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[转载]Maths: 多重共线性
lixujeremy 2015-3-30 09:36
随着预测变量数目增加而出现的一个首要问题是多重共线性( Multicollinearity )。严格说来,两个变量只有在完全相关时才会共线性,但是这个术语常被用来表示变量之间高度相关。然而,当预测变量很多时,即使变量之间没有一对高度相关,仍有可能出现多重共线性;当一个预测变量可以很好地被其他预测变量组合所预测时,也可能出现多重共线性。 一个预测变量和其他一组预测变量之间的相关通常叫做互相关( Cross-Correlation )。如果你把互相关平方,然后从 1.0 当中减去的话,就得到一个容忍度( Tolerance )的指标。这个指标通常用来决定某个变量是否可能在回归模型中作为一个强有力的贡献变量。 容忍度 =1 — R j 2 R j 2 是 x j 对模型中所有其他自变量的“回归”决定系数。 其中 R j 代表互相关。互相关越高,容忍度就越低。容忍度低就说明在其他预测变量都在方程里时,这个预测变量十分冗余而且 sr 也不会很高。预测变量越多,那么就更有可能有至少一个预测变量相对于其他变量来说容忍度很低,在它们都有较高效度时尤为如此。 容忍度高意味着你关心的这个变量跟其他变量是相对独立的。容忍度等于 1 说明这个变量和其他任何预测变量或预测变量组合完全没有相关。另一方面,容忍度为零说明这个预测变量和其他某个预测变量组合完全相关。当一个预测变量的容忍度为零时,回归方程的 β 值无法计算出来。 除了一些特殊情况,零容忍度对于实际变量是很常见的。例如,如果一个问卷有几个分量表。这些分量表的分数加起来是总分。如果这个总分和各分量表的分数一起作为预测变量,那么总分的容忍度就是零(当然每个分量表的容忍度也是零)。当所有分量表分数之和总是等于一个固定值(如 100 )时,也会出现相同的问题。当你把所有分量表都放进回归方程,那么其中任何一个都可以被其他变量完全预测。删除掉其中任何一个分量表就能解决这个问题。 作为容忍度的一个替代指标,容忍度的倒数即方差膨胀因子( Variance Inflation Factor , VIF )。如果一个预测变量有高 VIF (低容忍度),那么其 β 值的变异就大,因此在新随机样本中,容易出现巨大改变。试举一个极端的例子,假设两个抑郁量表之间的相关是 .9 ,而且两者有类似的效度,即 r 1y =.42 , r 2y =.40 。 β 值分别为: 请注意,虽然两个效度很接近,但是它们的 β 值却很不同。在一个新样本中,很有可能两个效度就互换了位置,但是它们之间的相关却保持一致。然而,转换了效度同样会导致 β 值的相互改变,因此效度的一点很小改变就可能导致 β 值发生剧烈变化。在上例中,两个变量的容忍度都很小( .19 ),导致它们的 β 值不稳定(也就是说,很容易被小的样本波动所影响)。因此,如果你的目的是有稳定的 β 值,那么你就应该避免使用容忍度低的变量。其中一个办法是将相似变量合并成同一个指标,如把收入、教育程度和职位整合成一个社会经济地位指标。因素分析可以帮助你找出哪些预测变量高度相关。 参考文献 Cohen BH.Explaining psychological statistics . New York, US:John Wiley Sons,2008. 中译本 : 高定国等译 , 心理统计学 ( 第三版 ) . 上海 : 华东师范大学出版社 , 2011. p713. Freund RJ, WilsonWJ, Sa P. Regression analysis: Statistical Modeling of a response Variable . Waltham, Massachusetts: Academic Press, 2006. 中译本 : 沈崇麟等译 , 回归分析 : 因变量统计模型 . 重庆 : 重庆大学出版社 , 2012.
