{"id":4728,"date":"2015-02-12T22:34:02","date_gmt":"2015-02-12T21:34:02","guid":{"rendered":"http:\/\/emilkirkegaard.dk\/en\/?p=4728"},"modified":"2015-02-12T22:34:02","modified_gmt":"2015-02-12T21:34:02","slug":"simpler-way-to-correct-for-restriction-of-range","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2015\/02\/simpler-way-to-correct-for-restriction-of-range\/","title":{"rendered":"Simpler way to correct for restriction of range?"},"content":{"rendered":"

Restriction of range is when the variance in some variable is reduced compared to the true population variance. This lowers the correlation between this variable and other variables. It is a common problem with research on students which are selected for general intelligence (GI) and hence have a lower variance. This means that correlations between GI and whatever found in student samples is too low.<\/p>\n

There are some complicated ways to correct for restriction of range<\/a>. The usual formula used is this:<\/p>\n

\"restriction<\/a><\/p>\n

which is also known as Thorndike’s case 2, or Pearson’s 1903 formula. Capital XY are the unrestricted variables, xy the restricted. The hat on r means estimated.<\/p>\n

However, in a paper in review<\/a> I used the much simpler formula, namely: corrected r = uncorrected r \/ (SD_restricted\/SD_unrestricted) which seemed to give about the right results. But I wasn’t sure this was legit, so I did some simulations.<\/p>\n

First, I selected a large range of true population correlations (.1 to .8) and a large range of selectivity (.1 to .9), then I generated very large datasets with each population correlation. Then for each restriction, I cut off the datapoints where the one variable was below the cutoff point, and calculated the correlation in that restricted dataset. Then I calculated the corrected correlation. Then I saved both pieces of information.<\/p>\n

This gives us these correlations in the restricted samples (N=1,000,000)<\/p>\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
cor\/restriction<\/span><\/b><\/td>\nR 0.1<\/span><\/b><\/td>\nR 0.2<\/span><\/b><\/td>\nR 0.3<\/span><\/b><\/td>\nR 0.4<\/span><\/b><\/td>\nR 0.5<\/span><\/b><\/td>\nR 0.6<\/span><\/b><\/td>\nR 0.7<\/span><\/b><\/td>\nR 0.8<\/span><\/b><\/td>\nR 0.9<\/span><\/b><\/td>\n<\/tr>\n
r 0.1<\/span><\/b><\/td>\n0.09<\/span><\/td>\n0.08<\/span><\/td>\n0.07<\/span><\/td>\n0.07<\/span><\/td>\n0.06<\/span><\/td>\n0.06<\/span><\/td>\n0.05<\/span><\/td>\n0.05<\/span><\/td>\n0.04<\/span><\/td>\n<\/tr>\n
r 0.2<\/span><\/b><\/td>\n0.17<\/span><\/td>\n0.15<\/span><\/td>\n0.14<\/span><\/td>\n0.13<\/span><\/td>\n0.12<\/span><\/td>\n0.11<\/span><\/td>\n0.10<\/span><\/td>\n0.09<\/span><\/td>\n0.08<\/span><\/td>\n<\/tr>\n
r 0.3<\/span><\/b><\/td>\n0.26<\/span><\/td>\n0.23<\/span><\/td>\n0.22<\/span><\/td>\n0.20<\/span><\/td>\n0.19<\/span><\/td>\n0.17<\/span><\/td>\n0.16<\/span><\/td>\n0.14<\/span><\/td>\n0.12<\/span><\/td>\n<\/tr>\n
r 0.4<\/span><\/b><\/td>\n0.35<\/span><\/td>\n0.32<\/span><\/td>\n0.29<\/span><\/td>\n0.27<\/span><\/td>\n0.26<\/span><\/td>\n0.24<\/span><\/td>\n0.22<\/span><\/td>\n0.20<\/span><\/td>\n0.17<\/span><\/td>\n<\/tr>\n
r 0.5<\/span><\/b><\/td>\n0.44<\/span><\/td>\n0.40<\/span><\/td>\n0.37<\/span><\/td>\n0.35<\/span><\/td>\n0.33<\/span><\/td>\n0.31<\/span><\/td>\n0.28<\/span><\/td>\n0.26<\/span><\/td>\n0.23<\/span><\/td>\n<\/tr>\n
r 0.6<\/span><\/b><\/td>\n0.53<\/span><\/td>\n0.50<\/span><\/td>\n0.47<\/span><\/td>\n0.44<\/span><\/td>\n0.41<\/span><\/td>\n0.38<\/span><\/td>\n0.36<\/span><\/td>\n0.33<\/span><\/td>\n0.29<\/span><\/td>\n<\/tr>\n
r 0.7<\/span><\/b><\/td>\n0.64<\/span><\/td>\n0.60<\/span><\/td>\n0.57<\/span><\/td>\n0.54<\/span><\/td>\n0.51<\/span><\/td>\n0.48<\/span><\/td>\n0.45<\/span><\/td>\n0.42<\/span><\/td>\n0.37<\/span><\/td>\n<\/tr>\n
r 0.8<\/span><\/b><\/td>\n0.75<\/span><\/td>\n0.71<\/span><\/td>\n0.68<\/span><\/td>\n0.65<\/span><\/td>\n0.63<\/span><\/td>\n0.60<\/span><\/td>\n0.56<\/span><\/td>\n0.53<\/span><\/td>\n0.48<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

