This function simulates a meta-analytic dataset based on the random-effects model. The simulated effect size is Hedges' G, an estimator of the Standardized Mean Difference (Hedges, 1981; Li, Dusseldorp, & Meulman, 2017). The functional form of the model can be specified, and moderators can be either normally distributed or Bernoulli-distributed. See Van Lissa, in preparation, for a detailed explanation of the simulation procedure.
Usage
simulate_smd(
k_train = 20,
k_test = 100,
mean_n = 40,
es = 0.5,
tau2 = 0.04,
alpha = 0,
moderators = 5,
distribution = "normal",
model = "es * x[, 1]"
)Arguments
- k_train
Atomic integer. The number of studies in the training dataset. Defaults to 20.
- k_test
Atomic integer. The number of studies in the testing dataset. Defaults to 100.
- mean_n
Atomic integer. The mean sample size of each simulated study in the meta-analytic dataset. Defaults to
40. For each simulated study, the sample size n is randomly drawn from a normal distribution with mean mean_n, and sd mean_n/3.- es
Atomic numeric vector. The effect size, also known as beta, used in the model statement. Defaults to
.5.- tau2
Atomic numeric vector. The residual heterogeneity. For a range of realistic values encountered in psychological research, see Van Erp, Verhagen, Grasman, & Wagenmakers, 2017. Defaults to
0.04.- alpha
Vector of slant parameters, passed to sn::rsn.
- moderators
Atomic integer. The number of moderators to simulate for each study. Make sure that the number of moderators to be simulated is at least as large as the number of moderators referred to in the model parameter. Internally, the matrix of moderators is referred to as
"x". Defaults to 5.- distribution
Atomic character. The distribution of the moderators. Can be set to either
"normal"or"bernoulli". Defaults to"normal".- model
Expression. An expression to specify the model from which to simulate the mean true effect size, mu. This formula may use the terms
"es"(referring to the es parameter of the call to simulate_smd), and"x\[, \]"(referring to the matrix of moderators, x). Thus, to specify that the mean effect size, mu, is a function of the effect size and the first moderator, one would pass the valuemodel = "es * x\[ , 1\]". Defaults to"es * x\[ , 1\]".
Value
List of length 4. The "training" element of this list is a data.frame with k_train rows. The columns are the variance of the effect size, vi; the effect size, yi, and the moderators, X. The "testing" element of this list is a data.frame with k_test rows. The columns are the effect size, yi, and the moderators, X. The "housekeeping" element of this list is a data.frame with k_train + k_test rows. The columns are n, the sample size n for each simulated study; mu_i, the mean true effect size for each simulated study; and theta_i, the true effect size for each simulated study.
Examples
set.seed(8)
simulate_smd()
#> $training
#> vi yi X1 X2 X3 X4
#> 1 0.10123023 -0.16012845 -1.1444094 -1.04043881 0.062535228 1.0148301
#> 2 0.08088794 -0.80729991 -1.7215353 0.02465913 0.231113964 -0.8321755
#> 3 0.11803209 0.63219536 -0.3696855 0.86220033 1.517608501 -1.4727851
#> 4 0.12802095 0.76916686 1.8220755 0.70828681 -0.498742894 0.4537334
#> 5 0.08189427 0.66239160 0.4775898 -0.63656810 0.004252849 0.6631271
#> 6 0.10243131 -0.34194013 0.1405485 0.90875200 0.359516304 -0.7153895
#> 7 0.10480936 -0.54557741 -1.7260245 -0.58273245 2.082965890 2.0207644
#> 8 0.14436434 0.06504549 0.2765317 0.08109775 -1.408034082 1.9224919
#> 9 0.38418205 0.31267138 -1.3627597 -0.04364549 1.217850494 -0.5379136
#> 10 0.12307917 0.52473228 0.8354238 0.27538614 0.721791139 -1.1210611
#> 11 0.15875395 1.39707761 2.2256232 1.03476676 -0.201646518 -0.7519621
#> 12 0.08878501 0.31292809 0.1722670 -0.44401335 0.095368307 -0.4055921
#> 13 0.10208681 -1.28993059 -1.5005928 -1.34238940 -2.032627280 -0.1743360
#> 14 0.17384976 -0.49542668 -1.3466174 -0.16337964 -1.775771585 0.9972979
#> 15 0.10038187 -0.58759913 -2.4010823 -0.24919870 0.066025885 0.5076123
#> 16 0.14694100 1.11492088 0.7935204 0.66247074 -1.224103992 -0.9695288
