Simulate (un)clustered data assuming multivariate non-normal distributions

Simulate 1 or 2 clusters assuming multivariate non-normal distributions (specifying correlations, skewness, kurtosis, and the number of indicators) and the degree of separation (effect size) in standard deviation units (standardized data). The function can works in two different ways.

When udata is NULL: need to be specified or left to the default value
When udata is provided: parameters are taken from udata that is the result of calling the prep_user_data function.

Usage

sim_clust(
  nclust = 1,
  n = NULL,
  dmin = 0,
  dmax = NULL,
  rmin = NULL,
  rmax = NULL,
  nind = NULL,
  skewmin = 0,
  skewmax = NULL,
  kurtmin = 0,
  kurtmax = NULL,
  pn1 = 0.5,
  debug = FALSE,
  udata = NULL
)

Arguments

nclust: The number of clusters. Can be 1 or 2, default to 1
n: The total number of observations. If nclust is 1, n is the number of observations, if nclust is 2, n * (1 - pn1) is the number of observations for the cluster 2.
dmin: the lower bound for the range of effect sizes (in ~Cohen's d like scale).
dmax: the lower bound for the range of effect sizes (in ~Cohen's d like scale). If not specified, dmax takes the value of dmin thus the effect size is the same for all indicators.
rmin: the lower bound for the range of correlations between indicators. TODO The correlation is assumed to be the same within each cluster.
rmax: the upper bound for the range of correlations between indicators. If not specified, rmax takes the value of rmin thus using a single value.
nind: the number of indicators
skewmin: the lower bound for the range of skewness.
skewmax: the upper bound for the range of skewness. If not specified, skewmax takes the value of skewmin thus using a single value.
kurtmin: the lower bound for the range of kurtosi
kurtmax: the upper bound for the range of kurtosi. If not specified, kurtmax takes the value of kurtmin thus using a single value.
pn1: the proportion of observations belonging to the 1 cluster. Default to 0.5.
debug: logical indicating if returning the vectors of true values when sampling from a range.
udata: list of summary statistics to use in the simulation. When specified, previous arguments are ignored.

