Run Gibbs sampler for the random moderator placement design
Usage
prepost_gibbs(
formula,
data,
prepost,
moderator,
covariates,
iter = 1000,
thin = 1,
burn = 0,
offset = 0,
monotonicity = TRUE,
stable = TRUE,
saturated = TRUE,
priors
)Arguments
- formula
A formula with syntax
y ~ t, whereyis the (unquoted) name of the outcome andtis the (unquoted) name of the treatment.- data
A data.frame containing variables in the formula, moderator, and covariates arguments.
- prepost
A one-sided formula with syntax
~ z, wherezis the indicator variable for whether the moderator was measured pre- or post-treatment.- moderator
A one-sided formuala with syntax
~ d, wheredis the (unquoted) name of the moderator variable for the CATE.- covariates
A one-sided formula with syntax
~ x1 + x2, where the right-hand side variables signify which covariates the Gibbs will use to try and narrow the bounds.- iter
Integer indicating the number of iterations for the Gibbs sampler.
- thin
Integer indicating how often the Gibbs sampler should save a draw.
- burn
Integer indicating how many iterations should be performed before saving draws in the Gibbs sampler.
- offset
A numeric value indicating the center of the prior distribution for the covariate coefficients.
- monotonicity
A logical signifying whether the model assumes monotonicity.
- stable
A logical signifying whether the model assumes that the the pre vs post indicator does not affect the moderator under the control condition for treatment.
- saturated
A logical indicating whether the coefficients on the covariates are allowed to vary by the principal strata.
- priors
A list object containing the priors for the Gibbs sampler. Priors include beta.precision, psi.precision, alpha, y.alpha, and y.beta.
Examples
data(land_experiment)
prepost_gibbs(
support ~ treat_comb,
data = land_experiment,
moderator = ~ land_insecure,
prepost = ~ prepost,
covariates = ~ educ + age,
iter = 50
)
#> $betas
#> (Intercept) educ age treat_comb prepost
#> [1,] 5.360947 0.7496439 0.199111833 -0.880491615 -3.04026633
#> [2,] 6.714527 -0.8714747 0.015179307 1.895980741 1.17678890
#> [3,] 3.603818 -1.2197017 -0.037954492 -0.727038254 -1.49949742
#> [4,] 4.329912 -1.0216453 -0.043535796 -1.383183150 -2.12506999
#> [5,] 4.661942 -0.7874893 -0.018695431 -2.703682322 -1.59698100
#> [6,] 2.888665 -0.7753985 0.002136428 -1.139469597 0.23131052
#> [7,] 3.456364 -0.6561641 0.001429577 -0.154246841 -1.04199287
#> [8,] 3.439634 -0.4932303 -0.002740113 0.233083104 -1.09324380
#> [9,] 3.852158 -0.5729627 -0.013327202 1.014437446 -0.30406544
#> [10,] 2.608060 -0.3221372 -0.001654098 0.460988550 0.18890387
#> [11,] 3.531512 -0.4102868 -0.014713613 0.353572355 -0.08642819
#> [12,] 4.183591 -0.3549070 -0.036776005 0.524247351 0.38503920
#> [13,] 3.906570 -0.4870842 -0.021512545 0.953922691 0.18520519
#> [14,] 4.486802 -0.4918302 -0.015890503 0.228722024 -0.36309049