#> 17 0.06776487 0.58157303 0.4438913 0.64397076 1.578454567 0.2136013
#> 18 0.11094361 0.58270488 0.5038261 -0.85192796 -0.204568006 -0.6238114
#> 19 0.07510350 1.10402148 1.4280847 -0.72472537 0.413325429 0.3302807
#> 20 0.12887103 -1.27683963 -1.8320869 -0.13801556 -0.355544375 -1.3008866
#> X5
#> 1 0.88819728
#> 2 0.29270972
#> 3 0.31683564
#> 4 -2.02425302
#> 5 -0.91530048
#> 6 -0.34304121
#> 7 -0.61830454
#> 8 1.96917331
#> 9 1.28234666
#> 10 1.21800036
#> 11 -1.27702516
#> 12 2.08310267
#> 13 -0.65815868
#> 14 -0.34382308
#> 15 0.74423183
#> 16 -1.32233177
#> 17 0.39138003
#> 18 -0.09488615
#> 19 1.13265525
#> 20 0.46624137
#>
#> $testing
#> yi X1 X2 X3 X4 X5
#> 21 0.0697442490 1.34278280 -0.345707310 1.57818995 -0.44913981 0.705276551
#> 22 0.6610788203 2.43894434 0.407881830 -1.09289061 0.02348950 -1.346451232
#> 23 0.9563700453 0.67693611 -0.542383594 -0.76616169 0.32860881 1.606175428
#> 24 -0.4565151859 -1.96898063 -2.233980278 -2.44080992 -0.65851847 2.978035548
#> 25 0.2097207276 0.08038142 1.317620135 -0.66787498 -0.69390119 0.889280799
#> 26 -0.0699897413 -0.70476923 0.421883928 -0.87779243 -1.02011480 -0.364122280
#> 27 0.1125065157 0.59725232 -0.742518989 -0.24948742 -1.10058841 0.054619107
#> 28 0.5799963557 0.79577963 0.246548388 -0.91454381 -1.61812166 -0.589375171
#> 29 -0.4113890204 -1.03083607 -0.534765887 0.08087580 2.14679976 0.050225736
#> 30 -0.1466466750 -0.41952683 -1.375543934 -0.08288448 -0.71783589 2.617582843
#> 31 0.2641604408 0.16009113 -0.410783842 -0.40642879 0.89826920 0.627148220
#> 32 0.5488677329 -0.56448033 1.072109345 0.69900714 -1.15007197 -0.827227458
#> 33 -0.1410646978 0.22750654 0.944193458 0.47244670 -1.04069937 0.504060258
#> 34 -0.1047712893 0.25707888 -0.660594907 0.98195504 -0.06291613 -0.394589512
#> 35 0.5656267024 -0.33770080 0.463225218 -1.44548947 1.37773115 0.357938059
#> 36 0.3871240265 0.30457246 -0.833497207 0.01650441 0.62319204 -0.115376387
#> 37 0.2289248513 0.72443709 -1.656108832 -0.19116183 -0.69531851 0.680534148
#> 38 -0.7671912986 -0.68517330 -0.242947018 0.60615056 0.34736006 0.377851898
#> 39 0.8280179901 0.66148590 -0.734829314 1.11059186 -1.66093486 0.386261629
#> 40 1.7946267727 1.72541962 0.288050068 -0.02910979 1.22541007 0.549553058
#> 41 0.1113967154 0.32134570 -2.519865202 -0.29233821 1.04911272 0.613320135
#> 42 0.0488309692 0.57631589 0.559240717 1.47869193 0.07042518 -0.795713800
#> 43 -0.6429384837 -1.40999218 -0.370775118 0.73176907 0.34117199 -1.490813982
#> 44 -0.0108968411 -0.99550207 -0.246350631 -1.19898977 -0.45694682 -0.769902613
#> 45 1.1389625045 1.56029895 -1.068533578 1.51577158 0.36241300 1.625447491
#> 46 0.0464288770 0.20359400 0.188859634 -0.36821179 0.43088979 0.903666849
#> 47 -0.7271016178 -0.38763480 -0.700101046 -0.61153291 -3.28193174 -0.938239707
#> 48 0.3385902120 0.91961483 -0.054871878 -0.99407239 0.07959148 -0.863328748
#> 49 -0.3364394483 -0.37973893 0.004724072 0.22384503 0.28338913 -0.012054345
#> 50 0.0721290798 0.74424525 0.513744294 1.24460620 -1.13800059 -1.018069491
#> 51 -0.5792457661 -1.18318210 -0.232082803 -2.14666505 0.55833481 -1.304871448
#> 52 0.5368899917 0.27641906 -0.503803381 0.52658047 1.45478371 -0.907842475
#> 53 0.0869024855 -0.35621772 0.931147030 -0.13259284 0.91997026 0.045246555
#> 54 0.0793080670 0.98772386 0.866682884 -0.36330720 -2.45861485 1.591761639
#> 55 -0.4977438187 -0.26723365 -1.615076668 -0.89040754 1.35749161 0.146493228
#> 56 0.4946680032 0.48002729 -0.414854751 -0.54416473 -0.73312796 -0.463292606
#> 57 0.8300930074 0.76742274 0.295879429 -0.46053733 0.38481593 0.236661956
#> 58 0.4046279101 0.93944209 -0.501413917 -0.19810448 0.92773032 0.664210399
#> 59 -0.9582677316 -1.05321259 0.168396365 -0.05398731 -1.23938949 0.629995102
#> 60 1.0929122623 1.01361777 -1.484505096 0.06713632 1.73655423 -0.219841525
#> 61 -1.2446328798 -1.25417324 -0.935164736 1.37062115 0.46932808 0.001456405
#> 62 -0.0447009949 -0.38058363 -1.318323265 -1.71261554 0.27094446 -0.450508307
#> 63 -0.9829585596 0.20908883 -0.843522645 -1.54077184 -0.66946378 -0.418097081