Value

a dataframe with the simulated values

Examples

# simulating with parameters
X <- sim_clust(nclust = 2, n = 100, dmin = 2, rmin = 0.5, nind = 5)
X
#>              x1           x2          x3          x4           x5 group
#> 1   -1.98401049 -4.527229427 -2.63707458 -2.84033387 -1.738574224     1
#> 2   -2.72787907 -2.548290505 -2.47074550 -3.08151078 -3.781461092     1
#> 3   -2.34641061 -2.610768507 -1.46967636 -1.30770608 -3.008965336     1
#> 4   -0.65496744 -0.434667621  0.42467850 -0.33175420 -1.925022815     1
#> 5   -0.96467654 -1.350053151 -1.38822578 -2.06679334 -0.976647660     1
#> 6   -3.17648915 -3.964206046 -2.94910305 -3.38263724 -2.814942395     1
#> 7   -2.25613078 -2.696396578 -0.83205286 -1.93596130 -2.899296376     1
#> 8   -4.39539574 -2.502936068 -3.60835290 -2.75589339 -2.934781123     1
#> 9   -2.42184029 -2.511673079 -2.94727946 -1.27554629 -1.286244927     1
#> 10  -2.21180426 -0.331547438 -1.32062872 -0.36953761 -0.478215429     1
#> 11  -2.01163581 -1.990314196 -3.08021736 -2.00999292 -2.606292922     1
#> 12  -1.16133485 -1.671341771 -1.98717173 -0.34013351 -1.116116486     1
#> 13  -3.23455393 -3.571337474 -3.56244131 -2.15986052 -2.182705742     1
#> 14  -0.46221008 -1.222816816 -1.69894416 -2.10613706 -1.486207416     1
#> 15  -1.26623752 -0.786665588 -1.99827231 -2.30143136 -1.004882978     1
#> 16   0.68559875 -0.983113596 -0.40441256 -0.64518242  0.035862793     1
#> 17  -1.33808584 -1.576065721 -2.98399323 -2.31769683 -2.482365846     1
#> 18  -2.46331033 -1.779480439 -3.26449692 -3.05193459 -2.467539905     1
#> 19  -1.39930031 -0.977492935 -0.51711611 -2.35339030 -1.045359298     1
#> 20  -2.11795637 -2.101054575 -2.39447121 -1.13949644 -2.601039396     1
#> 21  -2.59431792 -1.042756031 -1.22810586 -1.73230738 -1.792351057     1
#> 22  -2.77479242 -1.369882085 -0.67393157 -0.52651796 -2.093193558     1
#> 23  -3.40386457 -3.079028557 -2.07027852 -2.80998078 -1.285858319     1
#> 24  -2.39067259 -1.676589872 -2.95469488 -2.56915909 -3.865073249     1
#> 25  -0.48542566 -2.730753345 -1.52493008 -1.57669108 -0.866898930     1
#> 26  -2.18636074 -3.639744636 -2.75429819 -2.99055387 -2.363002268     1
#> 27  -2.01228246 -0.920602942 -2.20069433 -1.46462287 -1.869670622     1
#> 28  -2.96211506 -4.268241161 -4.56223015 -3.08372852 -3.487435505     1
#> 29  -3.08666467 -3.225876129 -3.86381080 -4.09560109 -4.308957860     1
#> 30  -2.43070379 -0.754248638 -1.85662270 -1.10450992 -2.863527009     1
#> 31  -2.73207668 -1.936193060 -1.88098716 -2.61728848 -2.004225333     1
#> 32  -1.07361372 -2.194920435 -1.66316144 -1.81910932 -0.670543217     1
#> 33  -1.49033081 -0.783050033 -3.80214072 -0.60300822 -0.625636751     1
#> 34  -1.89193237 -2.138393869 -2.92948226 -1.63304851 -4.053714916     1
#> 35  -0.90638721 -1.155780406 -2.08801319 -1.73935933 -1.828208105     1
#> 36  -1.40491642 -1.871584447 -2.72228211 -1.92907034 -1.785183600     1
#> 37  -0.52306608 -1.947950773 -1.59043182 -0.69509906 -0.935645095     1
#> 38  -1.80539245 -2.253457236 -0.85682373 -1.61017458 -1.184977745     1
#> 39  -3.65993925 -2.522223795 -1.18820422 -2.71135152 -3.237213419     1
#> 40  -1.63272830 -3.458565147 -3.10561845 -1.46918230 -2.304841427     1
#> 41  -1.38037017 -2.764150054 -2.40142960 -2.54089832 -2.451128645     1
#> 42  -2.80390133 -1.345647375 -2.00955707 -2.97806394 -2.360734687     1
#> 43  -2.60015778 -2.759411121 -2.06980954 -2.10612760 -1.898025244     1
#> 44  -3.11607015 -2.372057432 -3.45504708 -2.57345021 -2.498586414     1
#> 45  -2.92521116 -4.265734359 -4.08862886 -3.41953635 -4.436347065     1
#> 46  -0.56707430 -2.879469673 -1.75150747 -1.47799623  0.214413297     1
#> 47  -3.38475365 -3.671726513 -3.10281484 -2.05448719 -2.726593126     1
#> 48  -0.23084556 -0.914203998 -1.14444604 -1.22869734 -0.908235105     1
