我後来直接寄信去问Dr. Goodue了。 Dr. Goodhue, sorry for my poor English, I am a graduate student in Taiwan, having a question about your article "Statistical Power in Analyzing Interaction Effects: Questioning the Advantage of PLS With Product Indicators". I wonder how many bootstrapping resamples would be enough for estimating the parameter? Is that "the more, the better" making sense? And, why the five hundred resamples is the usual recommendation? An article of Stata (http://www.stata.com/support/faqs/stat/reps.html) suggests that "the right answer is that you should choose an infinite number of replications because, at a formal level, that is what the bootstrap requires", and recommend three steps for identifying the reasonable number of resamples: "1. Choose a large but tolerable number of replications. Obtain the bootstrap estimates. 2. Change the random-number seed. Obtain the bootstrap estimates again, using the same number of replications. 3. Do the results change meaningfully? If so, the first number you chose was too small. Try a larger number. If results are similar enough, you probably have a large enough number. To be sure, you should probably perform step 2 a few more times, but I seldom do." Is that true? I hope I've explained my questions well, and hope they make sense. Thanks for your help! Chen, Y-T 刚刚收到Dr. Goodue的回覆： Chen, Attached is the material from the paper on the number of resamples. As you can see, we did carry out a version of what is recommended by Stata. 他那篇文章的部份内容，也确实是依照比较不同resamples数而来，可见Appendix E: Comparing Bootstrapping With 100 and 500 Resamples。 因此，跟我之前所提的论点一样（这样下结论应该可以吧）。 ※ 引述《chenyutn (人生要死，何为苦心。)》之铭言： : ※ 引述《danny789 (这其中一定有什麽误会)》之铭言： : : 对於我来说 PLS 只是一个工具而已 : : 我只要知道如何使用及了解它的假设及限制, 而能产出 outcome 并解读就可以了 : : 如同您会操作电脑, 但您知道半导体是如何制造的吗? 毕竟电脑只是一个工具而已 : : 也许您只是站在纯数学的观点来看, 认为 resample 设越大越好 : : 但这样反而太过操弄统计这个工具了, 这样统计的结果真的就是事实的结果吗? : : 如果您可以提供文献证明 resample 设越大越好, 那我也可以修正我原来的看法. : : 若如您所言, 对於 resample 设越大越好, 我一个合理的怀疑 : : 那麽这许多作研究的学者应该会有人提到这点, 但是并没有 ... : : 至少我看过的 papers 没人提到此点 : : 而且我相信这些学者的电脑应该不会太差, resample 设100万也不是问题才对 : : 所以我认为这并不是电脑执行速度的问题 : : 我後来还是找到了 Goodhue et al.(2007) 这篇 pdf 档 (ISR 在 MIS 排前五大期刊) : : 也许底下的片段可以解答您的问题, 所以我的建议还是设 500 比较恰当 : : 因为这是大多数学者所使用的数值 : : It might be suggested that we should use bootstrapping : : with 500 resamples (rather than 100). Five hundred : : resamples is the usual recommendation when : : using bootstrapping to estimate a parameter using a : : single sample (Chin 1998). However, we draw 500 : : samples (500 researchers) from the same population : : for each cell in our analysis, and use bootstrapping : : with 100 resamples on each of those. This amounts to : : 50,000 resamples for each cell, and hence we expect : : that moving from 50,000 to 250,000 resamples in each : : cell would not affect the outcome. : bootstrapping的目的本就是 : Estimate parameters that we don't know how to estimate analytically : (Howell, 2002, http://tinyurl.com/q6v3c2) . : 以下取自Stata的guidelines（http://www.stata.com/support/faqs/stat/reps.html）， : 懒得翻了，仅标重点。 : 这段告诉我们一点： : 数字设多大不一定，但越大必然会获得越精确的CI估计。 : 只是我们需不需要这麽精确的数字而已。 : 我想其实danny789板友也是想表达这个意思，只是在回文时我太注重500这个数字了， : 因为我觉得能越精确当然越好啊。:P : 所以bmka板友前几篇推文给的建议非常实用，设个500次、1000次跑看看， : 再跟2000次比较一下有没有太大的差异，如果没有，就放心报告吧。 : How large should the bootstrapped samples be relative to the total number : of cases in the dataset? : In terms of the number of replications, there is no fixed answer such as : “250” or “1,000”to the question. The right answer is that you should : choose an infinite number of replications because, at a formal level, that : is what the bootstrap requires. : The key to the usefulness of the bootstrap is that it converges in terms of : numbers of replications reasonably quickly, and so running a finite number : of replications is good enough—assuming the number of replications chosen : is large enough. : The above statement contains the key to choosing the right number of : replications. Here is the recipe: : 1. Choose a large but tolerable number of replications. Obtain the : bootstrap estimates. : 2. Change the random-number seed. Obtain the bootstrap estimates : again, using the same number of replications. : 3. Do the results change meaningfully? If so, the first number you chose : was too small. Try a larger number. If results are similar enough, you : probably have a large enough number. To be sure, you should probably : perform step 2 a few more times, but I seldom do. : Whether results change meaningfully is a matter of judgment and has to be : interpreted given the problem at hand. How accurately do you need the : standard errors, confidence intervals, etc.? Often, a few digits of precision : is good enough because, even if you had the standard error calculated : perfectly, you have to ask yourself how much you believe your model in terms : of all the other assumptions that went into it. For instance, in a Becker : earnings model of the return to schooling, you might tell me that return is : 6% with a standard error of 1, and I might believe you. If you told me the : return is 6.10394884% and the standard error is .9899394, you have more : precision but have not provided any additional useful information. -- ◤◢ 玄妙系列作第二部《黄泉路》 全家、福客多、OK便利商店热卖中 ▊▋▌▍▎ ▇▆◣▅▇▇▅▆▇█▋ ▇▆▇▍▄▇ ▇▅▂▄▆▇▏ ▇ ． ． ▏ ‧ ═▉ ▎ 发生过命案的三重宾馆857号房 ▏ ‧ … ═ ▉ ▏ 凭空传来的诡异歌声 ▏ ▎ ． ‥ ‥ ． ═ ˙▊ ▉ ‧ 归来的恶灵即将带走他们的性命.◢▉ . ． ◣ ﹎ ▄ ‧ ▊ ▉▇◣ ▄▅ http://kuso.cc/4ltv ﹒ ▎▊ ▆ ﹊ --

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