#> 64 -0.2109305739 -0.12475618 -0.180237064 1.42855685 0.54643929 0.338293573
#> 65 1.2770131383 2.18637793 -1.473517194 -1.19629850 0.29537750 -0.393182816
#> 66 -0.6904278987 0.08202324 0.296855110 0.88030339 -1.13881229 -0.354461946
#> 67 0.9332104802 2.11210205 0.483606325 -1.68208244 1.29022620 -1.206672296
#> 68 0.4295536525 1.03434270 0.068466459 1.69888450 -2.22984375 -0.412220453
#> 69 -0.5541784759 -0.19817321 0.288832146 -0.15496161 1.28430248 0.386628349
#> 70 0.1773691167 -1.03922958 1.314781376 -1.27400097 -1.41318801 -0.619818844
#> 71 -1.1119527377 -0.13366410 -0.295572687 -0.58194548 -0.69842091 1.081208993
#> 72 -0.2327487049 -0.58203619 -0.064578436 -0.43066068 0.82325010 -1.678908961
#> 73 -0.6881029992 -0.90301123 0.776282190 0.30444699 -1.14748923 -1.440690533
#> 74 0.2872110208 -0.80183175 -1.079610620 0.33526170 0.02986996 -1.422982215
#> 75 0.9580626631 1.32082067 0.592149208 -2.28425822 -0.05187127 -1.138380472
#> 76 0.6505781727 1.03917965 0.326762664 -0.87895358 -0.29070076 -1.560017465
#> 77 0.6396433924 0.55811104 -2.295856107 0.98105921 -0.06218890 -0.468259305
#> 78 -0.4669543062 -1.32868715 -0.402928719 0.74271560 -1.07172843 0.467356785
#> 79 -0.9769101988 -1.92455679 1.125903449 0.10056759 -1.16839102 -0.146917636
#> 80 -0.2932424292 0.02269541 1.063092737 0.16902021 -0.19654398 1.624582143
#> 81 -0.1995739488 -0.58148841 -1.156393348 0.34330655 -1.23256601 0.424045409
#> 82 0.2074836427 -0.22415163 -0.954671006 1.03191632 1.67582582 -0.560888865
#> 83 1.0590227386 1.19843419 -0.642356883 1.61580763 0.14981857 -0.229831775
#> 84 -0.9464700091 -1.35857871 -0.129691509 -2.05943539 1.10504698 0.994997471
#> 85 0.0501360937 -0.02007139 0.295829171 0.71146123 -0.16625956 -0.669661078
#> 86 0.7211893129 0.89013344 0.824899518 -0.19750984 -1.62326723 0.071204845
#> 87 -0.0192254232 -0.02785890 -1.148831250 -1.55998272 0.54408680 -1.183813504
#> 88 -0.2100014832 -0.87933866 1.585573941 0.39203385 0.43202330 -0.976633307
#> 89 0.5415433122 0.76532204 -0.132846093 -0.10443202 -1.73795791 1.869923666
#> 90 -0.3031373341 -0.97758855 -0.118899731 -0.30398595 1.32981739 -0.575898320
#> 91 -0.2433747657 0.53030495 0.119426695 -0.37146423 -0.82576253 -1.019094922
#> 92 0.9812211327 0.93490598 0.193494092 1.28880895 -0.74782165 -0.649659900
#> 93 0.0312254970 0.34618828 1.469472441 0.16832416 -2.13353795 1.533933071
#> 94 -0.4437473468 -0.73358085 -2.160397828 0.79351401 0.36263912 -0.107787116
#> 95 -0.1699726514 0.71044321 2.309691146 -1.43665381 -0.23749230 0.169535331
#> 96 -0.6784711467 -0.32270804 0.984586572 -2.80920276 -0.91259245 1.008258732
#> 97 0.0008929241 -0.36063854 1.510773654 0.24555120 -0.54637269 1.177163008
#> 98 0.3171494928 0.15515330 -0.044507754 -0.42755197 0.17847832 0.837676659
#> 99 -0.3849614859 -1.39090615 -1.153481015 0.32787243 -0.99193808 0.669284255
#> 100 0.7591054389 1.37319401 2.294143138 0.24435018 -0.86142982 -0.243659774
#> 101 -0.5768676823 -0.86514969 0.538671399 0.94024364 0.45566891 1.129335915
#> 102 -1.1473919063 -1.30250885 -0.146357462 -0.13692522 -2.05915568 -0.041590377
#> 103 0.7351544763 0.89342076 -0.979218618 -1.85424344 0.16398290 0.914060323
#> 104 -0.8653556107 -0.88037666 -1.831172832 1.64373845 0.78839628 0.432991085
#> 105 0.0245160987 -0.41661945 1.870035998 -0.14302351 -1.09377744 -0.936613809
#> 106 0.3512162331 -0.04062916 -1.503020392 -0.52419166 -0.53807090 -0.582746486
#> 107 0.1455497552 0.14358965 2.318318542 0.78931815 -0.22432943 -0.090653685
#> 108 0.0719350527 0.09751138 -1.256282212 0.96144097 1.46733421 1.957436095
#> 109 0.2745557083 0.16642969 -0.938503513 1.29350891 -1.60605679 0.843387407
#> 110 1.0883455067 1.47631110 -0.526780039 -1.35604594 -0.54841970 0.115736923
#> 111 -1.5142330943 -1.54600953 -1.733278053 -0.85199073 -1.12518922 0.051878985
#> 112 0.5818380085 1.37092704 -1.078728380 -1.10291173 0.37742996 -0.559855595
#> 113 0.3096846021 -0.30687696 -0.369739572 0.84291478 -0.35847353 0.039211626
#> 114 -0.3923435819 -0.17814964 1.418624142 -0.40487444 0.02549246 0.573795451