#> [15,] 3.918320 -0.3446895 -0.019037139 0.098968121 -0.05121159
#> [16,] 2.237825 -0.1846009 -0.016602714 1.007077130 1.08243165
#> [17,] 2.992241 -0.1760367 -0.018924983 0.179090823 0.46482387
#> [18,] 3.886705 -0.3650398 -0.017437826 0.489927203 0.03373340
#> [19,] 4.195434 -0.4776127 -0.005108270 0.709705666 -0.42909845
#> [20,] 3.807008 -0.4658234 -0.004802488 1.053860439 -0.29129125
#> [21,] 3.857503 -0.2863276 -0.014720723 0.498700942 0.10533767
#> [22,] 4.948322 -0.5115256 -0.018862937 0.377871138 -0.05084449
#> [23,] 4.310637 -0.4744525 -0.018021618 0.716041936 0.57531299
#> [24,] 4.866601 -0.3869392 -0.035247121 0.033869985 -0.02119845
#> [25,] 5.229875 -0.4509056 -0.037299195 -0.194935150 -0.03658707
#> [26,] 4.991199 -0.5222834 -0.034247806 0.646719002 0.69101428
#> [27,] 2.967274 -0.4404479 -0.008563264 1.453252193 1.19846629
#> [28,] 2.445298 -0.2740878 -0.002319318 0.997870513 0.27379740
#> [29,] 3.260362 -0.3928394 -0.003472819 0.602114066 0.18101252
#> [30,] 3.912892 -0.3519501 -0.017222998 0.163619125 -0.44926131
#> [31,] 4.153306 -0.3229375 -0.023142783 -0.343951559 0.17714056
#> [32,] 4.180858 -0.4255618 -0.026774770 0.342679002 0.10997527
#> [33,] 3.564354 -0.3502674 -0.020395209 0.265361940 0.08314498
#> [34,] 4.376807 -0.4180846 -0.030489212 0.781994739 -0.16815800
#> [35,] 3.722347 -0.2772692 -0.006631316 -0.382254406 -0.75787283
#> [36,] 4.076711 -0.3841140 -0.017984278 -0.357254609 -0.47179245
#> [37,] 3.886690 -0.2696448 -0.009747825 -0.872833059 -1.01196561
#> [38,] 4.258991 -0.3246719 -0.031963127 -0.108704469 -0.27600809
#> [39,] 4.479448 -0.4191827 -0.028199230 0.076520091 -0.03522273
#> [40,] 4.582739 -0.3058748 -0.018975827 -0.514655439 -0.72725236
#> [41,] 3.923768 -0.2908268 -0.018348379 0.008104617 -0.59757639
#> [42,] 4.327726 -0.2845248 -0.018465207 -0.676603906 -0.95411346
#> [43,] 3.166889 -0.2064517 0.009343143 -0.117050488 -0.91000514
#> [44,] 4.105548 -0.2702820 -0.019812702 -0.274852030 -0.97558549
#> [45,] 4.355335 -0.3636126 -0.015863134 -0.154373866 -0.47663151
#> [46,] 4.809209 -0.4697346 -0.025356329 0.256147203 0.11176420
#> [47,] 4.847277 -0.4140777 -0.027827286 -0.164341310 -0.63880817
#> [48,] 5.267361 -0.4335057 -0.031873993 -0.170242763 -0.45402553
#> [49,] 5.198040 -0.4598486 -0.034333084 -0.359589837 -0.51636658
#> [50,] 3.865670 -0.2663263 -0.012473444 -0.240341564 -0.67307356
#> treat_comb:prepost s111 s100 treat_comb:s111 treat_comb:s100
#> [1,] 7.167873237 -8.4724579 7.3099974 4.71032137 4.2063118
#> [2,] 4.029491973 -3.9021044 12.0297851 2.57401695 1.4954315
#> [3,] 10.668701448 2.5581941 19.1999546 2.36590676 2.2534755
#> [4,] 8.856810558 0.8889463 16.1762592 2.16987305 3.6970858
#> [5,] 6.313822895 -1.8729291 15.8371347 4.40775230 4.2172097
#> [6,] 3.230513517 -0.3689113 14.9849090 1.89791018 5.3908529
#> [7,] 1.693774274 -2.3657336 11.4715557 2.75487378 4.6593446
