influenza.RdThe data frame influenza provides cases of influenza and inhabitants for administrative districts of Germany in 2007.
data(influenza)
A data frame with 424 observations on the following 4 variables.
ida numeric vector
districta factor with levels LK Aachen, LK Ahrweiler, ..., SK Zweibruecken, names of administrative districts in Germany
populationa numeric vector specifying the number of inhabitants in the specific administrative district
casesa numeric vector specifying the number of influenza cases in the specific administrative district
Data of 2007. If you want to use the population numbers in the future, be aware of local governmental reorganizations, e.g. district unions.
Database SurvStat of Robert Koch-Institute. Many thanks to Hermann Claus.
Database of Robert Koch-Institute http://www3.rki.de/SurvStat/
Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.
#> id district population cases #> Min. : 1001 LK Aachen : 1 Min. : 34719 Min. : 0.00 #> 1st Qu.: 5877 LK Ahrweiler : 1 1st Qu.: 104553 1st Qu.: 9.00 #> Median : 8331 LK Aichach-Friedberg: 1 Median : 145130 Median : 27.00 #> Mean : 8468 LK Alb-Donau-Kreis : 1 Mean : 193910 Mean : 44.58 #> 3rd Qu.: 9778 LK Altenburger Land : 1 3rd Qu.: 244154 3rd Qu.: 59.00 #> Max. :16077 LK Altenkirchen : 1 Max. :1770629 Max. :410.00 #> (Other) :418# 1) Usage of pps.sampling set.seed(108506) pps <- pps.sampling(z=influenza$population,n=20,method='midzuno') pps#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Midzuno: #> #> PPS sample: #> [1] 35 83 107 109 130 140 157 210 219 223 257 273 290 294 324 342 361 371 418 #> [20] 423 #> #> Sample probabilities: #> [,1] [,2] [,3] [,4] [,5] #> [1,] 0.090052479 0.0053250174 0.0059535012 0.0047392541 0.0034975812 #> [2,] 0.005325017 0.0622266431 0.0040841690 0.0032027173 0.0023764993 #> [3,] 0.005953501 0.0040841690 0.0702093391 0.0036435201 0.0026981161 #> [4,] 0.004739254 0.0032027173 0.0036435201 0.0549863651 0.0020847939 #> [5,] 0.003497581 0.0023764993 0.0026981161 0.0020847939 0.0401586824 #> [6,] 0.003732237 0.0025338499 0.0028776442 0.0022220297 0.0016004173 #> [7,] 0.006483352 0.0045523488 0.0050892276 0.0040569473 0.0029997593 #> [8,] 0.008401858 0.0060389695 0.0067597276 0.0053697111 0.0039575729 #> [9,] 0.012398528 0.0088061102 0.0098845055 0.0078132411 0.0057404116 #> [10,] 0.005174948 0.0035019448 0.0039719917 0.0030984806 0.0023004465 #> [11,] 0.002864379 0.0019502481 0.0022124945 0.0017123914 0.0012252743 #> [12,] 0.008450507 0.0060727695 0.0067978960 0.0053995583 0.0039793498 #> [13,] 0.009647954 0.0069047173 0.0077373683 0.0061342117 0.0045153648 #> [14,] 0.003036693 0.0020665218 0.0023448451 0.0018140834 0.0012971039 #> [15,] 0.006431964 0.0045069425 0.0050384741 0.0040168511 0.0029705044 #> [16,] 0.004274207 0.0028953870 0.0032909440 0.0025366183 0.0018582626 #> [17,] 0.001019824 0.0006958571 0.0007887969 0.0006115611 0.0004389276 #> [18,] 0.021162722 0.0148352675 0.0166928972 0.0131373023 0.0096249324 #> [19,] 0.001754391 0.0011966398 0.0013566479 0.0010515130 0.0007543015 #> [20,] 0.007120642 0.0051154636 0.0057186561 0.0045542072 0.0033625680 #> [,6] [,7] [,8] [,9] [,10] #> [1,] 0.0037322373 0.0064833515 0.008401858 0.012398528 0.0051749484 #> [2,] 0.0025338499 0.0045523488 0.006038970 0.008806110 0.0035019448 #> [3,] 0.0028776442 0.0050892276 0.006759728 0.009884505 0.0039719917 #> [4,] 