the goodness of fit approach. It is shown that the suggested test is better than the one introduced by Kulasekara and Park (1987) in the sense of Pitman asymptotic efficiency values.

• 물과 미래
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• 제7권2호
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• pp.99-106
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• 1974

The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

• 아동학회지
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• 제6권1호
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• pp.3-16
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• 1985

The purpose of this study was the application of sequential analysis to mother-infant interaction data, with particular reference to goodness of fit. The subjects of this study were 22 7- to 16-month-old infants(12 girls and 10 boys) and their mothers. Each mother-infant dyad was videotaped in a 5-min free-play session in the playroom. The videotaped data was transcribed on the behavioral checklist every 3 seconds. The recorded raw data were lagged by one time interval (3 sec.). Transitional probabilities from behavior at time t-1 to behavior at time t were gathered. The statistical analysis of frequency data and transitional probabilities consisted of Z test, t test, and sign test. It was found that regarding 1) direction of effect: the transitional probability of infant vocalization following maternal vocalization was significantly higher than the reverse; the transitional probability of a 'Coacting State' following a 'Mother Active State' was significantly higher than the reverse; the probability of a 'Mother Active State' following 'Quiescent State' was significantly higher than that of a 'Coacting State' following an 'Infant Active State'; 2) sex differences: male infants' transitional probability from an 'Infant Active State' to a 'Quiescent State' was significantly higher than that of female infants; 3) age differences: more than younger infants older infants had higher transitional probabilities from a 'Mother Active State' to a 'Coacting State', from a 'Parallel State' to a 'Coacting State', and from a 'Quiescent State' to a 'Parallel State'. These showed goodness of fit for sex and age differences, particularily for direction of effect.

• 한국보육지원학회지
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• 제13권1호
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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.