#> 115 0.7116822116 0.84086555 -0.960515383 0.34463034 -0.83657908 -1.722671808
#> 116 -0.2505867019 -0.70385466 0.444572597 0.11589273 0.34432991 1.525124902
#> 117 -0.7169171557 -0.38034853 0.920231427 0.02267681 1.26276866 -0.035198961
#> 118 -0.0128238583 -0.61284745 0.248415976 1.81038765 0.32824879 -0.187316677
#> 119 0.7318241641 -0.84761010 -0.258117777 0.18494050 -0.03846550 0.602229762
#> 120 1.0879095578 1.45125747 2.300613151 -0.42790075 0.55285433 0.401261034
#>
#> $housekeeping
#> n mu_i theta_i
#> 1 38 -0.57220472 -0.705987796
#> 2 52 -0.86076766 -0.698131590
#> 3 34 -0.18484276 0.040520862
#> 4 32 0.91103776 0.737997061
#> 5 50 0.23879490 0.339999953
#> 6 38 0.07027426 0.095919189
#> 7 38 -0.86301223 -0.878455945
#> 8 26 0.13826583 0.473640449
#> 9 8 -0.68137984 -0.498834172
#> 10 32 0.41771190 0.574197305
#> 11 30 1.11281162 1.334479699
#> 12 44 0.08613348 0.187929740
#> 13 46 -0.75029639 -0.764245280
#> 14 22 -0.67330868 -0.720849180
#> 15 40 -1.20054114 -0.965045888
#> 16 30 0.39676020 0.489142940
#> 17 60 0.22194567 0.447451857
#> 18 36 0.25191305 0.072457827
#> 19 60 0.71404233 0.894284264
#> 20 36 -0.91604347 -1.271038423
#> 21 58 0.67139140 0.335185599
#> 22 40 1.21947217 0.989581609
#> 23 34 0.33846806 0.403643679
#> 24 40 -0.98449031 -0.564007419
#> 25 64 0.04019071 0.170906391
#> 26 26 -0.35238462 -0.077853808
#> 27 26 0.29862616 0.117139104
#> 28 66 0.39788982 0.752628158
#> 29 48 -0.51541804 -0.610055705
#> 30 14 -0.20976341 -0.655667187
#> 31 60 0.08004557 0.183319624
#> 32 52 -0.28224017 -0.214589007
#> 33 20 0.11375327 -0.229213055
#> 34 30 0.12853944 0.019967531
#> 35 56 -0.16885040 -0.060407138
#> 36 46 0.15228623 0.177478933
#> 37 52 0.36221854 0.294360825
#> 38 30 -0.34258665 -0.255392535
#> 39 40 0.33074295 0.446835494
#> 40 46 0.86270981 1.136663478
#> 41 44 0.16067285 0.281965264
#> 42 32 0.28815795 0.421205467
#> 43 44 -0.70499609 -0.520115340
#> 44 36 -0.49775103 -0.413206121
#> 45 48 0.78014947 0.729160272
#> 46 14 0.10179700 0.141820091
#> 47 32 -0.19381740 -0.832247539
#> 48 44 0.45980742 0.602377723
#> 49 44 -0.18986946 -0.463477153
#> 50 32 0.37212263 0.238516369
#> 51 54 -0.59159105 -0.651683154
#> 52 36 0.13820953 0.236078495
#> 53 48 -0.17810886 -0.303963048
#> 54 38 0.49386193 0.091643728
#> 55 52 -0.13361682 -0.319818014
#> 56 48 0.24001364 0.545196640
#> 57 30 0.38371137 0.265529533
#> 58 32 0.46972104 0.274561431
#> 59 20 -0.52660630 -0.234668518
#> 60 50 0.50680889 0.596736262
#> 61 48 -0.62708662 -0.687148534
#> 62 42 -0.19029182 -0.001593116
#> 63 16 0.10454441 -0.033059907
#> 64 26 -0.06237809 -0.001719045
#> 65 36 1.09318897 1.388980572
#> 66 26 0.04101162 -0.312696335
#> 67 34 1.05605102 0.759007683
#> 68 62 0.51717135 0.575608950
#> 69 46 -0.09908660 -0.027193541
#> 70 18 -0.51961479 -0.693083484
#> 71 20 -0.06683205 -0.329647608
#> 72 54 -0.29101810 -0.368656232
#> 73 50 -0.45150561 -0.354471888
#> 74 34 -0.40091587 -0.057682519
#> 75 42 0.66041034 0.977170894
#> 76 48 0.51958982 0.658157047
#> 77 8 0.27905552 0.265934113
#> 78 48 -0.66434357 -0.351926634
#> 79 72 -0.96227839 -0.938916485
#> 80 32 0.01134770 -0.051035547
#> 81 44 -0.29074421 -0.697014238
#> 82 30 -0.11207581 -0.029428910
#> 83 26 0.59921709 0.676334065
#> 84 68 -0.67928936 -0.787838095
#> 85 18 -0.01003569 -0.224804131
#> 86 56 0.44506672 0.608669640
#> 87 38 -0.01392945 -0.154583120
#> 88 28 -0.43966933 -0.262234146
#> 89 48 0.38266102 0.219259279
#> 90 8 -0.48879427 -0.612113070
#> 91 50 0.26515247 0.173957761
#> 92 60 0.46745299 0.660231719
#> 93 34 0.17309414 0.544501930
#> 94 32 -0.36679042 -0.179546808
#> 95 22 0.35522160 0.490301625
#> 96 50 -0.16135402 -0.179158919
#> 97 44 -0.18031927 -0.198168992
#> 98 40 0.07757665 -0.104464305
#> 99 32 -0.69545307 -0.536135214
#> 100 40 0.68659701 0.997765972
#> 101 44 -0.43257484 -0.469403356
#> 102 14 -0.65125442 -1.002375278
#> 103 18 0.44671038 0.558136376
#> 104 16 -0.44018833 -0.552172900
#> 105 40 -0.20830972 -0.036721502
#> 106 34 -0.02031458 0.003837812
#> 107 48 0.07179483 0.125910961
#> 108 36 0.04875569 0.074342221