0.0022220297 0.0040569473 0.005369711 0.007813241 0.0030984806 #> [5,] 0.0016004173 0.0029997593 0.003957573 0.005740412 0.0023004465 #> [6,] 0.0429213432 0.0032000875 0.004223948 0.006129724 0.0024525529 #> [7,] 0.0032000875 0.0776962790 0.007376869 0.010839972 0.0044258747 #> [8,] 0.0042239481 0.0073768695 0.101469709 0.013610984 0.0058670986 #> [9,] 0.0061297244 0.0108399724 0.013610984 0.145720691 0.0085497394 #> [10,] 0.0024525529 0.0044258747 0.005867099 0.008549739 0.0603389749 #> [11,] 0.0013160329 0.0024584545 0.003239456 0.004693184 0.0018882346 #> [12,] 0.0042472268 0.0074191704 0.009478120 0.013668384 0.0058998664 #> [13,] 0.0048202032 0.0084603611 0.010675567 0.015081223 0.0067064091 #> [14,] 0.0013934264 0.0026058836 0.003434764 0.004977611 0.0020007067 #> [15,] 0.0031688154 0.0055617878 0.007317016 0.010747307 0.0043818549 #> [16,] 0.0019798777 0.0036619353 0.004839951 0.007032667 0.0028018497 #> [17,] 0.0004710923 0.0008759647 0.001152750 0.001667949 0.0006738797 #> [18,] 0.0102821064 0.0183855203 0.023526910 0.031543156 0.0143947850 #> [19,] 0.0008096773 0.0015067189 0.001983242 0.002870225 0.0011588027 #> [20,] 0.0035879141 0.0062419697 0.008119152 0.011989184 0.0049717937 #> [,11] [,12] [,13] [,14] [,15] #> [1,] 0.0028643788 0.008450507 0.009647954 0.0030366928 0.0064319641 #> [2,] 0.0019502481 0.006072769 0.006904717 0.0020665218 0.0045069425 #> [3,] 0.0022124945 0.006797896 0.007737368 0.0023448451 0.0050384741 #> [4,] 0.0017123914 0.005399558 0.006134212 0.0018140834 0.0040168511 #> [5,] 0.0012252743 0.003979350 0.004515365 0.0012971039 0.0029705044 #> [6,] 0.0013160329 0.004247227 0.004820203 0.0013934264 0.0031688154 #> [7,] 0.0024584545 0.007419170 0.008460361 0.0026058836 0.0055617878 #> [8,] 0.0032394561 0.009478120 0.010675567 0.0034347640 0.0073170160 #> [9,] 0.0046931835 0.013668384 0.015081223 0.0049776115 0.0107473066 #> [10,] 0.0018882346 0.005899866 0.006706409 0.0020007067 0.0043818549 #> [11,] 0.0327578552 0.003257213 0.003694280 0.0010480086 0.0024346001 #> [12,] 0.0032572130 0.102010224 0.010724216 0.0034536096 0.0073589162 #> [13,] 0.0036942799 0.010724216 0.115314393 0.0039174705 0.0083902417 #> [14,] 0.0010480086 0.003453610 0.003917471 0.0347627729 0.0025805668 #> [15,] 0.0024346001 0.007358916 0.008390242 0.0025805668 0.0769701592 #> [16,] 0.0015276777 0.004866735 0.005525980 0.0016180460 0.0036259547 #> [17,] 0.0003527623 0.001159043 0.001313939 0.0003761049 0.0008675107 #> [18,] 0.0078606233 0.023638836 0.026393757 0.0083392295 0.0182213615 #> [19,] 0.0006059566 0.001994077 0.002260750 0.0006461439 0.0014921643 #> [20,] 0.0027542889 0.008166424 0.009329958 0.0029198540 0.0061912162 #> [,16] [,17] [,18] [,19] [,20] #> [1,] 0.0042742071 0.0010198236 0.021162722 0.0017543911 0.007120642 #> [2,] 0.0028953870 0.0006958571 0.014835268 0.0011966398 0.005115464 #> [3,] 0.0032909440 0.0007887969 0.016692897 0.0013566479 0.005718656 #> [4,] 0.0025366183 0.0006115611 0.013137302 0.0010515130 0.004554207 #> [5,] 0.0018582626 0.0004389276 0.009624932 0.0007543015 0.003362568 #> [6,] 0.0019798777 0.0004710923 0.010282106 0.0008096773 0.003587914 #> [7,] 0.0036619353 0.0008759647 0.018385520 0.0015067189 0.006241970 #> [8,] 0.0048399514 0.0011527504 0.023526910 0.0019832423 0.008119152 #> [9,] 0.0070326670 0.0016679492 0.031543156 0.0028702253 0.011989184 #> [10,] 0.0028018497 