#> 49  -2.61038155 -2.676119544 -1.07607948 -1.77839818 -2.006745376     1
#> 50  -1.98967343 -2.039634604 -1.28167132 -1.60328125 -1.135412668     1
#> 51  -2.56452142 -2.442070719 -1.95702454 -1.97222605 -2.603699785     2
#> 52   1.09861981  0.844090474  0.61028399  0.42149934 -0.005354655     2
#> 53  -2.11099175 -1.279929031 -1.34460018 -0.37437183 -1.954085930     2
#> 54  -0.68817604 -1.224910519  0.40067543  1.04865269 -0.349474794     2
#> 55   0.09715730  0.044005927  0.55752121  0.94986423 -0.389921148     2
#> 56  -1.29271773 -1.532307294 -0.50305818 -1.30998862 -1.624719817     2
#> 57  -2.06322037 -0.639133728 -0.78916698 -2.33377477 -1.844784676     2
#> 58  -1.44020364 -0.319014620 -0.82006004  0.25677953 -0.061847459     2
#> 59   1.54124872  1.829268114  2.25405929  2.61642504  1.712258404     2
#> 60  -0.37961093  0.414012613  0.94046097 -1.47103560 -0.067036022     2
#> 61   0.02144019  0.320994584 -0.09580214 -0.47671101 -0.654281345     2
#> 62   1.83320404  1.595355681  1.21401290  1.63638232  1.315434459     2
#> 63   1.15527929  0.626810696  1.11327612 -0.57700617  1.258151384     2
#> 64   1.51542064  0.866325326  0.55105334  1.61350762  0.532153243     2
#> 65   0.77395342  0.715442596  1.13805811  1.61961590 -0.088109791     2
#> 66   0.82616564 -0.207787039  1.14813274  1.09616576  0.583234184     2
#> 67  -0.09062488  0.127013084 -0.05070234 -0.23174065 -0.893779742     2
#> 68  -0.82058882 -0.900614518 -0.22177936  0.16415166 -0.757552163     2
#> 69   0.11660759 -0.245504173 -1.36537396 -1.24953546 -0.708789382     2
#> 70   0.48514954  0.152697067  0.91770860  0.31921079  0.104013513     2
#> 71   1.00681704  1.287832122  1.31865081  0.88405691 -0.180343930     2
#> 72   0.72037154  0.503000260  1.86892651  1.94704746  1.089736835     2
#> 73  -0.31990618 -0.024621277 -0.42419004  0.05841436 -0.657600664     2
#> 74   0.41388271  0.622580103 -0.49992256  0.25036277 -0.740156544     2
#> 75  -1.09690059 -0.694412921  0.38233938 -1.12912729 -0.760806737     2
#> 76  -0.70858012 -0.212652029 -0.22128056  0.45670740  0.329955649     2
#> 77   1.28744485  1.717289164  1.41148441  1.99592231  1.665735943     2
#> 78   0.25201231  1.919085090  1.13410498  0.52036075  0.297959339     2
#> 79  -1.88929077  1.476362269 -0.95579809 -1.03378462 -0.553372287     2
#> 80   2.02859424  1.335924164  1.15460321  1.28578532  0.048674999     2
#> 81   2.07872913 -0.630401734 -0.09644347  0.42399087 -1.056295720     2
#> 82   1.66745838  0.002585383 -0.88127474  0.75337354  1.186452184     2
#> 83   0.02033544 -0.805458612  1.16304143  0.53683250 -0.807700350     2
#> 84   0.62580106  0.672799069  0.11611506  0.08123568  0.555597069     2
#> 85  -0.18620956 -0.342089263 -0.94889551 -1.15991168 -1.214108167     2
#> 86   0.29041169 -0.942156928  0.45213803  1.21639623 -0.516029450     2
#> 87   0.45705344  0.777586805  0.10113160 -1.29287736  0.303146176     2
#> 88   1.85395866  0.282932886  2.02348129  1.13845513  0.854551715     2
#> 89   0.75449886 -0.466904446 -1.41840127  0.07009583 -0.533430375     2
#> 90  -0.83073003 -1.158256526 -0.49495581 -1.24208331 -2.365108644     2
#> 91  -0.81193974 -0.979326087 -1.30648205 -2.36302950 -1.011314381     2
#> 92   1.27128060  0.164552490 -1.77582863 -0.01216554  0.598762786     2
#> 93   0.86703493  1.097882038  1.20251960  1.71441447  1.201807758     2
#> 94  -0.92317071  0.516964442 -0.29119191 -2.30586101 -1.855177203     2
#> 95  -0.99130839 -0.483686308 -0.14047633 -0.04084626  0.352968480     2
#> 96  -0.41537993  0.978417196  0.06407567 -0.38945631 -0.137361596     2
#> 97   0.51241034  0.997156367  1.70514734 -0.14765827  0.155688100     2
#> 98   0.43519424  0.404155296  1.53402766  2.25042188  1.206219725     2
#> 99   0.38727387 -0.309931700 -1.17484387 -1.03085387 -1.146486811     2