#> 109 42 0.08321484 0.125550152
#> 110 48 0.73815555 0.573441346
#> 111 38 -0.77300477 -0.945305162
#> 112 28 0.68546352 0.998741107
#> 113 48 -0.15343848 -0.152354218
#> 114 26 -0.08907482 -0.524721658
#> 115 60 0.42043278 0.865017910
#> 116 58 -0.35192733 -0.467546114
#> 117 44 -0.19017427 -0.417262393
#> 118 60 -0.30642373 -0.517382143
#> 119 24 -0.42380505 -0.059420545
#> 120 36 0.72562874 1.012973300
#>
#> $tau2_est
#> [1] 0.5012652
#>
simulate_smd(k_train = 50, distribution = "bernoulli")
#> $training
#> vi yi X1 X2 X3 X4 X5
#> 1 0.08942930 0.39321957 1 0 1 0 0
#> 2 0.12811877 -0.33721651 0 0 0 0 1
#> 3 0.10706848 0.24604020 1 0 1 0 0
#> 4 0.09230692 0.22982552 0 1 0 0 1
#> 5 0.38332496 0.28991385 1 0 0 0 0
#> 6 0.08071917 0.09584201 0 0 1 0 1
#> 7 0.07765022 -0.11982391 1 1 1 0 0
#> 8 0.08410053 0.09583085 1 1 0 1 1
#> 9 0.07567228 0.33061352 1 1 1 1 1
#> 10 0.05974381 -0.27076113 0 1 0 0 1
#> 11 0.08200838 0.67094921 1 1 1 1 0
#> 12 0.09189174 -0.13395876 1 1 1 1 0
#> 13 0.09168652 -0.02657789 0 1 0 1 0
#> 14 0.10949411 0.48495426 1 1 1 0 1
#> 15 0.17029310 0.84633347 1 0 1 1 0
#> 16 0.12764148 0.29168029 0 0 1 0 0
#> 17 0.09285864 0.31490347 1 1 0 0 0
#> 18 0.22939280 0.43531063 0 1 1 0 0
#> 19 0.06495430 -0.03096112 0 0 1 1 1
#> 20 0.10637747 1.28298894 1 1 0 0 1
#> 21 0.09028827 -0.47980299 0 0 1 1 0
#> 22 0.10448141 -0.82050940 0 0 1 0 0
#> 23 0.20296312 0.22458034 1 0 1 1 1
#> 24 0.11217933 0.04102836 1 1 0 0 0
#> 25 0.07033191 0.31444003 1 1 0 0 0
#> 26 0.11898230 -0.11464852 0 0 0 1 1
#> 27 0.09034614 1.40981795 1 1 0 0 0
#> 28 0.07466851 -0.07008951 1 1 0 0 1
#> 29 0.08476435 0.85192169 1 1 1 1 0
#> 30 0.06957263 0.11761361 0 0 1 0 0
#> 31 0.09200744 0.16632550 1 1 1 0 0
#> 32 0.23375408 1.07652726 1 1 0 1 0
#> 33 0.08920365 0.36710309 1 1 1 0 1
#> 34 0.20875650 0.50891856 1 1 0 0 1
#> 35 0.09845814 0.43746378 1 0 1 1 0
#> 36 0.08012978 -0.51216548 0 1 1 0 0
#> 37 0.10101764 -0.09738429 0 1 1 0 0
#> 38 0.10631629 0.07986114 0 0 0 1 1
#> 39 0.11530796 0.46306563 0 0 0 1 0
#> 40 0.06733517 0.53540920 1 1 1 0 0
#> 41 0.12459935 0.91991545 1 0 1 0 1
#> 42 0.04837183 0.28764929 0 1 1 0 0
#> 43 0.06760571 0.23677321 1 1 1 1 1
#> 44 0.10118482 -0.14896282 0 1 0 0 0
#> 45 0.07235750 0.57073451 1 0 1 0 1
#> 46 0.12754742 -0.28184082 0 0 0 1 0
#> 47 0.09899778 -0.48429881 0 1 1 1 0
#> 48 0.10535158 0.58211960 0 1 1 0 1
#> 49 0.16895308 0.17318762 1 0 1 1 0
#> 50 0.09225451 -0.22004001 0 0 0 0 1
#>
#> $testing
#> yi X1 X2 X3 X4 X5
#> 51 1.3610589057 1 0 1 0 1
#> 52 0.9905762093 1 1 1 1 1
#> 53 -0.5663433441 0 1 0 0 0
#> 54 0.0325784399 0 1 0 1 0
#> 55 -0.3987294694 0 0 0 0 0
#> 56 1.4394713431 1 1 0 1 0
#> 57 0.8641291202 1 1 0 0 0
#> 58 -0.4664070750 0 1 1 0 0
#> 59 -0.2271211308 0 1 0 0 1
#> 60 0.4873625931 0 1 1 0 0
#> 61 1.0251315589 1 1 1 1 1
#> 62 0.2576578399 1 1 0 1 1
#> 63 -0.1346760556 1 1 1 1 1
#> 64 0.2827026925 0 1 0 0 0
#> 65 0.1992093839 1 0 0 0 0
#> 66 1.4388694026 1 0 1 0 0
#> 67 1.0564717221 0 1 1 0 0
#> 68 -0.0698590974 0 1 1 1 1
#> 69 -0.4445950100 0 0 1 1 0
#> 70 0.7217065925 1 1 0 0 1
#> 71 0.3877110174 1 1 1 1 1
#> 72 0.7805664984 1 1 1 0 1
#> 73 -0.0028772005 1 0 0 1 1
#> 74 1.1211745574 1 0 1 1 1
#> 75 0.3766041939 1 0 0 0 0
#> 76 0.1909042313 0 0 1 1 0
#> 77 0.4634482049 1 1 1 1 0
#> 78 0.1673482322 1 0 0 1 1
#> 79 0.5069101185 0 0 0 1 0
#> 80 0.5934150967 1 1 1 0 0
#> 81 0.2657470211 0 0 1 0 1
#> 82 -0.8205912639 0 1 0 1 1
#> 83 0.2563534563 0 0 0 1 1
#> 84 -0.3914667582 0 1 1 0 1
#> 85 0.7507259369 1 0 1 0 0
#> 86 0.6421525361 0 0 0 1 0
#> 87 0.0385397449 0 0 0 0 1
#> 88 0.4260140167 1 0 1 1 0
#> 89 0.5677753989 1 1 1 1 0
#> 90 0.3754579113 0 0 1 0 1
#> 91 0.0480205794 0 0 1 1 0
#> 92 0.3682180208 0 0 0 0 1
#> 93 0.5023048015 0 0 0 1 1
#> 94 0.2122716736 1 0 0 0 1
#> 95 1.1781509262 1 0 0 0 0
#> 96 0.1483738906 0 1 1 1 0
#> 97 -0.4509965470 0 1 0 0 0
#> 98 0.7176483438 1 0 0 1 0
#> 99 -0.1933798945 0 0 1 0 1
#> 100 0.6545642916 1 0 1 0 0
#> 101 0.7374296942 1 0 1 1 0
#> 102 1.0594813192 1 1 0 1 1
#> 103 0.0912794627 0 0 0 0 1
#> 104 -0.4199702552 0 0 1 0 0