#> [8,] 1.261210527 -0.8716101 8.5882015 0.33745337 5.3235180
#> [9,] -0.392926248 -1.4075869 9.9349022 0.83235352 3.1407092
#> [10,] -0.010414596 -3.7022213 8.4823429 4.14186042 3.9326271
#> [11,] 0.362174191 -0.8563141 7.6428295 -1.04613953 3.6469506
#> [12,] -0.823580153 -2.4689234 6.8688173 1.34565931 2.9706067
#> [13,] -0.730495476 -0.4300353 8.4129075 -0.28471535 0.9595057
#> [14,] -0.780487263 -1.7290088 6.0641847 1.38792676 2.4145619
#> [15,] -0.590861558 -2.2660108 3.5453154 1.89839087 4.3240185
#> [16,] -1.559294780 -1.2691653 6.0964465 0.81677580 3.0968318
#> [17,] -0.922941541 -2.4874703 6.4088780 1.86248867 1.9783284
#> [18,] -0.876519357 -1.8312803 7.1877352 0.17392555 -0.6739680
#> [19,] -0.717099204 -1.9092122 5.7557637 0.20428391 -1.5794005
#> [20,] -1.109849556 -1.2161418 3.8172080 -0.62949693 1.0847547
#> [21,] -1.507705888 -1.4116722 6.8174744 -0.64881415 -2.2324662
#> [22,] -0.672980637 -2.1845786 1.8721733 -0.02676394 2.4531559
#> [23,] -1.906720183 -1.7154823 3.0315244 -0.87681170 -0.9360357
#> [24,] -1.028372285 -4.1460860 2.5476552 4.37575398 2.0760578
#> [25,] -0.400761114 -3.3573554 1.4318431 2.09933751 3.8364817
#> [26,] -1.083258674 -2.7706163 2.5887199 1.25893498 1.3227017
#> [27,] -1.590882362 -1.1730419 2.9254009 -1.67893505 1.7195773
#> [28,] -1.068659750 -0.3206608 1.9737958 -1.49993018 3.0907766
#> [29,] -0.796110069 -1.9729831 1.9586502 0.71916621 1.9122387
#> [30,] -0.470997536 -1.0141708 4.0477372 -0.06718887 1.4342257
#> [31,] -0.578170457 -2.6801781 3.0130879 0.98184860 2.8297680
#> [32,] -0.424862775 -1.4744869 4.5253842 1.33988513 2.3099822
#> [33,] 0.012410287 -0.3970104 4.1569299 -0.36743325 2.3517212
#> [34,] -0.823415423 -1.5409556 3.2307775 -0.14538325 0.7907857
#> [35,] 0.176022078 -1.4126312 3.3593832 1.16402650 -0.1018005
#> [36,] -0.009652835 -2.3437229 1.3694301 2.61645770 1.6019303
#> [37,] 0.631833541 -2.3054986 0.2426254 2.42936854 2.9611904
#> [38,] -0.492181515 -1.3090243 0.2649634 0.63690252 2.7011017
#> [39,] -0.362760156 -2.7952177 0.8298639 1.54788155 3.0841085
#> [40,] -0.029289480 -3.1250368 1.4917796 1.61472830 1.2254280
#> [41,] -0.450159171 -2.5703002 0.1970804 2.41334401 3.5115585
#> [42,] 0.092390935 -1.5316279 -1.9023171 0.34556802 5.9496794
#> [43,] -0.605576459 -2.8749448 -0.4777297 0.84327700 2.0060643
#> [44,] 0.397987836 -2.4234397 -2.2792875 1.49169913 3.7091463
#> [45,] -0.305131115 -0.6449853 -3.7542911 -0.54116584 4.7656308
#> [46,] -0.982566733 -0.4885519 -3.0534556 0.31189270 3.0232693
#> [47,] -0.204880922 -1.3471927 -2.2183581 2.62954265 2.6352843
#> [48,] -0.470675859 -4.3986593 -1.5467762 5.00691300 3.1853404
#> [49,] -0.020463119 -2.9418250 -1.9871704 1.63062768 3.4413358
#> [50,] -0.246128494 -1.7638947 -1.9615075 -0.50080409 0.7416147
#> prepost:s111 prepost:s100 treat_comb:prepost:s111 treat_comb:prepost:s100
#> [1,] -4.54077343 -0.563594400 10.90837981 0.94059415
