{"id":7022,"date":"2017-12-06T10:09:15","date_gmt":"2017-12-06T09:09:15","guid":{"rendered":"http:\/\/emilkirkegaard.dk\/en\/?p=7022"},"modified":"2017-12-06T15:24:59","modified_gmt":"2017-12-06T14:24:59","slug":"national-chess-skill-european-culture-intelligence","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2017\/12\/national-chess-skill-european-culture-intelligence\/","title":{"rendered":"National chess skill: European culture, intelligence"},"content":{"rendered":"<ul>\n<li>http:\/\/www.unz.com\/jthompson\/chisalas-last-word\/<\/li>\n<\/ul>\n<blockquote><p>How far should the net be cast as regards intellectual achievements? I suggest as far and wide as possible, or it will be assumed that some results are being held back. I favour those achievements which are in a \u201cuniversal language\u201d like maths, science and <strong>chess<\/strong>. There will always be some doubt about whether people in poor countries have access to knowledge and training, though the spread of internet access goes a long way to dealing with this. (In fact, it should level the playing field in terms of access to knowledge). Poker, Bridge, Backgammon, and Mahjong could be added to the list, because there are international competitions and rankings. I am not suggesting anyone should take part in such activities. Live and let live.<\/p><\/blockquote>\n<p>Chess a universal language like math? Methinks not. I took a quantitative look at <a href=\"https:\/\/2700chess.com\/all-fide-players\">FIDE players<\/a>. Using data science tricks, I obtained a list of top 5k players and their countries. Then I did some plotting and modeling. Details can be found at http:\/\/rpubs.com\/EmilOWK\/chess_top5k_fide<\/p>\n<p>Per capita rate ~ IQ<\/p>\n<p><a href=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7024\" src=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-1-1024x731.png\" alt=\"\" width=\"720\" height=\"514\" \/><\/a><\/p>\n<p>Obviously there are issues with country size, so we can weigh cases by sqrt(population) as we usually do.<\/p>\n<p><a href=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7025\" src=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-2-1024x731.png\" alt=\"\" width=\"720\" height=\"514\" \/><\/a><\/p>\n<p>Did not help. It is obvious that East Asian countries are outliers, and that we have issues with a large number of countries with no top chess players at all. If we use the log count approach that Noah used in <a href=\"https:\/\/openpsych.net\/paper\/52\">the terrorism papers<\/a>, which seems superior to the per capita approach (though the reason for this is unclear to me, somehow handles sampling error better), then a simple model finds a strongish effect of IQ:<\/p>\n<pre>Linear Regression Model\r\n rms::ols(formula = log_count ~ log_pop + IQ, data = natdata)\r\n                Model Likelihood     Discrimination    \r\n                   Ratio Test           Indexes        \r\n Obs     197    LR chi2    140.48    R2       0.510    \r\n sigma0.5491    d.f.            2    R2 adj   0.505    \r\n d.f.    194    Pr(&gt; chi2) 0.0000    g        0.636    \r\n \r\n Residuals\r\n      Min       1Q   Median       3Q      Max \r\n -1.68341 -0.31570 -0.01964  0.39061  1.28864 \r\n \r\n           Coef    S.E.   t      Pr(&gt;|t|)\r\n Intercept -4.9833 0.4018 -12.40 &lt;0.0001 \r\n log_pop    0.3281 0.0416   7.88 &lt;0.0001 \r\n IQ         0.0405 0.0036  11.21 &lt;0.0001 \r\n<\/pre>\n<p>Note that these are unstandardized coefficients, and thus not easy to compare. Neither is the effect size easy to understand since the outcome is a log10 count. The model output says that for 1 IQ increase, the expected number of log10(count + 1) FIDE champions increase by 0.04. So, if I&#8217;m not mistaken, this translates into 10^.04. The scaling is not linear. The model predicted number of FIDE players for countries with IQ 70, 80, &#8230;, 110 are 0.15, 1.93, 6.45, 17.93, 47.11. Or a factor of ~300 going from Africa level IQ to good cities.