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)

Arguments

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 'id = 1:N', where 'N' is length of 'z'.

method

the sampling method to be used. Options are 'sampford', 'tille', 'midzuno' or 'madow'.

return.PI

logical. If TRUE the pairwise inclusion probabilities for all individuals in the population are returned.

Details

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'.

Value

The function pps.sampling returns a value, which is a list consisting of the components

call

is a list of call components: z vector of quantity data, n sample size, id identification values, and method sampling method

sample

resulted sample

pik

inclusion probabilities

PI

sample second order inclusion probabilities

PI.full

full second order inclusion probabilities

References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

Author

Juliane Manitz

See also

Examples

## 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$z, n=2, method='tille') pps.sample_tille
#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Tille: #> #> PPS sample: #> [1] 1 3 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.23076923 0.05955335 #> [2,] 0.05955335 0.41025641
set.seed(178209) pps.sample_midzuno <- pps.sampling(z=data$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
set.seed(178209) pps.sample_madow <- pps.sampling(z=data$z, n=2, method='madow')
#> Warning: Systematic Sample with zeros in 'PI': For calculating estimates use approximate methods.
pps.sample_madow
#> #> pps.sampling object: Sample with probabilities proportional to size #> Method of Madow: #> #> PPS sample: #> [1] 3 6 #> #> Sample probabilities: #> [,1] [,2] #> [1,] 0.4102564 0.2307692 #> [2,] 0.2307692 0.2564103
## 2) influenza data(influenza) summary(influenza)
#> id district population cases #> Min. : 1001 LK Aachen : 1 Min. : 34719 Min. : 0.00 #> 1st Qu.: 5877 LK Ahrweiler : 1 1st Qu.: 104553 1st Qu.: 9.00 #> Median : 8331 LK Aichach-Friedberg: 1 Median : 145130 Median : 27.00 #> Mean : 8468 LK Alb-Donau-Kreis : 1 Mean : 193910 Mean : 44.58 #> 3rd Qu.: 9778 LK Altenburger Land : 1 3rd Qu.: 244154 3rd Qu.: 59.00 #> Max. :16077 LK Altenkirchen : 1 Max. :1770629 Max. :410.00 #> (Other) :418
set.seed(108506) pps <- pps.sampling(z=influenza$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 0.086701381
sample <- 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