#> [2,] 1.09582061 -5.235717264 1.59381386 2.68404394
#> [3,] 2.76045840 -6.136286438 1.94354248 -0.98263472
#> [4,] 1.13586540 -3.497740189 1.29746961 -0.90128627
#> [5,] 3.28212656 -6.614979174 -4.49654208 1.18617108
#> [6,] 1.17627462 -5.999071937 4.13109611 2.17730199
#> [7,] 0.38179395 -2.584663456 0.45815288 -1.24587243
#> [8,] 1.90886505 -0.389360460 -2.08720490 0.29404154
#> [9,] -1.09277618 -3.602593375 -1.66190071 -0.01616376
#> [10,] 2.12269859 -2.225772783 -4.22661117 -1.18661525
#> [11,] 2.10968970 1.713467287 1.51210310 -3.14500094
#> [12,] 1.72524130 1.803831882 -0.64289765 -1.29253809
#> [13,] 1.26534865 -2.222498633 -2.48563442 0.80503581
#> [14,] 1.11536985 0.507079570 -2.74407497 -2.71035746
#> [15,] 1.58218017 1.783326671 0.03537488 -5.27891244
#> [16,] -0.29282561 -2.424438760 5.43894976 -2.32047319
#> [17,] -0.13527509 -2.677134835 4.23855683 -1.84588453
#> [18,] 0.72811587 -5.761531845 -4.81320792 3.07118648
#> [19,] 0.92210692 -1.814272112 2.02912123 0.51565262
#> [20,] 0.65573768 -0.006698406 -0.82339095 -1.58114497
#> [21,] 0.29181293 -4.553275055 3.59446270 3.22822282
#> [22,] -0.36897274 -0.481118395 -0.11743942 -2.21911850
#> [23,] 1.97120346 -1.878994309 1.78490185 2.25804107
#> [24,] 2.55221825 0.541880983 0.31569062 -4.29678890
#> [25,] 1.42151206 -0.038732955 1.72433265 -4.93671940
#> [26,] 0.75804249 -1.389223712 4.79253783 -1.87215846
#> [27,] -0.80747143 -1.209124323 5.37985714 -2.37819910
#> [28,] -1.48790938 -0.758462546 5.64552412 -3.96541195
#> [29,] 0.64845471 -1.668098809 3.02193609 0.04952381
#> [30,] 1.55667584 -3.877053912 3.25113841 -0.40959352
#> [31,] 1.56953904 -1.228707555 -1.55329280 -2.17289906
#> [32,] 0.83901862 -4.973859392 -2.95428194 -1.59602143
#> [33,] 0.45729870 -4.448164551 1.85197270 -2.50280452
#> [34,] 1.26075753 -0.563142816 -0.11157724 -3.78080925
#> [35,] -0.12957266 0.192629836 0.01428784 -2.10945754
#> [36,] -0.40354418 1.620395266 -2.96511206 -2.41202361
#> [37,] 1.25657557 1.840117638 -2.81011007 -2.92981993
#> [38,] -0.01411209 0.997123965 1.11116463 -0.64134832
#> [39,] 1.01835690 5.418637336 0.04365759 -6.43133424
#> [40,] 2.59906610 -1.109268329 -0.64973127 0.97619253
#> [41,] 0.55687070 -1.521341548 -0.43789462 1.81990202
#> [42,] 1.06674736 1.119264843 0.99525121 -0.57238991
#> [43,] 2.60766639 -0.632710839 1.99614151 3.80086499
#> [44,] 1.30853688 1.053793599 -0.29989813 -0.37136612
#> [45,] 0.93629045 0.401264268 0.58702787 2.38866394
#> [46,] -0.84881895 0.909794139 4.94044310 2.99613180
#> [47,] 1.00372283 5.707885174 4.25242117 -2.62099627
#> [48,] 2.46967016 4.213904820 0.06982383 -2.81513942
#> [49,] 1.52279855 4.346143980 1.64401889 -2.89110794
#> [50,] -0.41594699 3.298315709 2.43127897 0.18780024
#>
#> $psis
#> $psis$s111
#> (Intercept) educ age
#> [1,] -4.930791 -1.775707e+01 -1.709647575
#> [2,] -16.937355 -1.463235e+01 -1.187990176
#> [3,] -20.605408 -1.290646e+01 -0.839898196