#> 105 0.2211928770 1 1 0 0 1
#> 106 0.3246312380 1 1 1 1 1
#> 107 -0.0611561721 1 0 0 0 1
#> 108 0.3621610330 0 1 1 0 1
#> 109 0.2245841914 1 1 1 1 0
#> 110 -0.3058386101 0 1 0 1 0
#> 111 0.4660112449 1 1 0 1 0
#> 112 0.3991601309 1 1 0 0 1
#> 113 -0.1605873821 0 1 1 1 1
#> 114 -0.5967452625 1 1 0 1 1
#> 115 0.7097746996 1 0 0 1 0
#> 116 -0.2909741799 0 0 0 1 0
#> 117 0.0046824741 0 1 0 0 0
#> 118 0.1028707296 0 0 1 0 1
#> 119 0.1224422551 1 0 1 1 1
#> 120 0.3166730050 1 1 0 0 1
#> 121 0.1847810047 1 1 0 0 0
#> 122 0.4427034907 1 0 0 1 1
#> 123 0.1658383133 0 0 0 1 1
#> 124 0.2188132119 0 1 1 1 0
#> 125 1.0097088477 1 0 0 0 0
#> 126 1.3221468005 1 0 1 0 0
#> 127 0.1205266678 1 1 0 1 0
#> 128 -0.1723679990 0 0 1 1 1
#> 129 0.0823549821 0 0 1 1 0
#> 130 0.0805914564 1 0 1 0 1
#> 131 -0.1978631622 0 1 0 0 0
#> 132 -0.0005349054 1 0 1 0 0
#> 133 0.8448169996 0 0 1 0 0
#> 134 -0.1343452325 0 0 0 1 1
#> 135 0.4488476618 0 1 1 1 1
#> 136 0.2748160495 0 1 0 1 1
#> 137 0.2079566028 1 1 1 0 1
#> 138 -0.1336638343 1 0 1 0 0
#> 139 0.2469264903 0 1 1 0 0
#> 140 0.3855105100 0 1 1 1 0
#> 141 0.2140559227 0 0 1 1 1
#> 142 0.0700871731 0 1 0 0 0
#> 143 0.8108545496 1 0 0 0 0
#> 144 0.2166929222 1 0 0 0 0
#> 145 1.3390181875 1 0 0 1 0
#> 146 0.5456515402 1 1 0 0 0
#> 147 -0.3318034211 1 1 1 1 0
#> 148 0.8911191771 1 0 1 0 0
#> 149 0.1317889141 0 0 0 0 0
#> 150 -0.0743895794 0 0 0 0 0
#>
#> $housekeeping
#> n mu_i theta_i
#> 1 44 0.5 0.751593116
#> 2 30 0.0 -0.333319987
#> 3 36 0.5 0.259946504
#> 4 42 0.0 0.203900854
#> 5 8 0.5 0.333272677
#> 6 48 0.0 -0.101590063
#> 7 50 0.5 0.500086117
#> 8 46 0.5 0.575034492
#> 9 52 0.5 0.523972886
#> 10 66 0.0 -0.245329443
#> 11 50 0.5 0.192303599
#> 12 42 0.5 0.305490443
#> 13 42 0.0 -0.024421633
#> 14 36 0.5 0.549976149
#> 15 24 0.5 0.431615110
#> 16 30 0.0 -0.252439422
#> 17 42 0.5 0.479428248
#> 18 16 0.0 0.002462566
#> 19 60 0.0 -0.115571313
#> 20 44 0.5 0.916370461
#> 21 44 0.0 0.076819223
#> 22 40 0.0 0.031935406
#> 23 18 0.5 0.855925180
#> 24 34 0.5 0.544843473
#> 25 56 0.5 0.339226445
#> 26 32 0.0 -0.022609364
#> 27 54 0.5 0.940078186
#> 28 52 0.5 0.766181107
#> 29 50 0.5 0.331731433
#> 30 56 0.0 -0.116785319
#> 31 42 0.5 0.164752731
#> 32 18 0.5 0.632419021
#> 33 44 0.5 0.358384228
#> 34 18 0.5 0.394927198
#> 35 40 0.5 0.322318975
#> 36 50 0.0 -0.116699700
#> 37 38 0.0 0.042058371
#> 38 36 0.0 -0.414291477
#> 39 34 0.0 -0.134362368
#> 40 60 0.5 0.648517760
#> 41 34 0.5 0.616871721
#> 42 82 0.0 0.022864382
#> 43 58 0.5 0.263974696
#> 44 38 0.0 0.002218353
#> 45 56 0.5 0.508134057
#> 46 30 0.0 -0.339267568
#> 47 40 0.0 -0.437684389
#> 48 38 0.0 0.365781498
#> 49 22 0.5 0.851941905
#> 50 42 0.0 -0.165840739
#> 51 18 0.5 0.444477451
#> 52 32 0.5 0.529667395
#> 53 38 0.0 0.034483966
#> 54 40 0.0 -0.157414388
#> 55 54 0.0 -0.364823301
#> 56 46 0.5 0.680246853
#> 57 34 0.5 0.676100483
#> 58 28 0.0 -0.244393314
#> 59 44 0.0 0.328934539
#> 60 54 0.0 0.311210623
#> 61 56 0.5 0.455421861
#> 62 50 0.5 0.424529812
#> 63 10 0.5 0.575313592
#> 64 30 0.0 0.248007282
#> 65 28 0.5 0.621103649
#> 66 38 0.5 0.674340196
#> 67 46 0.0 0.497120688
#> 68 58 0.0 -0.261939925
#> 69 40 0.0 -0.339623134
#> 70 42 0.5 0.581938491
#> 71 28 0.5 0.454697744
#> 72 56 0.5 0.430230952
#> 73 34 0.5 0.601482092
#> 74 54 0.5 1.016411035
#> 75 62 0.5 0.455983640
#> 76 30 0.0 0.323725024
#> 77 78 0.5 0.550542960
#> 78 42 0.5 0.253060913
#> 79 50 0.0 0.176795679
#> 80 26 0.5 0.771009613
#> 81 54 0.0 0.129566696
#> 82 46 0.0 -0.116406274
#> 83 34 0.0 0.069236541
#> 84 36 0.0 -0.194299499
#> 85 32 0.5 0.781030782
#> 86 62 0.0 0.343158794
#> 87 42 0.0 0.166258046
#> 88 50 0.5 0.702321785
#> 89 34 0.5 0.464791569
#> 90 42 0.0 0.210350910
#> 91 42 0.0 0.003151477
#> 92 46 0.0 0.008161278
#> 93 30 0.0 0.074808844
#> 94 32 0.5 0.536789276
#> 95 14 0.5 0.777536531
#> 96 28 0.0 0.382863686
#> 97 46 0.0 -0.111754255
#> 98 38 0.5 0.694209077
#> 99 40 0.0 -0.165236592
#> 100 42 0.5 0.721944321
#> 101 36 0.5 0.504473660
#> 102 32 0.5 0.733613486
#> 103 46 0.0 -0.094132651
#> 104 24 0.0 -0.018162156
#> 105 50 0.5 0.370018449
