翻訳と辞書 Words near each other ・ Testimony Live ・ Testimony of equality ・ Testimony of Evil (Dead Men Don't Laugh) ・ Testimony of integrity ・ Testimony of Simplicity ・ Testimony of the Ancients ・ Testimony of the Evangelists ・ Testimony of Truth ・ Testin ・ Testing and performance of IC engines ・ Testing Anywhere ・ Testing cosmetics on animals ・ Testing effect ・ Testing high-performance computing applications ・ Testing hypotheses suggested by the data ・ Testing in binary response index models ・ Testing Maturity Model ・ Testing Mom ・ Testing Positive 4 the Funk ・ Testing reliability ・ Testing the Waters ・ Testing the waters ・ Testing Times ・ Testing, adjusting, balancing ・ Testis determining factor ・ TestLink ・ Testman, U.S. Virgin Islands ・ TestNG ・ Testo (rapper) ・ Testo Junkie Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Testing in binary response index models ： ウィキペディア英語版 Testing in binary response index models Denote a binary response index model as: $P(=\; 1\; \backslash mid\; X\_i)\; =\; G\; (X\_i\; \backslash beta)$, $(=\; 0\backslash mid\; X\_i)\; =\; 1-G\; (X\_i\text{'}\; \backslash beta)$ where $X\_i\; \backslash in\; R^N$. This type of model is applied in many economic contexts, especially in modelling the choice-making behavior. For instance, $Y\_i$ here denotes whether consumer $i$ chooses to purchase a certain kind of chocolate, and $X\_i$ includes many variables characterizing the features of consumer $i$ . Through function $G(\backslash cdot)$ , the probability of choosing to purchase is determined 〔 For an application example, refer to: Rayton, B. A. (2006): “Examining the Interconnection of Job Satisfaction and Organizational Commitment: an Application of the Bivariate Probit Model”,The International Journal of Human Resource Management, Vol. 17, Iss. 1.〕 . Now, suppose its maximum likelihood estimator (MLE) $\backslash hat\; \_$ has an asymptotic distribution as $\backslash sqrt\; (\; \backslash hat\; \_\; -\; \backslash beta)\; \backslash xrightarrow\; N\; (0,\; V)$ and there is a feasible consistent estimator for the asymptotic variance $V$ denoted as $\backslash hat$ . Usually, there are two different types of hypothesis needed to be tested in binary response index model. The first type is testing the multiple exclusion restrictions, namely, testing $\backslash beta\_2\; =\; 0\; with\; =(\backslash beta\_2)\; where\; \backslash beta\; \_\; 2\; \backslash in\; R^Q$. If the unrestricted MLE can be easily computed, it is convenient to use the Wald test 〔 Greene, W. H. (2003), Econometric Analysis , Prentice Hall , Upper Saddle River, NJ .〕 whose test statistic is constructed as: $(D\; \backslash hat\; \_)^\; (D\backslash hat\; D^/n)^\; (D\backslash hat\; \_)\; \backslash xrightarrow\; X\_^$ Where ''D'' is a diagonal matrix with the last ''Q'' diagonal entries as 0 and others as 1. If the restricted MLE can be easily computed, it is more convenient to use the Score test (LM test). Denote the maximum likelihood estimator under the restricted model as $(\backslash hat\; \_)$ and define $\backslash hat\; \_\; \backslash equiv\; Y\_i\; -\; G(X\_i\text{'}\; \backslash hat\; \_),\; \backslash hat\; \_\; \backslash equiv\; G(X\_i\text{'}\; \backslash hat\; \_)$ and $\backslash hat\; \_\; \backslash equiv\; g(X\_i\text{'}\; \backslash hat\; \_$, where $g(\backslash cdot)\; =\; G\text{'}\; (\backslash cdot)$. Then run the OLS regression $\backslash frac\; \}\; (1-\backslash hat\; \_)\; \}\}$ on $\backslash frac\; \}\; (1-\backslash hat\; \_)\; \}\}X\_\text{'},\; \backslash frac\; \}\; (1-\backslash hat\; \_)\; \}\}X\_\text{'}$, where $X\_i\; =\; (;\; X\_)$ and $X\_\backslash varepsilon\; R^Q$. The LM statistic is equal to the explained sum of squares from this regression 〔 Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.〕 and it is asymptotically distributed as $X\_Q^2$. If the MLE can be computed easily under both of the restricted and unrestricted models, Likelihood-ratio test is also a choice: let $L\_u$ denote the value of the log-likelihood function under the unrestricted model and let $L\_r$ denote the value under the restricted model, then $2(L\_u\; -\; L\_r)$ has an asymptotic $X\_Q^2$ distribution. The second type is testing a nonlinear hypothesis about $\backslash beta$, which can be represented as $H\_0\; :\; c(\backslash beta)\; =\; 0$ where $c(\backslash beta)$ is a Q×1 vector of possibly nonlinear functions satisfying the differentiability and rank requirements. In most of the cases, it is not easy or even feasible to compute the MLE under the restricted model when $c(\backslash beta)$ include some complicated nonlinear functions. Hence, Wald test is usually used to deal with this problem. The test statistic is constructed as: $c(\backslash hat\; \_\text{'})\; (c(\backslash hat\; \_)\; \backslash hat\; \backslash nabla\_\backslash beta\; c(\backslash hat\; \_)\text{'})^\; c(\backslash hat\; \_)\; \backslash xrightarrow\; X\_Q^2$ where $\backslash nabla\_\backslash beta\; c(\backslash hat\; \_)$ is the Q×N Jacobian of $c(\backslash beta)$ evaluated at $\backslash hat\; \_$. For the tests with very general and complicated alternatives, the formula of the test statistics might not have the exactly same representation as above. But we can still derive the formulas as well as its asymptotic distribution by Delta Method 〔 Casella, G., and Berger, R. L. (2002). Statistical inference. Duxbury Press.〕 and implement Wald test, Score test or Likelihood-ratio test 〔 Engle, Robert F. (1983). "Wald, Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics". In Intriligator, M. D.; and Griliches, Z. Handbook of Econometrics II. Elsevier. pp. 796–801. ISBN 978-0-444-86185-6.〕. Which test should be used is determined by the relative computation difficulty of the MLE under restricted and unrestricted models. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Testing in binary response index models」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.