#> [4,] -16.641018 -1.223794e+01 -0.729981238
#> [5,] -17.573579 -1.128451e+01 -0.502147725
#> [6,] -19.566128 -9.805020e+00 -0.347622719
#> [7,] -16.740244 -9.111698e+00 -0.232280550
#> [8,] -21.567732 -7.368487e+00 -0.103687328
#> [9,] -24.487560 -5.944618e+00 0.009977187
#> [10,] -19.599389 -5.692360e+00 -0.033676939
#> [11,] -17.917162 -5.156318e+00 -0.022704015
#> [12,] -18.480911 -4.407352e+00 0.028379108
#> [13,] -16.271399 -3.867590e+00 0.046367207
#> [14,] -12.097064 -4.134123e+00 0.042253258
#> [15,] -15.348618 -2.969216e+00 0.084148925
#> [16,] -15.344483 -2.316298e+00 0.089851474
#> [17,] -14.932350 -1.954656e+00 0.116813957
#> [18,] -14.554829 -1.662970e+00 0.151799278
#> [19,] -16.385666 -1.061163e+00 0.173240388
#> [20,] -19.959739 -2.252623e-01 0.230500610
#> [21,] -17.152863 -2.679732e-01 0.197239675
#> [22,] -13.559912 -4.352659e-01 0.158150852
#> [23,] -12.391973 -5.317492e-01 0.154562184
#> [24,] -11.567622 -4.847561e-01 0.147905690
#> [25,] -9.758542 -7.576124e-01 0.158385371
#> [26,] -8.470929 -6.777807e-01 0.138451902
#> [27,] -8.115154 -2.871098e-01 0.108339321
#> [28,] -7.328825 -3.066888e-01 0.106439057
#> [29,] -6.019044 -1.641870e-01 0.069736447
#> [30,] -5.049540 -1.989936e-01 0.057582078
#> [31,] -5.743910 4.732739e-02 0.057379012
#> [32,] -4.997933 -4.659854e-02 0.049728632
#> [33,] -4.393671 -4.371625e-02 0.039913397
#> [34,] -5.365844 5.033166e-02 0.051925231
#> [35,] -5.355648 -6.184357e-02 0.066727192
#> [36,] -5.150964 -2.104963e-02 0.050871609
#> [37,] -4.113169 5.117100e-03 0.024399033
#> [38,] -4.813761 4.085078e-02 0.049487018
#> [39,] -3.134781 -1.580112e-01 0.032401903
#> [40,] -2.650138 -1.881319e-01 0.025114682
#> [41,] -3.053820 -7.908971e-02 0.028487758
#> [42,] -2.589771 -9.155068e-02 0.012807073
#> [43,] -3.068741 -5.191935e-02 0.017071395
#> [44,] -2.905475 -6.193064e-03 0.014054048
#> [45,] -3.211287 8.334605e-04 0.015787931
#> [46,] -3.520862 1.356842e-01 0.020771510
#> [47,] -3.985732 1.511815e-01 0.030019961
#> [48,] -3.176961 6.309308e-02 0.009135593
#> [49,] -3.540515 1.487967e-01 0.002990984
#> [50,] -4.492773 1.974119e-01 0.034227492
#>
#> $psis$s100
#> (Intercept) educ age
#> [1,] 3.50931677 0.334565784 0.761926059
#> [2,] 2.28531281 0.515095226 0.161010976
#> [3,] 2.53139460 -0.063519048 -0.012791798
#> [4,] 1.28832459 -0.136864539 -0.011932868
#> [5,] 0.40083153 -0.022005800 -0.005580178
#> [6,] 0.64700870 -0.032312268 -0.022562714
#> [7,] -0.28648066 0.153470580 -0.017240829
#> [8,] -0.02827326 0.100068560 -0.029486047
#> [9,] -0.86617700 0.082734685 -0.014042959
#> [10,] -1.68585845 0.159867744 -0.008476409
#> [11,] -0.62359593 -0.070238113 -0.013688965
#> [12,] -1.47538251 -0.077366820 0.004998075
#> [13,] -1.00382127 -0.028537641 -0.011698018
#> [14,] -0.35510050 -0.082526509 -0.027826072
#> [15,] -0.21678030 -0.128277826 -0.028663070
#> [16,] -1.40896755 -0.002360689 -0.009622891