#> 106 54 0.5 0.451048736
#> 107 34 0.5 0.367677401
#> 108 56 0.0 0.024588526
#> 109 48 0.5 0.315783208
#> 110 42 0.0 -0.153688502
#> 111 22 0.5 0.751588557
#> 112 28 0.5 0.440816462
#> 113 46 0.0 -0.241672109
#> 114 50 0.5 0.528996773
#> 115 48 0.5 0.565896920
#> 116 28 0.0 -0.242492584
#> 117 34 0.0 -0.025367043
#> 118 38 0.0 0.122714748
#> 119 56 0.5 0.123237904
#> 120 56 0.5 0.555290144
#> 121 20 0.5 0.708371544
#> 122 42 0.5 0.371526301
#> 123 56 0.0 0.082036300
#> 124 28 0.0 0.103376035
#> 125 30 0.5 0.517528926
#> 126 18 0.5 0.624071906
#> 127 26 0.5 0.708166163
#> 128 26 0.0 0.045687466
#> 129 60 0.0 0.128322816
#> 130 30 0.5 0.456718548
#> 131 48 0.0 0.064661647
#> 132 20 0.5 0.360405969
#> 133 40 0.0 0.117729175
#> 134 66 0.0 -0.050175225
#> 135 44 0.0 -0.036823966
#> 136 28 0.0 -0.017780269
#> 137 70 0.5 0.179446748
#> 138 42 0.5 0.413166195
#> 139 56 0.0 0.262883275
#> 140 44 0.0 0.451997423
#> 141 22 0.0 0.362111531
#> 142 44 0.0 -0.154110854
#> 143 66 0.5 0.371361599
#> 144 28 0.5 0.315437282
#> 145 22 0.5 0.900416075
#> 146 36 0.5 0.542047973
#> 147 46 0.5 0.240674876
#> 148 48 0.5 0.384783500
#> 149 14 0.0 -0.073030411
#> 150 40 0.0 0.029996208
#>
#> $tau2_est
#> [1] 0.09684336
#>
simulate_smd(distribution = "bernoulli", model = "es * x[ ,1] * x[ ,2]")
#> $training
#> vi yi X1 X2 X3 X4 X5
#> 1 0.06299004 0.101690648 0 0 1 0 1
#> 2 0.07851046 -0.316829310 0 1 1 0 0
#> 3 0.06494661 0.006000258 1 1 0 0 1
#> 4 0.06248350 0.437081405 1 1 1 1 1
#> 5 0.08151884 0.633419001 1 1 0 0 0
#> 6 0.08845043 -0.261689473 1 0 1 1 1
#> 7 0.11223374 0.073369528 1 1 0 1 0
#> 8 0.07377923 0.445377026 1 0 0 0 1
#> 9 0.13569134 -0.240723218 1 0 1 0 0
#> 10 0.09745917 -0.333850759 1 0 1 0 1
#> 11 0.10503473 0.561055136 1 1 0 1 0
#> 12 0.08011055 -0.510284534 0 0 1 1 0
#> 13 0.08773877 -0.076520868 0 1 1 0 0
#> 14 0.11216053 0.020116090 1 0 0 1 0
#> 15 0.09195915 0.153647028 1 0 0 0 0
#> 16 0.09752529 0.700830454 0 1 0 1 0
#> 17 0.20205706 0.133484765 0 0 1 0 0
#> 18 0.08863228 -0.290661784 0 1 1 1 1
#> 19 0.07446868 0.749793883 1 1 0 1 0
#> 20 0.07985105 0.737493474 1 1 1 0 0
#>
#> $testing
#> yi X1 X2 X3 X4 X5
#> 21 0.043815464 0 0 1 1 0
#> 22 -0.048966725 0 1 0 0 1
#> 23 -0.392490028 0 0 1 1 1
#> 24 0.433750412 0 0 1 1 1
#> 25 -0.140216911 1 0 0 1 1
#> 26 0.297429275 1 1 1 0 0
#> 27 0.376034576 1 1 1 0 1
#> 28 0.582961055 1 0 0 1 0
#> 29 0.609602364 0 0 1 1 1
#> 30 0.061378434 0 0 0 0 1
#> 31 0.490004390 1 1 1 1 0
#> 32 0.102490938 1 1 0 1 1
#> 33 0.277943674 1 1 0 1 1
#> 34 0.750090467 1 1 0 1 1
#> 35 -0.126124106 0 0 0 1 0
#> 36 -0.134621588 1 1 0 1 1
#> 37 0.281455564 0 0 1 1 1
#> 38 0.024912072 0 0 0 1 0
#> 39 -0.246580973 1 0 1 1 0
#> 40 -0.210515066 0 1 1 1 1
#> 41 0.329798576 0 0 1 1 0
#> 42 0.129320549 0 1 1 1 1
#> 43 -0.318387047 0 1 1 0 1
#> 44 0.321880461 0 1 1 0 0
#> 45 -0.014817962 1 0 0 1 0
#> 46 -0.013445415 0 0 1 1 0
#> 47 -0.383711975 1 0 1 0 0
#> 48 0.017690162 1 0 0 0 1
#> 49 0.064626566 1 1 0 0 0
#> 50 0.136806194 1 1 0 0 1
#> 51 0.233782428 0 1 0 1 0
#> 52 0.429324364 0 1 0 0 1
#> 53 0.546178309 1 1 0 0 0
#> 54 -1.046527040 1 0 0 0 1
#> 55 0.130567846 0 1 0 1 0
#> 56 0.568800820 1 1 1 1 0
#> 57 0.131183163 0 0 1 1 1
#> 58 -0.274906568 0 0 0 1 0
#> 59 -0.242326268 0 0 0 0 0
#> 60 0.282678008 0 1 1 0 1
#> 61 0.156371610 0 1 1 1 0
#> 62 0.566442533 1 0 0 0 1
#> 63 0.735351939 1 1 1 1 1
#> 64 -0.290157779 0 1 0 1 1
#> 65 0.358903351 0 0 1 0 1
#> 66 -0.517552114 1 0 0 0 0
#> 67 -0.214688133 0 1 1 1 0
#> 68 0.350995191 0 1 0 1 1
#> 69 -0.008986599 1 1 1 0 1
#> 70 0.175530772 0 1 0 0 0
#> 71 -0.111710942 1 0 0 1 1
#> 72 0.069247766 0 1 0 0 0
#> 73 0.040908692 0 0 0 1 0
#> 74 -0.654383762 0 1 0 0 1
#> 75 0.239617380 1 0 1 1 1
#> 76 0.328919754 0 1 0 0 0
#> 77 0.393856139 0 1 1 1 1
#> 78 0.843287275 1 1 0 1 1
#> 79 -0.443871361 0 0 0 1 0
#> 80 -0.096871180 0 1 0 0 1
#> 81 -0.406524790 0 1 1 1 1
#> 82 0.428544929 1 0 0 0 0
#> 83 -0.045226124 0 0 0 1 1
#> 84 -0.312313647 1 0 0 0 0
#> 85 -0.528063152 1 1 1 1 0
#> 86 0.677445564 1 1 1 1 0
#> 87 -0.109778764 1 0 1 0 0
#> 88 0.397106369 1 1 0 1 0
