pps.sampling.Rd
The function provides sample techniques with sampling probabilities which are proportional to the size of a quantity z.
pps.sampling(z, n, id = 1:N, method = 'sampford', return.PI = FALSE)
z | vector of quantities which determine the sampling probabilities in the population |
---|---|
n | positive integer for sample size |
id | an optional vector with identification values for population elements. Default is |
method | the sampling method to be used. Options are |
return.PI | logical. If |
The different methods vary in their run time. Therefore, method='sampford'
is stopped if N > 200
or if n/N < 0.3
. method='tille'
is stopped if N > 500
.
In case of large populations use method='midzuno'
or method='madow'
.
The function pps.sampling
returns a value, which is a list consisting of the components
is a list of call components: z
vector of quantity data, n
sample size, id
identification values, and method
sampling method
resulted sample
inclusion probabilities
sample second order inclusion probabilities
full second order inclusion probabilities
Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.
Juliane Manitz
## 1) simple suppositious example data <- data.frame(id = 1:7, z = c(1.8, 2 ,3.2 ,2.9 ,1.5 ,2.0 ,2.2)) # Usage of pps.sampling for Sampford method set.seed(178209) pps.sample_sampford <- pps.sampling(z=data$z, n=2, method='sampford', return.PI=FALSE) pps.sample_sampford#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Sampford: #> #> PPS sample: #> [1] 3 7 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.41025641 0.07281474 #> [2,] 0.07281474 0.28205128# sampling elements id.sample <- pps.sample_sampford$sample id.sample#> [1] 3 7# other methods set.seed(178209) pps.sample_tille <- pps.sampling(z=data$z, n=2, method='tille') pps.sample_tille#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Tille: #> #> PPS sample: #> [1] 1 3 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.23076923 0.05955335 #> [2,] 0.05955335 0.41025641set.seed(178209) pps.sample_midzuno <- pps.sampling(z=data$z, n=2, method='midzuno') pps.sample_midzuno#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Midzuno: #> #> PPS sample: #> [1] 3 4 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.41025641 0.08974359 #> [2,] 0.08974359 0.37179487#> Warning: Systematic Sample with zeros in 'PI': For calculating estimates use approximate methods.pps.sample_madow#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Madow: #> #> PPS sample: #> [1] 3 6 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.4102564 0.2307692 #> [2,] 0.2307692 0.2564103#> 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#> #> 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