#> [17,] -0.59687647 -0.040091973 -0.028829438
#> [18,] -1.19567854 0.006900232 -0.020305978
#> [19,] 0.11301983 -0.239224494 -0.036518699
#> [20,] 0.70721775 -0.313096967 -0.052262068
#> [21,] 0.33006323 -0.381604820 -0.034898672
#> [22,] -0.04773094 -0.290717461 -0.036761981
#> [23,] -0.69248299 -0.261039426 -0.019910462
#> [24,] -0.07296766 -0.257178817 -0.040455484
#> [25,] -0.14157324 -0.183151857 -0.037157163
#> [26,] -0.86868253 -0.102797810 -0.019650437
#> [27,] -0.35368342 -0.110357357 -0.037775382
#> [28,] -0.18400075 -0.093266326 -0.046006746
#> [29,] 0.45593787 -0.141040453 -0.061196700
#> [30,] 0.15105230 -0.166931924 -0.050091475
#> [31,] 0.16518530 -0.242418861 -0.039776081
#> [32,] -0.61787018 -0.125817217 -0.028072443
#> [33,] 0.16242252 -0.302347456 -0.033876447
#> [34,] 0.18881026 -0.301491932 -0.038044094
#> [35,] 0.21991823 -0.210381028 -0.050205286
#> [36,] -1.13519491 0.029154617 -0.039963558
#> [37,] -1.06273340 0.107211858 -0.045158119
#> [38,] -1.25749311 0.028337402 -0.041999193
#> [39,] -1.51190638 0.002016648 -0.033316851
#> [40,] -1.51382233 -0.078979944 -0.031928841
#> [41,] -1.06637602 -0.132949508 -0.031848531
#> [42,] -0.67743132 -0.157455167 -0.044817995
#> [43,] -1.08077187 -0.134173404 -0.028863634
#> [44,] -2.00677838 -0.110081698 -0.004091785
#> [45,] -0.75051503 -0.229039489 -0.024138728
#> [46,] -1.19173718 -0.101140339 -0.032245003
#> [47,] -0.95093197 -0.037690282 -0.047994238
#> [48,] -0.15548767 0.001540447 -0.073736653
#> [49,] 0.43575002 -0.073300752 -0.082652175
#> [50,] 0.56381759 -0.014684008 -0.079868644
#>
#> $psis$s000
#> (Intercept) educ age
#> [1,] 0 0 0
#> [2,] 0 0 0
#> [3,] 0 0 0
#> [4,] 0 0 0
#> [5,] 0 0 0
#> [6,] 0 0 0
#> [7,] 0 0 0
#> [8,] 0 0 0
#> [9,] 0 0 0
#> [10,] 0 0 0
#> [11,] 0 0 0
#> [12,] 0 0 0
#> [13,] 0 0 0
#> [14,] 0 0 0
#> [15,] 0 0 0
#> [16,] 0 0 0
#> [17,] 0 0 0
#> [18,] 0 0 0
#> [19,] 0 0 0
#> [20,] 0 0 0
#> [21,] 0 0 0
#> [22,] 0 0 0
#> [23,] 0 0 0
#> [24,] 0 0 0
#> [25,] 0 0 0
#> [26,] 0 0 0
#> [27,] 0 0 0
#> [28,] 0 0 0
#> [29,] 0 0 0
#> [30,] 0 0 0
#> [31,] 0 0 0
#> [32,] 0 0 0
#> [33,] 0 0 0
#> [34,] 0 0 0
#> [35,] 0 0 0
#> [36,] 0 0 0
#> [37,] 0 0 0
#> [38,] 0 0 0
#> [39,] 0 0 0
#> [40,] 0 0 0
#> [41,] 0 0 0
#> [42,] 0 0 0
#> [43,] 0 0 0
#> [44,] 0 0 0
#> [45,] 0 0 0
#> [46,] 0 0 0
#> [47,] 0 0 0
#> [48,] 0 0 0
#> [49,] 0 0 0
#> [50,] 0 0 0
#>
#>
#> $s.tab
#> s111 s100 s000
#> [1,] 0.09333333 0.61333333 0.2933333
#> [2,] 0.05333333 0.65333333 0.2933333
#> [3,] 0.05333333 0.59466667 0.3520000
#> [4,] 0.05333333 0.56800000 0.3786667
#> [5,] 0.05333333 0.51733333 0.4293333
#> [6,] 0.05333333 0.47466667 0.4720000
#> [7,] 0.05333333 0.42400000 0.5226667
#> [8,] 0.05333333 0.32800000 0.6186667
#> [9,] 0.05333333 0.26666667 0.6800000
#> [10,] 0.05333333 0.19466667 0.7520000
#> [11,] 0.05333333 0.18133333 0.7653333
#> [12,] 0.05333333 0.16000000 0.7866667