#> 89 0.041568034 1 0 0 1 1
#> 90 -0.102783661 0 1 0 1 1
#> 91 0.215353291 0 0 1 1 0
#> 92 -0.139109751 0 0 0 1 0
#> 93 0.075468378 1 0 1 1 0
#> 94 0.749387268 1 1 0 1 0
#> 95 -0.263918561 0 0 1 0 1
#> 96 0.304536926 1 0 0 1 0
#> 97 0.524325007 1 1 0 1 0
#> 98 0.294376356 1 1 0 1 0
#> 99 -0.625542875 0 0 1 0 0
#> 100 0.154216232 0 0 1 0 1
#> 101 -0.459311288 0 1 0 1 1
#> 102 -0.707305530 1 1 1 0 0
#> 103 0.605729758 0 0 1 0 1
#> 104 0.403280400 0 1 0 0 0
#> 105 -0.174587977 0 1 1 1 0
#> 106 -0.791154047 0 1 1 0 0
#> 107 0.055850735 0 1 1 1 1
#> 108 0.457637433 0 1 1 0 1
#> 109 -0.583514471 1 0 0 1 0
#> 110 -0.206441167 0 0 0 1 0
#> 111 1.139266569 1 1 0 0 1
#> 112 1.244348667 1 1 0 0 0
#> 113 -0.090969869 0 1 1 1 0
#> 114 -0.227222012 1 0 0 1 0
#> 115 -0.381972955 1 0 0 1 1
#> 116 0.412649206 1 0 0 0 1
#> 117 0.172336439 1 0 1 0 0
#> 118 0.643561153 0 0 1 1 1
#> 119 0.407833256 0 0 0 0 0
#> 120 -0.189808725 0 1 1 1 1
#>
#> $housekeeping
#> n mu_i theta_i
#> 1 62 0.0 -0.195914572
#> 2 50 0.0 0.117754379
#> 3 60 0.5 0.504442832
#> 4 64 0.5 0.334986895
#> 5 50 0.5 0.635909615
#> 6 44 0.0 -0.166799419
#> 7 34 0.5 0.348473153
#> 8 54 0.0 0.263732698
#> 9 28 0.0 -0.015865433
#> 10 40 0.0 -0.145624750
#> 11 38 0.5 0.653275533
#> 12 50 0.0 -0.065551359
#> 13 44 0.0 -0.101508381
#> 14 34 0.0 0.178484836
#> 15 42 0.0 0.016898242
#> 16 42 0.0 -0.037448007
#> 17 18 0.0 0.063490797
#> 18 44 0.0 0.028640294
#> 19 56 0.5 0.583168654
#> 20 52 0.5 0.708355141
#> 21 14 0.0 0.112886227
#> 22 28 0.0 -0.052430244
#> 23 50 0.0 -0.177821497
#> 24 40 0.0 0.301221132
#> 25 16 0.0 -0.031030426
#> 26 22 0.5 0.374363232
#> 27 44 0.5 0.592962634
#> 28 46 0.0 0.235904218
#> 29 26 0.0 0.119646973
#> 30 44 0.0 0.132285001
#> 31 52 0.5 0.592947727
#> 32 48 0.5 0.639643034
#> 33 30 0.5 0.213354069
#> 34 40 0.5 0.766491423
#> 35 44 0.0 -0.118927588
#> 36 22 0.5 0.505247036
#> 37 60 0.0 0.107720332
#> 38 42 0.0 -0.264762986
#> 39 28 0.0 0.090561793
#> 40 46 0.0 0.129762741
#> 41 30 0.0 -0.058243852
#> 42 48 0.0 0.050742996
#> 43 60 0.0 -0.002325187
#> 44 40 0.0 0.027255662
#> 45 34 0.0 -0.090533400
#> 46 74 0.0 0.139379741
#> 47 46 0.0 -0.084093802
#> 48 44 0.0 -0.098884221
#> 49 54 0.5 0.485284650
#> 50 24 0.5 0.288016313
#> 51 52 0.0 0.061619277
#> 52 24 0.0 -0.086395939
#> 53 48 0.5 0.537067726
#> 54 26 0.0 -0.369489297
#> 55 62 0.0 -0.025679440
#> 56 62 0.5 0.517027953
#> 57 28 0.0 -0.128003046
#> 58 52 0.0 0.165316992
#> 59 44 0.0 0.088843384
#> 60 50 0.0 -0.081190727
#> 61 38 0.0 0.030984774
#> 62 66 0.0 0.172610146
#> 63 30 0.5 0.374923318
#> 64 34 0.0 0.023183774
#> 65 28 0.0 -0.095491210
#> 66 36 0.0 -0.047627377
#> 67 42 0.0 -0.070378435
#> 68 34 0.0 0.199668073
#> 69 22 0.5 0.310584248
#> 70 14 0.0 -0.179261501
#> 71 50 0.0 -0.200384649
#> 72 80 0.0 -0.130594376
#> 73 56 0.0 0.018470968
#> 74 46 0.0 -0.008432395
#> 75 36 0.0 0.263752308
#> 76 44 0.0 0.203247060
#> 77 50 0.0 0.128966290
#> 78 52 0.5 0.566950146
#> 79 20 0.0 -0.041844479
#> 80 44 0.0 0.157175036
#> 81 32 0.0 0.088085262
#> 82 28 0.0 -0.187514419
#> 83 28 0.0 -0.044539113
#> 84 14 0.0 -0.170822472
#> 85 26 0.5 0.125015758
#> 86 26 0.5 0.658994613
#> 87 24 0.0 -0.274062994
#> 88 32 0.5 0.849156412
#> 89 32 0.0 -0.124885419
#> 90 60 0.0 -0.122154816
#> 91 56 0.0 0.449999010
#> 92 50 0.0 0.227325783
#> 93 60 0.0 -0.062310670
#> 94 64 0.5 0.566832273
#> 95 34 0.0 -0.047588972
#> 96 48 0.0 -0.307326853
#> 97 42 0.5 0.524976277
#> 98 36 0.5 0.514501304
#> 99 28 0.0 -0.089717080
#> 100 34 0.0 -0.022378912
#> 101 36 0.0 -0.284214283
#> 102 30 0.5 0.093212443
#> 103 26 0.0 0.299978974
#> 104 38 0.0 0.255503634
#> 105 20 0.0 -0.348699761
#> 106 36 0.0 -0.114085754
#> 107 34 0.0 0.015713373
#> 108 54 0.0 0.213715345
#> 109 38 0.0 -0.131536879
#> 110 54 0.0 -0.045867605
#> 111 46 0.5 0.903520519
#> 112 40 0.5 0.781926271
#> 113 36 0.0 -0.401014680
#> 114 36 0.0 0.133779366
#> 115 64 0.0 -0.275685450
#> 116 50 0.0 0.311662217
#> 117 34 0.0 0.227026447
#> 118 52 0.0 0.126597864
#> 119 34 0.0 0.280484974
#> 120 30 0.0 -0.170053996
#>
#> $tau2_est
#> [1] 0.07936629
#>