#> 100 -0.95615025 -1.248384669 -1.39667448 -1.14022800 -0.548282270     2
# with external data
udata <- prep_user_data(X)
sim_clust(udata = udata)
#>              x1            x2          x3           x4           x5 x6
#> 1   -1.11046053 -1.7045173125 -0.23298673 -0.560472970  0.035581235  1
#> 2    0.07787598  0.5528600921 -0.23476503 -0.270296051  0.348671089  1
#> 3   -0.05960887  0.0284960921  0.93128862 -0.619379330 -0.043296908  1
#> 4    1.27764288  0.6336756339 -0.13397348 -0.051261695  1.434925531  1
#> 5    1.36827020  1.3395996022  1.20956754  2.043442648  1.490220408  1
#> 6    0.32379480 -0.0166131268 -0.32173566  0.052908887  0.033568652  1
#> 7   -1.78519278 -1.9668540068 -1.72068244 -1.397537080 -2.444093379  1
#> 8    0.15523903  0.2097105178 -1.18700628 -0.419173484  0.533113309  1
#> 9    0.21000449  1.1013939366  0.52113735 -0.161236165  0.200127280  1
#> 10   0.08412244 -0.3362396835  0.37925864  0.003724700 -0.686510770  1
#> 11   1.10593665  1.2891923225  1.66401754  1.387311746  1.059053794  1
#> 12  -1.28317835 -2.2072511103 -1.41035800 -1.638849717 -1.493139848  1
#> 13   0.02659329  1.0140106042  0.63594650  0.261732891  0.284600137  1
#> 14   0.86465642  0.5675854492  1.04338777  1.094381715  0.041350184  1
#> 15  -0.80354004 -0.1036467428  0.26657960 -0.158887295  0.870660835  1
#> 16   0.50765342  0.0017913503 -0.61433587 -0.728250644 -0.268071006  1
#> 17   1.47252405 -0.2920142121 -0.15264008  0.525762877  0.697349376  1
#> 18  -0.15129841 -0.6307995221 -0.30751562 -0.753480912 -0.373801220  1
#> 19   1.69074294  1.5828922862  1.29159876  1.579471646  0.847941548  1
#> 20   1.06412994  1.7556917522  1.09715881  0.854643844  0.974097710  1
#> 21  -1.35682626 -1.5907766371 -0.61577003 -0.665061482 -1.098134844  1
#> 22  -1.31358793 -1.0864167041 -1.07013427 -0.641040428 -0.860370777  1
#> 23   2.01522809  1.9541279271  2.04750750  2.073757178  2.043872947  1
#> 24  -0.95066288  0.0383811063  0.28503424 -0.052901815  0.024155028  1
#> 25   0.60863948  0.6754888760  0.97918147  0.881070486  0.272750481  1
#> 26  -0.37268269  1.6530090064  0.99444428  1.191851192  0.928031038  1
#> 27   0.92815565  1.1534413550  0.55612110  0.685137147  0.866330492  1
#> 28   1.30644840  1.1503639701  0.71526582  1.151717283  1.191919029  1
#> 29   1.45475950  0.9174046735  0.84893596 -0.455686377  0.839255825  1
#> 30  -1.14895214 -1.3764331474 -0.67053730 -1.542221232 -0.756056608  1
#> 31   1.13461112  0.8481213412  0.62275576  0.493460971  0.812344745  1
#> 32   1.58154161  0.8851297525  0.77061697  1.669943396  1.375061847  1
#> 33   0.68189124 -0.1324547394  0.75752784  0.629312121 -0.742471409  1
#> 34   0.48570866  0.0743344018  0.97047311  0.907408811  0.405914648  1
#> 35   1.25698484  1.7214378223  1.55200919  1.899047876  1.731787286  1
#> 36   0.36904122 -0.3876554433 -0.17229325 -0.968923101  0.134958514  1
#> 37   1.30002870  1.2789821678  1.33830454  1.234074595  1.504841036  1
#> 38  -0.77579444 -0.3774239388 -0.52609531  0.010032889 -0.033405152  1
#> 39  -0.22592891 -0.4040572139 -0.42051062 -0.172522412  0.244426861  1
#> 40  -0.82705139 -1.7178794056 -1.61700848 -0.831787520 -0.845642736  1
#> 41   0.60184635 -0.0968280246 -0.10110556 -0.257564384 -1.281860480  1
#> 42   0.25501892 -0.7420591314 -1.10165700 -0.747774236 -0.197475014  1
#> 43   1.80849729  1.4196399170  0.68236525  0.827243534  0.343919781  1
#> 44  -0.46483953 -0.7345626937 -0.53372362 -0.528681950 -0.097410386  1
#> 45   0.86723810  0.9981224027  1.34507051  0.836917617  1.087448677  1
#> 46  -0.42241093 -0.9557473546 -0.15860504  0.102474420  0.809670286  1
#> 47   1.59848351  1.2313393985  1.44210397  1.374590601  1.434396865  1
#> 48   0.80036384  0.8090307445  0.79503460  0.602922745  0.754821936  1