#> [13,] 0.05333333 0.14933333 0.7973333
#> [14,] 0.05333333 0.16533333 0.7813333
#> [15,] 0.05333333 0.16000000 0.7866667
#> [16,] 0.05333333 0.14933333 0.7973333
#> [17,] 0.05333333 0.13066667 0.8160000
#> [18,] 0.05333333 0.12533333 0.8213333
#> [19,] 0.05333333 0.11733333 0.8293333
#> [20,] 0.05333333 0.10133333 0.8453333
#> [21,] 0.05333333 0.10666667 0.8400000
#> [22,] 0.05600000 0.10133333 0.8426667
#> [23,] 0.05600000 0.10133333 0.8426667
#> [24,] 0.05333333 0.10400000 0.8426667
#> [25,] 0.05600000 0.11733333 0.8266667
#> [26,] 0.05600000 0.11466667 0.8293333
#> [27,] 0.05600000 0.12533333 0.8186667
#> [28,] 0.06133333 0.12266667 0.8160000
#> [29,] 0.05600000 0.09066667 0.8533333
#> [30,] 0.05333333 0.11466667 0.8320000
#> [31,] 0.05866667 0.11466667 0.8266667
#> [32,] 0.05333333 0.11733333 0.8293333
#> [33,] 0.06133333 0.08800000 0.8506667
#> [34,] 0.06133333 0.10133333 0.8373333
#> [35,] 0.06666667 0.10133333 0.8320000
#> [36,] 0.06133333 0.07733333 0.8613333
#> [37,] 0.05866667 0.11733333 0.8240000
#> [38,] 0.05866667 0.12000000 0.8213333
#> [39,] 0.06933333 0.08000000 0.8506667
#> [40,] 0.07466667 0.05333333 0.8720000
#> [41,] 0.08000000 0.04000000 0.8800000
#> [42,] 0.06666667 0.06666667 0.8666667
#> [43,] 0.06666667 0.07200000 0.8613333
#> [44,] 0.07200000 0.06400000 0.8640000
#> [45,] 0.08000000 0.04800000 0.8720000
#> [46,] 0.06933333 0.05600000 0.8746667
#> [47,] 0.07466667 0.04266667 0.8826667
#> [48,] 0.06666667 0.08000000 0.8533333
#> [49,] 0.06666667 0.09333333 0.8400000
#> [50,] 0.06666667 0.08533333 0.8480000
#>
#> $delta.1
#> [1] 0.698319328 0.233802817 0.154225352 0.251408451 0.328169014
#> [6] 0.420422535 0.373239437 0.004225352 -0.190140845 0.127464789
#> [11] 0.071830986 0.186619718 -0.269718310 -0.240845070 0.231690141
#> [16] 0.411971831 0.818309859 -0.654929577 0.244366197 -0.316197183
#> [21] 0.331690141 0.045197740 0.225181598 0.595774648 0.350686037
#> [26] 0.594430993 0.400726392 0.613512846 0.515738499 0.270422535
#> [31] 0.005408190 -0.283098592 0.125617589 -0.003705534 0.268571429
#> [36] -0.107707510 0.050991501 0.389132114 0.215230328 0.067414574
#> [41] 0.466666667 0.000000000 0.251428571 0.222222222 0.101449275
#> [46] 0.575710822 0.289213668 0.742857143 0.437142857 0.314285714
#>
#> $delta.2
#> [1] 0.66419619 0.19118488 0.32349365 0.58479436 0.11465438 0.19484369
#> [7] 0.59464668 -0.18763856 -0.09396083 0.04072558 -0.01761476 0.09543704
#> [13] -0.47207433 -0.32096438 0.23515557 0.44902715 0.69550700 -0.61109934
#> [19] 0.29156778 -0.31093893 0.31254138 -0.05960177 0.11975199 0.50636976
#> [25] 0.49102045 0.45251868 0.46022338 0.56250019 0.39795722 0.16104217
#> [31] -0.21833151 -0.35782657 0.10862501 -0.02622874 0.24599800 -0.04088311
#> [37] -0.11031763 0.30612624 0.29735842 0.11921913 0.38739048 0.18338280
#> [43] 0.25457316 0.20821511 -0.04280595 0.36874537 0.29757897 0.55073578
#> [49] 0.43879792 0.39496059
#>