<\/p>\n<p>However, most of this is due to the confound with European culture. If we add continent dummies, we get:<\/p>\n<pre>Linear Regression Model\r\n rms::ols(formula = log_count ~ log_pop + IQ + UN_continent, data = natdata)\r\n\r\n                Model Likelihood     Discrimination    \r\n                   Ratio Test           Indexes        \r\n Obs     197    LR chi2    219.72    R2       0.672    \r\n sigma0.4537    d.f.            6    R2 adj   0.662    \r\n d.f.    190    Pr(&gt; chi2) 0.0000    g        0.730    \r\n \r\n Residuals\r\n      Min       1Q   Median       3Q      Max \r\n -1.22161 -0.24685 -0.01719  0.25710  1.34260 \r\n\r\n                       Coef    S.E.   t     Pr(&gt;|t|)\r\n Intercept             -2.7309 0.4861 -5.62 &lt;0.0001 \r\n log_pop                0.4035 0.0392 10.28 &lt;0.0001 \r\n IQ                     0.0164 0.0048  3.44 0.0007  \r\n UN_continent=Africa   -1.1256 0.1464 -7.69 &lt;0.0001 \r\n UN_continent=Americas -0.6569 0.1191 -5.52 &lt;0.0001 \r\n UN_continent=Asia     -0.9505 0.1044 -9.10 &lt;0.0001 \r\n UN_continent=Oceania  -0.7782 0.1512 -5.15 &lt;0.0001\r\n<\/pre>\n<p>The IQ coefficient declines substantially. If we imagine possible European countries with IQs from 70 to 110, they are expected to have 13, 19, 28, 41, 60 top 5k persons, or factor ~4.6, down from ~300 before. 4.6 is still quite a few, of course. Empirically, this model predicts that reality should work like this:<\/p>\n<p><a href=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7028\" src=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-3-1024x731.png\" alt=\"\" width=\"720\" height=\"514\" \/><\/a><\/p>\n<p>Whereas, if we plot the IQs and counts with slopes by continent, they look like this:<\/p>\n<p><a href=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7029\" src=\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/fide-plot-4-1024x731.png\" alt=\"\" width=\"720\" height=\"514\" \/><\/a><\/p>\n<p>Notice the lack of a noticeable slope for Asia, mainly due to the Singapore, Japan, Koreas (but not China). So, we are probably grouping some countries that shouldn&#8217;t. We can also use UN&#8217;s provided smaller regions, though these are arguably too small. We get (setting Western Europe as the comparison):<\/p>\n<pre>Linear Regression Model\r\n rms::ols(formula = log_count ~ log_pop + IQ + UN_region, data = natdata)\r\n                Model Likelihood     Discrimination    \r\n                   Ratio Test           Indexes        \r\n Obs     197    LR chi2    267.20    R2       0.742    \r\n sigma0.4227    d.f.           24    R2 adj   0.706    \r\n d.f.    172    Pr(&gt; chi2) 0.0000    g        0.767    \r\n \r\n Residuals\r\n      Min       1Q   Median       3Q      Max \r\n -1.08552 -0.22309 -0.01046  0.22147  1.15614 \r\n \r\n                                     Coef    S.E.   t     Pr(&gt;|t|)\r\n Intercept                           -4.3280 0.7710 -5.61 &lt;0.0001 \r\n log_pop                              0.4198 0.0408 10.30 &lt;0.0001 \r\n IQ                                   0.0316 0.0072  4.37 &lt;0.0001 \r\n UN_region=Australia and New Zealand -0.6845 0.3344 -2.05 0.0422  \r\n UN_region=Caribbean                 -0.2719 0.2528 -1.08 0.2836  \r\n UN_region=Central America           -0.6612 0.2456 -2.69 0.0078  \r\n UN_region=Central Asia              -0.1106 0.2775 -0.40 0.6907  \r\n UN_region=Eastern Africa            -0.8351 0.2534 -3.30 0.0012  \r\n UN_region=Eastern Asia              -1.5121 0.2154 -7.02 &lt;0.0001 \r\n UN_region=Eastern Europe             0.1641 0.2029  0.81 0.4198  \r\n UN_region=Europe                    -1.1183 0.4521 -2.47 0.0143  \r\n UN_region=Melanesia                 -0.8061 0.2655 -3.04 0.0028  \r\n UN_region=Micronesia                -0.3599 0.2910 -1.24 