#> 49  -1.78913184 -1.7135340650 -2.00152703 -1.540171442 -1.855374080  1
#> 50  -1.57775174 -1.7469082382 -1.49843758 -1.511148029 -1.857586645  1
#> 51  -1.52549448  0.6116754842  0.35078824  0.144219316 -0.729017109  1
#> 52  -0.63382018  0.1664441615  0.57034979 -0.637421632 -0.457585661  1
#> 53  -0.08024854  0.0857036720 -0.18711685 -0.144977195 -0.323538960  1
#> 54  -0.31863148  0.2491147538  0.35154494  0.477473389  0.383562120  1
#> 55  -1.06815848  0.0694373245  0.15717776  0.085693699  0.072077667  1
#> 56   1.07508606  1.1147718604  1.23521378  0.743907475  0.929173021  1
#> 57   1.19039628  0.9020042138  0.90683280  2.037859335  1.689566932  1
#> 58   0.95459244  0.3279031879 -0.06602360  0.439179457  0.513575312  1
#> 59   0.09683995  0.3516977952  0.39073988 -0.864385464 -0.291524841  1
#> 60  -0.17534970 -0.9311509789 -0.18371116 -0.508109170 -0.540862230  1
#> 61   1.31436077  0.5042416808  1.00807379  0.927949496  1.239230668  1
#> 62   1.50283181  0.5836268056  0.82313506 -0.113215823  1.086985532  1
#> 63   0.25680477  0.9491985282  0.85351231 -0.009582913 -0.304896542  1
#> 64   0.08979999  1.7264988794  1.55478038  1.657898748  1.088321568  1
#> 65   0.33125084  0.8415003622  0.85927049  0.005630863  0.554367098  1
#> 66  -1.33681967 -1.4683130281 -2.01054065 -1.619019940 -2.009855871  1
#> 67  -0.89877124 -0.2493236850 -1.23773407 -0.987113119 -1.516408783  1
#> 68  -0.36473892 -0.5993678339 -1.01046820 -0.224033740  0.051851787  1
#> 69   1.83350790  1.7213191116  2.08548523  1.107959806  1.008234618  1
#> 70   0.57466961  0.3051187875 -0.11066724 -0.518795447  0.838263539  1
#> 71   0.32354226  0.6796806918  0.85040848 -0.912186369 -0.095417465  1
#> 72   0.39600003 -0.2118721770 -0.29625628  0.864478587  0.236247659  1
#> 73   1.53736768  0.4247281504  0.70141358  1.339618935  0.485537652  1
#> 74   0.14173084  0.8621591961  0.80401005 -0.133577361  0.691399753  1
#> 75  -1.65707415 -1.3154148026 -1.47660140 -1.392865135 -1.880355561  1
#> 76  -0.23766318 -0.2589966791 -1.44750312 -1.278129081 -1.420282943  1
#> 77  -1.73611302 -1.1247445960 -1.44781265 -1.158551263 -1.811814147  1
#> 78  -0.22368847 -0.1210521100 -0.45793906 -0.494030512 -0.237993888  1
#> 79   1.82776981  0.7899951888  0.03818428  1.457331833  0.843821359  1
#> 80   1.25913814  1.2997011375  1.29089425  1.467942697  1.258294161  1
#> 81   0.34471561 -0.2770806583 -0.35178121  0.734881007 -0.054392731  1
#> 82  -0.57091595  0.2586926214  0.02869660 -0.250571109 -0.003202099  1
#> 83   0.84927013  1.0303817535  0.48231415  0.580845715 -0.151378086  1
#> 84   1.83506882  0.1141015316  0.58996522  0.313875337  0.969661718  1
#> 85   0.61056196 -0.1497741081 -0.57611410  0.092065602 -0.657942547  1
#> 86  -0.77224603  0.1588532274 -0.11076221 -1.274228632 -1.362792869  1
#> 87   0.67000619  0.3156587734  0.94686698  1.070415826  1.024019377  1
#> 88   1.15089447  0.3737667426  0.64789724 -0.181540998  0.846528964  1
#> 89  -0.11607350 -1.1461157861 -0.60972259 -0.799094624 -1.483466944  1
#> 90   0.73956951  1.3483824133  0.29704235  0.256381837  0.447767277  1
#> 91  -0.01319368 -0.1065240817  0.52176269 -0.346656771  0.136561984  1
#> 92  -0.82379689  0.0003148991 -0.68981166  0.102902427 -0.410754217  1
#> 93   1.88791883  1.5084337656  1.15667681  1.696768203  1.611677588  1
#> 94  -0.25486939 -0.4633021591 -1.01540758 -0.653891670 -1.232643715  1
#> 95   0.44238924  0.4614166752  0.62863318  0.621590717  0.894458105  1
#> 96  -0.90808444 -0.7832954905 -1.60284083 -1.411685630 -1.460771182  1
#> 97  -0.67100693 -0.3133826766 -0.77588509 -0.327709378 -0.394767825  1
#> 98  -0.06239489  0.1633738650  0.15565656  0.055773610  1.003535584  1
#> 99  -0.62636797 -0.4902043435 -0.84896099 -0.325323782  0.470247464  1
#> 100 -1.62190094 -2.1596624019 -1.82090063 -1.552605866 -1.654394232  1