Comments on: How can I integrate a time sequence of correlations?
http://ask.metafilter.com/207149/How-can-I-integrate-a-time-sequence-of-correlations/
Comments on Ask MetaFilter post How can I integrate a time sequence of correlations?Wed, 01 Feb 2012 08:55:47 -0800Wed, 01 Feb 2012 09:54:08 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: How can I integrate a time sequence of correlations?
http://ask.metafilter.com/207149/How-can-I-integrate-a-time-sequence-of-correlations
Statistics filter: If I asses the same paired variables for the same population at multiple points in time, can I integrate the relation into an overall correlation? <br /><br /> Let's say I measure height and shoe size for the same 100 people every year for five years. For each year, I can calculate a regression / correlation between those variables, giving me r(2012), r(2013), r(2014), and so on.<br>
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Due to the same sample size of 100, the reliability of the effects will remain about the same. But shouldn't I be able to calculate an overall effect with a sample size of 500, i.e. at a higher level of confidence? <br>
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Obviously, I can't just take the 5x100 samples because the 5 measurements for each person are not independent. But what else could I do to postulate confidently: "5 years of study have shown that height and shoe size are strongly correlated"?post:ask.metafilter.com,2012:site.207149Wed, 01 Feb 2012 08:55:47 -0800lord_yostatisticsregressioncorrelationvariablestimesamplesconfidencereliabilityresolvedBy: ROU_Xenophobe
http://ask.metafilter.com/207149/How-can-I-integrate-a-time-sequence-of-correlations#2985752
The terms you want to google for are "robust clustered standard error" and, to be fancier, "multilevel model" and "hiearchical linear model."<br>
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<small>Your toy example would actually be even more complex because it could be considered a time-series multilevel model, bringing in all the gory details from both worlds, or a cross-classified model in which height/shoe size are clustered both in individuals and in years (maybe Genghis Khan shows up in year 3 and chops the toes off of a bunch of people).</small>comment:ask.metafilter.com,2012:site.207149-2985752Wed, 01 Feb 2012 09:54:08 -0800ROU_XenophobeBy: Pinback
http://ask.metafilter.com/207149/How-can-I-integrate-a-time-sequence-of-correlations#2985940
<em>"Due to the same sample size of 100, the reliability of the effects will remain about the same. But shouldn't I be able to calculate an overall effect with a sample size of 500, i.e. at a higher level of confidence?"</em><br>
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No. You'll want to look up "pseudoreplication", but put simply your replicates aren't statistically independent. You don't have 500 replicates, you have [group of 5 measurements from 1 person] replicated 100 times.comment:ask.metafilter.com,2012:site.207149-2985940Wed, 01 Feb 2012 12:27:36 -0800PinbackBy: lord_yo
http://ask.metafilter.com/207149/How-can-I-integrate-a-time-sequence-of-correlations#2988202
I'll check the search terms you've given me - thank you!<br>
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@Pinback: Yes, as I said, there is no independence, so I can't use all samples as a big list of measurements. But measuring something 5x as many times will still reduce statistical error, which somehow has to manifest in an increased confidence.comment:ask.metafilter.com,2012:site.207149-2988202Fri, 03 Feb 2012 03:16:45 -0800lord_yo