0.0006738797 0.014394785 0.0011588027 0.004971794 #> [11,] 0.0015276777 0.0003527623 0.007860623 0.0006059566 0.002754289 #> [12,] 0.0048667349 0.0011590435 0.023638836 0.0019940766 0.008166424 #> [13,] 0.0055259804 0.0013139393 0.026393757 0.0022607503 0.009329958 #> [14,] 0.0016180460 0.0003761049 0.008339229 0.0006461439 0.002919854 #> [15,] 0.0036259547 0.0008675107 0.018221362 0.0014921643 0.006191216 #> [16,] 0.0493637409 0.0005460989 0.011810244 0.0009388111 0.004108154 #> [17,] 0.0005460989 0.0116140248 0.002790485 0.0002041539 0.000980808 #> [18,] 0.0118102439 0.0027904849 0.242136509 0.0048028196 0.020421365 #> [19,] 0.0009388111 0.0002041539 0.004802820 0.0199937150 0.001687221 #> [20,] 0.0041081542 0.0009808080 0.020421365 0.0016872205 0.086701381sample <- influenza[pps$sample,] sample#> id district population cases #> 35 5554 LK Borken 370196 86 #> 83 8117 LK Goeppingen 255807 67 #> 107 3254 LK Hildesheim 288623 85 #> 109 6434 LK Hochtaunuskreis 226043 8 #> 130 3457 LK Leer 165088 5 #> 140 3355 LK Lueneburg 176445 57 #> 157 5770 LK Minden-Luebbecke 319401 86 #> 210 8119 LK Rems-Murr-Kreis 417131 110 #> 219 5382 LK Rhein-Sieg-Kreis 599042 72 #> 223 9187 LK Rosenheim 248047 67 #> 257 1061 LK Steinburg 134664 22 #> 273 5978 LK Unna 419353 42 #> 290 5170 LK Wesel 474045 8 #> 294 15091 LK Wittenberg 142906 22 #> 324 5314 SK Bonn 316416 11 #> 342 16051 SK Erfurt 202929 188 #> 361 9464 SK Hof 47744 12 #> 371 5315 SK Koeln 995397 35 #> 418 3405 SK Wilhelmshaven 82192 17 #> 423 5124 SK Wuppertal 356420 62# 2) Usage of htestimate set.seed(108506) pps <- pps.sampling(z=influenza$population,n=20,method='midzuno') sample <- influenza[pps$sample,] # htestimate() N <- nrow(influenza) # exact variance estimate PI <- pps$PI htestimate(sample$cases, N=N, PI=PI, method='ht')#> #> htestimate object: Estimator for samples with probabilities proportional to size #> Method of Horvitz-Thompson: #> #> Mean estimator: 40.36766 #> Standard Error: 8.227719 #>#> #> htestimate object: Estimator for samples with probabilities proportional to size #> Method of Yates and Grundy: #> #> Mean estimator: 40.36766 #> Standard Error: 8.059507 #># approximate variance estimate pk <- pps$pik[pps$sample] htestimate(sample$cases, N=N, pk=pk, method='hh')#> #> htestimate object: Estimator for samples with probabilities proportional to size #> Method of Hansen-Hurwitz (approximate variance): #> #> Mean estimator: 40.36766 #> Standard Error: 8.534792 #>#> #> htestimate object: Estimator for samples with probabilities proportional to size #> Method of Hajek (approximate variance): #> #> Mean estimator: 40.36766 #> Standard Error: 8.262482 #># without pik just approximative calculation of Hajek method htestimate(sample$cases, N=N, pk=pk, method='ha')#> Warning: Without input of 'pik' just approximative calculation of Hajek method is possible.#> #> htestimate object: Estimator for samples with probabilities proportional to size #> Method of Hajek (approximate variance): #> #> Mean estimator: 40.36766 #> Standard Error: 8.244296 #># calculate confidence interval based on normal distribution for number of cases est.ht <- htestimate(sample$cases, N=N, PI=PI, method='ht') est.ht$mean*N#> [1] 17115.89lower <- est.ht$mean*N - qnorm(0.975)*N*est.ht$se upper <- est.ht$mean*N + qnorm(0.975)*N*est.ht$se c(lower,upper)#> [1] 10278.45 23953.33#> [1] 18900