The true population correlation is in the left-margin. The amount of restriction in the columns. So we see the effect of restricting the range.<\/p>\n

Now, here’s the corrected correlations by my method:<\/p>\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
cor\/restriction<\/span><\/b><\/td>\nR 0.1<\/span><\/b><\/td>\nR 0.2<\/span><\/b><\/td>\nR 0.3<\/span><\/b><\/td>\nR 0.4<\/span><\/b><\/td>\nR 0.5<\/span><\/b><\/td>\nR 0.6<\/span><\/b><\/td>\nR 0.7<\/span><\/b><\/td>\nR 0.8<\/span><\/b><\/td>\nR 0.9<\/span><\/b><\/td>\n<\/tr>\n
r 0.1<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.09<\/span><\/td>\n<\/tr>\n
r 0.2<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.21<\/span><\/td>\n0.21<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n<\/tr>\n
r 0.3<\/span><\/td>\n0.30<\/span><\/td>\n0.31<\/span><\/td>\n0.31<\/span><\/td>\n0.31<\/span><\/td>\n0.31<\/span><\/td>\n0.31<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.29<\/span><\/td>\n<\/tr>\n
r 0.4<\/span><\/td>\n0.41<\/span><\/td>\n0.41<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n0.42<\/span><\/td>\n<\/tr>\n
r 0.5<\/span><\/td>\n0.52<\/span><\/td>\n0.53<\/span><\/td>\n0.53<\/span><\/td>\n0.54<\/span><\/td>\n0.54<\/span><\/td>\n0.55<\/span><\/td>\n0.55<\/span><\/td>\n0.56<\/span><\/td>\n0.56<\/span><\/td>\n<\/tr>\n
r 0.6<\/span><\/td>\n0.63<\/span><\/td>\n0.65<\/span><\/td>\n0.66<\/span><\/td>\n0.67<\/span><\/td>\n0.68<\/span><\/td>\n0.69<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.72<\/span><\/td>\n<\/tr>\n
r 0.7<\/span><\/td>\n0.76<\/span><\/td>\n0.79<\/span><\/td>\n0.81<\/span><\/td>\n0.83<\/span><\/td>\n0.84<\/span><\/td>\n0.86<\/span><\/td>\n0.87<\/span><\/td>\n0.89<\/span><\/td>\n0.90<\/span><\/td>\n<\/tr>\n
r 0.8<\/span><\/td>\n0.89<\/span><\/td>\n0.93<\/span><\/td>\n0.97<\/span><\/td>\n1.01<\/span><\/td>\n1.04<\/span><\/td>\n1.07<\/span><\/td>\n1.10<\/span><\/td>\n1.13<\/span><\/td>\n1.17<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Now, the first 3 rows are fairly close deviating by max .1, but it the rest deviates progressively more. The discrepancies are these:<\/p>\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
cor\/restriction<\/span><\/b><\/td>\nR 0.1<\/span><\/b><\/td>\nR 0.2<\/span><\/b><\/td>\nR 0.3<\/span><\/b><\/td>\nR 0.4<\/span><\/b><\/td>\nR 0.5<\/span><\/b><\/td>\nR 0.6<\/span><\/b><\/td>\nR 0.7<\/span><\/b><\/td>\nR 0.8<\/span><\/b><\/td>\nR 0.9<\/span><\/b><\/td>\n<\/tr>\n
r 0.1<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n-0.01<\/span><\/td>\n<\/tr>\n
r 0.2<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n<\/tr>\n
r 0.3<\/span><\/td>\n0.00<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.00<\/span><\/td>\n0.00<\/span><\/td>\n-0.01<\/span><\/td>\n<\/tr>\n
r 0.4<\/span><\/td>\n0.01<\/span><\/td>\n0.01<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n0.02<\/span><\/td>\n<\/tr>\n
r 0.5<\/span><\/td>\n0.02<\/span><\/td>\n0.03<\/span><\/td>\n0.03<\/span><\/td>\n0.04<\/span><\/td>\n0.04<\/span><\/td>\n0.05<\/span><\/td>\n0.05<\/span><\/td>\n0.06<\/span><\/td>\n0.06<\/span><\/td>\n<\/tr>\n
r 0.6<\/span><\/td>\n0.03<\/span><\/td>\n0.05<\/span><\/td>\n0.06<\/span><\/td>\n0.07<\/span><\/td>\n0.08<\/span><\/td>\n0.09<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.12<\/span><\/td>\n<\/tr>\n
r 0.7<\/span><\/td>\n0.06<\/span><\/td>\n0.09<\/span><\/td>\n0.11<\/span><\/td>\n0.13<\/span><\/td>\n0.14<\/span><\/td>\n0.16<\/span><\/td>\n0.17<\/span><\/td>\n0.19<\/span><\/td>\n0.20<\/span><\/td>\n<\/tr>\n
r 0.8<\/span><\/td>\n0.09<\/span><\/td>\n0.13<\/span><\/td>\n0.17<\/span><\/td>\n0.21<\/span><\/td>\n0.24<\/span><\/td>\n0.27<\/span><\/td>\n0.30<\/span><\/td>\n0.33<\/span><\/td>\n0.37<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