0.2179  \r\n UN_region=Middle Africa             -0.6288 0.3038 -2.07 0.0400  \r\n UN_region=Northern Africa           -0.7298 0.2578 -2.83 0.0052  \r\n UN_region=Northern America          -0.4391 0.2610 -1.68 0.0943  \r\n UN_region=Northern Europe            0.0283 0.2008  0.14 0.8882  \r\n UN_region=Polynesia                 -0.4774 0.3069 -1.56 0.1216  \r\n UN_region=South America             -0.4197 0.2131 -1.97 0.0505  \r\n UN_region=South-Eastern Asia        -0.9609 0.2065 -4.65 &lt;0.0001 \r\n UN_region=Southern Africa           -0.5514 0.3087 -1.79 0.0758  \r\n UN_region=Southern Asia             -0.8013 0.2472 -3.24 0.0014  \r\n UN_region=Southern Europe            0.0403 0.1946  0.21 0.8362  \r\n UN_region=Western Africa            -0.7804 0.2805 -2.78 0.0060  \r\n UN_region=Western Asia              -0.5917 0.2050 -2.89 0.0044\r\n<\/pre>\n<p>Now IQ&#8217;s beta went back up again (0.0316).<\/p>\n<h3>What if we use the per capita approach?<\/h3>\n<pre>Linear Regression Model\r\n rms::ols(formula = fide_per_million ~ IQ, data = natdata, weights = sqrt(population2017))\r\n \r\n                  Model Likelihood     Discrimination    \r\n                     Ratio Test           Indexes        \r\n Obs       197    LR chi2     14.86    R2       0.073    \r\n sigma264.0903    d.f.            1    R2 adj   0.068    \r\n d.f.      195    Pr(&gt; chi2) 0.0001    g        1.280    \r\n \r\n Residuals\r\n     Min      1Q  Median      3Q     Max \r\n -3.4973 -1.2864 -0.4563  0.4652 92.7449 \r\n \r\n           Coef    S.E.   t     Pr(&gt;|t|)\r\n Intercept -7.3254 2.2682 -3.23 0.0015  \r\n IQ         0.1024 0.0262  3.91 0.0001 \r\n<\/pre>\n<p>I changed the outcome to top players per million, otherwise all the coefficients were tiny. We see a coefficient of 0.10 here, meaning that 1 IQ point increases the per million player by 0.10. If we use the usual model predictions (for 70, &#8230;, 110), this gives us values of -0.16, 0.87, 1.89, 2.91, 3.94. Negative values are of course impossible, but this model isn&#8217;t constrained to disallow such values (could be done with e.g. Bayesian priors). The violation isn&#8217;t too great anyway. If we add the small regions:<\/p>\n<pre>Linear Regression Model\r\n rms::ols(formula = fide_per_million ~ IQ + UN_region, data = natdata, \r\n     weights = sqrt(population2017))\r\n \r\n                  Model Likelihood     Discrimination    \r\n                     Ratio Test           Indexes        \r\n Obs       197    LR chi2     77.29    R2       0.325    \r\n sigma239.2931    d.f.           23    R2 adj   0.235    \r\n d.f.      173    Pr(&gt; chi2) 0.0000    g        2.709    \r\n \r\n Residuals\r\n      Min       1Q   Median       3Q      Max \r\n -7.70820 -0.62140 -0.03586  0.31916 87.33090 \r\n \r\n                                     Coef    S.E.   t     Pr(&gt;|t|)\r\n Intercept                           -5.5729 8.0336 -0.69 0.4888  \r\n IQ                                   0.1117 0.0800  1.40 0.1647  \r\n UN_region=Australia and New Zealand -4.4978 3.1416 -1.43 0.1540  \r\n UN_region=Caribbean                 -1.4467 2.8945 -0.50 0.6178  \r\n UN_region=Central America           -3.5594 2.3098 -1.54 0.1251  \r\n UN_region=Central Asia              -2.3240 2.6887 -0.86 0.3886  \r\n UN_region=Eastern Africa            -2.4938 2.6692 -0.93 0.3515  \r\n UN_region=Eastern Asia              -6.0083 1.6921 -3.55 0.0005  \r\n UN_region=Eastern Europe             0.4284 1.7746  0.24 0.8095  \r\n UN_region=Europe                    -4.6798 7.4075 -0.63 0.5284  \r\n UN_region=Melanesia                 -3.7884 3.6618 -1.03 0.3023  \r\n UN_region=Micronesia                -3.7728 7.3435 -0.51 0.6081  \r\n UN_region=Middle Africa             -1.9938 3.1464 -0.63 0.5271  \r\n UN_region=Northern Africa           -3.4613 2.2871 -1.51 0.1320  \r\n UN_region=Northern America          -4.8395 2.0390 -2.37 0.0187  \r\n UN_region=Northern Europe            2.7450 2.0215  1.36 0.1762  \r\n UN_region=Polynesia                 -4.1905 8.1261 -0.52 0.6067  \r\n UN_region=South America             -3.4319 1.9566 -1.75 0.0812  \r\n UN_region=South-Eastern Asia        -4.2342 1.8029 -2.35 0.0200  \r\n UN_region=Southern Africa           -2.3886 3.2924 -0.73 0.4691  \r\n UN_region=Southern Asia             -3.4515 2.0883 -1.65 0.1002  \r\n UN_region=Southern Europe            2.6375 1.9077  1.38 0.1686  \r\n UN_region=Western Africa            -2.2252 2.8600 -0.78 0.4376  \r\n UN_region=Western Asia              -1.8373 1.9890 -0.92 0.3569  \r\n<\/pre>\n<p>The beta of IQ remained about the same, but it now has p = .16. There is too much noise to reliably see the signal. This can also be seen in the model fit&#8217;s across approaches: R2a: 0.706 vs. 0.235. So far, my intuitive thinking is that small populations and rare persons cause massive variation in the observed per capita rate. E.g. in this dataset, the observed rate per million of top FIDE is ~100 in Faroe Islands and Iceland but only 9-11 in the rest of Scandinavia. Are we supposed to believe this reflects some real difference? Hardly. Secondly, this massive sampling error is not (apparently) completely counteracted by down-weighing the importance of small samples in the model, at least not using the sqrt approach. Perhaps one can develop a more suitable weight to use. However, using counts, it doesn&#8217;t matter much if the count for a small country turns out to be 0 or 5 since a small number is predicted by the small population size in any event. For instance, Faroe Islands only has n = 5 (for population 50k), but it could have easily been 0 or 10 and neither value would have caused a major outlier using the counts approach, but would have done so using the per capita approach.<\/p>\n<p>Why not use the non-log version? Theoretically, the use of logs should cause nonlinear interactions between IQ and population size to occur, but with n=200, we don&#8217;t have a realistic chance to estimate these. I did try a model with the interaction, but we don&#8217;t really have enough precision to estimate them either (bizarrely, it resulted in p = .006\/.007 <em>negative<\/em> betas for IQ and population size, and the interaction with positive with p &lt; .0001). Perhaps if one collected chess champions for some smaller unit, e.g. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nomenclature_of_Territorial_Units_for_Statistics\">EU NUTS<\/a> or <a href=\"https:\/\/en.wikipedia.org\/wiki\/County_(United_States)\">USA counties<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>http:\/\/www.unz.com\/jthompson\/chisalas-last-word\/ How far should the net be cast as regards intellectual achievements? I suggest as far and wide as possible, or it will be assumed that some results are being held back. I favour those achievements which are in a \u201cuniversal language\u201d like maths, science and chess. There will always be some doubt about whether [&hellip;]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2591],"tags":[1899,2607,2606,2608],"class_list":["post-7022","post","type-post","status-publish","format-standard","hentry","category-intelligence-iq-cognitive-ability","tag-chess","tag-count-data","tag-national-iq","tag-rare-persons","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/7022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/comments?post=7022"}],"version-history":[{"count":6,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/7022\/revisions"}],"predecessor-version":[{"id":7032,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/7022\/revisions\/7032"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=7022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=7022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=7022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}