个人分类: Mathematics|1716 次阅读|0 个评论
群体容忍度 与 雾霾
seesky 2013-12-21 10:57
中国人的吃苦耐劳精神世界第一, 这里的一个“耐”字不光表现在劳动方面,也表现在对待不良行为或不良事件的态度上(negative tolerance)。 社会中的个体对社会不良事件或行为容忍度较高,并进而适应这种不良环境,其最终表现为社会群体性行为,譬如赵斌老师提到的湧現姓现象 (emergence)。 对不良行为的高群体性容忍度所带来的问题是显而易见的。一个典型例子就是 自己的环境的问题,所有人都知道问题在哪儿,但是 所有人都能够忍受这种不良行为。 所以面对雾霾,似乎只有一个死结:个人的容忍度需要再提高,以期更高的社会容忍度。 不断前进的社会发展一定是正面容忍度(positive tolerance)较高的社会,否则社会发展的驱动力较弱,当然 不断前进的社会发展对社会不良行为也一定是极低的容忍度,或者是zero tolerance. 几千年来的兴亡周期律表明: 社会群体的容忍度是存在极限的。 社会群体性不良行为在中国的历史上好像只能以革命形势来纠正。这显然不是现代社会最经济的处理方式。
4804 次阅读|0 个评论
Error Tolerance/Resilience(2010-08-31)
热度 1 freton 2010-8-31 22:25
There are some teminologies which are worthy of being discussed and distinguished. They are error tolerance, error resilience, error recovery, error concealment, error control, etc. First, have a look at some explanations about them from Vanguard Software Solutions: ------------------------------------------------------------------------------------------------------------------------------ http://www.vsofts.com/technology/error-resilience.html Streaming compressed video over communication channels that introduce errors, losses and excessive delay requires countermeasures to preserve the quality of the viewing experience. We refer to the ability of the system to minimize and to quickly recover from the damage as its robustness. VSofts achieves robustness through two separate and complementary techniques: error resilience and error concealment. Error resilience refers to mechanisms in the encoder that enhance the ability of the compressed bitstream to resist channel errors. Error resilience functionality in the encoder produces a bitstream that supports error recovery at the decoder. The following methods are used in VSofts encoders: Selective intra coding (including intra macroblocks update based on motion tracking, row based distribution, random distribution) Frame segmentation into slices Constrained texture prediction Flexible Macroblock Order (FMO) Error concealment refers to the actions taken by the decoder to analyze losses and conceal them in the displayed video by minimizing the visual artifacts. The concealment schemes can be spatial, temporal or combined. In spatial interpolation, the values of missing pixels are estimated from the surrounding pixels of the same frame, without using the temporal information. Temporal interpolation is based on the corresponding regions of the reference frames. If a motion vector is missing, it can be estimated based on the motion vectors of the surrounding regions. Combination schemes use an adaptive mechanism to choose the best concealment method for each lost macroblock. VSofts decoders use the following methods: Spatial texture interpolation Motion compensation Severe loss compensation ------------------------------------------------------------------------------------------------------------------------------ As far as I am concerned, these words have internal relations with each other. Error tolerance means the ability to tolerate errors, e.g., a circuit or HW/SW system inherently has the power of tolerating some errors that don't bring in too much degradation. Error resilience may have the meaning of error tolerance but it emphasizes somewhat ability to recover the error, i.e., the error recovery capacity. Error concealment means the actions to conceal errors. Error control refers to the countermeasures to help control or relieve the propagation/accumulation of errors. In sum, error control, error recovery and error concealment are some measures to make error tolerance and error resilience possible. I give the relations among them as follows(maybe not complete and not accurate): Error Rsilience = Error Tolerance + Error Recovery, Error Recovery = Error Control + Error Concealment. Error Rate, Error Significance and Error Accumulation are some general metrics that depict the severity of errors. SNR, PSNR and SSIM , etc., are some metrics used in signal/image/video quality evaluation.
个人分类: MyDailyScience|3618 次阅读|0 个评论
Science, Religion and Tolerance ( Helmut Moritz )
jlpemail 2009-8-13 19:44
Science, Religion and Tolerance by Helmut Moritz Abstract: Starting from modern thinking in mathematics and science, especially physics, the author discussed in 2005 its relevance to questions of religion such as the existence of God and the Christian Trinity. This includes a study of the significance of philosophers such as Plato, Kant, Hegel and Gdel for such considerations. Emphasis is on the problem of infinity and antinomies leading to Gdel's theorem which reveals a basic uncertainty of human thinking. This seems to be relevant to philosophical pluralism and to religious tolerance. 全文: http://www.helmut-moritz.at/SciencePage/Science-Religion-Tolerance1.pdf
个人分类: 资料库|3878 次阅读|0 个评论

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