So, if we can figure out how to predict the values in these cells from the two values in the row and column, one can make a simpler way to correct for restriction.<\/p>\n

Or, we can just use the correct formula, and then we get:<\/p>\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
cor\/restriction<\/span><\/b><\/td>\nR 0.1<\/span><\/b><\/td>\nR 0.2<\/span><\/b><\/td>\nR 0.3<\/span><\/b><\/td>\nR 0.4<\/span><\/b><\/td>\nR 0.5<\/span><\/b><\/td>\nR 0.6<\/span><\/b><\/td>\nR 0.7<\/span><\/b><\/td>\nR 0.8<\/span><\/b><\/td>\nR 0.9<\/span><\/b><\/td>\n<\/tr>\n
r 0.1<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.10<\/span><\/td>\n0.09<\/span><\/td>\n<\/tr>\n
r 0.2<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.20<\/span><\/td>\n0.21<\/span><\/td>\n0.20<\/span><\/td>\n<\/tr>\n
r 0.3<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n0.30<\/span><\/td>\n<\/tr>\n
r 0.4<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.40<\/span><\/td>\n0.39<\/span><\/td>\n0.39<\/span><\/td>\n<\/tr>\n
r 0.5<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.50<\/span><\/td>\n0.49<\/span><\/td>\n<\/tr>\n
r 0.6<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n0.60<\/span><\/td>\n<\/tr>\n
r 0.7<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.70<\/span><\/td>\n0.71<\/span><\/td>\n<\/tr>\n
r 0.8<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n0.80<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

With discrepancies:<\/p>\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
cor\/restriction<\/span><\/b><\/td>\nR 0.1<\/span><\/b><\/td>\nR 0.2<\/span><\/b><\/td>\nR 0.3<\/span><\/b><\/td>\nR 0.4<\/span><\/b><\/td>\nR 0.5<\/span><\/b><\/td>\nR 0.6<\/span><\/b><\/td>\nR 0.7<\/span><\/b><\/td>\nR 0.8<\/span><\/b><\/td>\nR 0.9<\/span><\/b><\/td>\n<\/tr>\n
r 0.1<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n-0.01<\/span><\/td>\n<\/tr>\n
r 0.2<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0.01<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
r 0.3<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
r 0.4<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n-0.01<\/span><\/td>\n-0.01<\/span><\/td>\n<\/tr>\n
r 0.5<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n-0.01<\/span><\/td>\n<\/tr>\n
r 0.6<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
r 0.7<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0.01<\/span><\/td>\n<\/tr>\n
r 0.8<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Pretty good!<\/p>\n

Also, I need to re-do my paper.<\/p>\n

\n

R code:<\/p>\n

library(MASS)\r\nlibrary(Hmisc)\r\nlibrary(psych)\r\n\r\npop.cors = seq(.1,.8,.1) #population correlations to test\r\nrestrictions = seq(.1,.9,.1) #restriction of ranges in centiles\r\nsample = 1000000 #sample size\r\n\r\n#empty dataframe for results\r\nresults = data.frame(matrix(nrow=length(pop.cors),ncol=length(restrictions)))\r\ncolnames(results) = paste(\"R\",restrictions)\r\nrownames(results) = paste(\"r\",pop.cors)\r\nresults.c = results\r\nresults.c2 = results\r\n\r\n#and fetch!\r\nfor (pop.cor in pop.cors){ #loop over population cors\r\n\u00a0 data = mvrnorm(sample, mu = c(0,0), Sigma = matrix(c(1,pop.cor,pop.cor,1), ncol = 2),\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 empirical = TRUE) #generate data\r\n\u00a0 rowname = paste(\"r\",pop.cor) #get current row names\r\n\u00a0 for (restriction in restrictions){ #loop over restrictions\r\n\u00a0\u00a0\u00a0 colname = paste(\"R\",restriction) #get current col names\r\n\u00a0\u00a0\u00a0 z.cutoff = qnorm(restriction) #find cut-off\r\n\u00a0\u00a0\u00a0 rows.to.keep = data[,1] > z.cutoff #which rows to keep\r\n\u00a0\u00a0\u00a0 rdata = data[rows.to.keep,] #cut away data\r\n\u00a0\u00a0\u00a0 cor = rcorr(rdata)$r[1,2] #get cor\r\n\u00a0\u00a0\u00a0 results[rowname,colname] = cor #add cor to results\r\n\u00a0\u00a0\u00a0 sd = describe(rdata)$sd[1] #find restricted sd\r\n\u00a0\u00a0\u00a0 cor.c = cor\/sd #corrected cor, simple formula\r\n\u00a0\u00a0\u00a0 results.c[rowname,colname] = cor.c #add cor to results\r\n\u00a0\u00a0 \u00a0\r\n\u00a0\u00a0\u00a0 cor.c2 = cor\/sqrt(cor^2+sd^2-sd^2*cor^2) #correct formula\r\n\u00a0\u00a0\u00a0 results.c2[rowname,colname] = cor.c2 #add cor to results\r\n\u00a0 }\r\n}\r\n\r\n#how much are they off by?\r\ndiscre = results.c\r\nfor (num in 1:length(pop.cors)){\r\n\u00a0 cor = pop.cors[num]\r\n\u00a0 discre[num,] = discre[num,]-cor\r\n}\r\n\r\ndiscre2 = results.c2\r\nfor (num in 1:length(pop.cors)){\r\n\u00a0 cor = pop.cors[num]\r\n\u00a0 discre2[num,] = discre2[num,]-cor\r\n}<\/pre>\n","protected":false},"excerpt":{"rendered":"
Restriction of range is when the variance in some variable is reduced compared to the true population variance. This lowers the correlation between this variable and other variables. It is a common problem with research on students which are selected for general intelligence (GI) and hence have a lower variance. This means that correlations between […]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1766],"tags":[2088,1202],"class_list":["post-4728","post","type-post","status-publish","format-standard","hentry","category-math-science","tag-restriction-of-range","tag-statistics","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/4728","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=4728"}],"version-history":[{"count":5,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/4728\/revisions"}],"predecessor-version":[{"id":4735,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/4728\/revisions\/4735"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=4728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=4728"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=4728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}