26 min read

Fitting the distributions

I’ve written the code to automatically fit all the untruncated distributions. Here it is, in helpers.R:

fit_dispersal_untruncated 
function(dispersal_data, zero = 7,
                                      model_list = c("hnorm", "exp", "lnorm", "gamma",
                                                     "weibull", "invgauss", "logis",
                                                     "invgamma")) {
# Fit untruncated dispersal models to data
# dispersal_data must be a data frame containing columns
#   ID, Density, Siliques, Seedlings, Distance
# All data in dispersal_data are used in a single fit, so if only a single rep is to 
#   be analyzed, it should be subset outside this function

  if ("invgauss" %in% model_list) library(actuar)
  if ("gengamma" %in% model_list) library(flexsurv)

  cens_data_tble <- cens_dispersal_data(dispersal_data, zero)
  
  result <- data.frame(ID = factor(), 
                       model = factor(), 
                       AIC = double(),
                       par1 = double(),
                       par2 = double(),
                       par3 = double(),
                       se1 = double(),
                       se2 = double(),
                       se3 = double())
  
  for (model in model_list) {
    fit_i <- try(fitdistcens(cens_data_tble, model, 
                             start = start_params(cens_data_tble, model)))
    if (class(fit_i) != "try-error") {
      par_i <- rep(NA, 3)
      se_i <- rep(NA, 3)
      n_par <- length(fit_i$est)
      par_i[1:n_par] <- fit_i$est
      se_i[1:n_par] <- fit_i$sd
      
      result <- rbind(result,
                      data.frame(ID = dispersal_data$ID[1],
                                 model = model,
                                 AIC = fit_i$aic,
                                 par1 = par_i[1], par2 = par_i[2], par3 = par_i[3],
                                 se1 = se_i[1], se2 = se_i[2], se3 = se_i[3]))
    }
  }
  
  result
}

And here are the results of fitting it to our test dataset:

temp <- filter(disperseLer, ID == "73_0")
fit_dispersal_untruncated(temp) 
    ID    model      AIC     par1      par2 par3        se1        se2 se3
1 73_0    hnorm 1530.806 5.267032        NA   NA 0.20882253         NA  NA
2 73_0      exp 1563.703 0.237446        NA   NA 0.01330460         NA  NA
3 73_0    lnorm 1555.858 1.135456 0.8428757   NA 0.04807217 0.03696496  NA
4 73_0    gamma 1533.055 1.630594 0.3855333   NA 0.13143278 0.03515710  NA
5 73_0  weibull 1530.989 1.342346 4.6042573   NA 0.06248417 0.20405702  NA
6 73_0 invgauss 1559.186 4.241039 4.6609548   NA 0.22664962 0.41547646  NA
7 73_0    logis 1647.386 3.890933 1.7743866   NA 0.17518410 0.08275183  NA
8 73_0 invgamma 1600.887 1.660444 3.7678829   NA 0.13029647 0.36331315  NA

When I first ran it, I had set the “zero” to 0, and I got an error for gengamma. So this distribution might not be too robust.

And now, fitting all the reps:

library(tidyverse)
result <- fiteach_disp_unt(disperseLer)
<simpleError in optim(par = vstart, fn = fnobjcens, fix.arg = fix.arg, gr = gradient,     rcens = rcens, lcens = lcens, icens = icens, ncens = ncens,     ddistnam = ddistname, pdistnam = pdistname, hessian = TRUE,     method = meth, lower = lower, upper = upper, ...): non-finite finite-difference value [1]>
Error in fitdistcens(cens_data_tble, model, start = start_params(cens_data_tble,  : 
  the function mle failed to estimate the parameters, 
        with the error code 100
Error in fitdist(cens_data_tble[, 2], model, start = start, ...) : 
  the function mle failed to estimate the parameters, 
                with the error code 1

<simpleError in optim(par = vstart, fn = fnobjcens, fix.arg = fix.arg, gr = gradient,     rcens = rcens, lcens = lcens, icens = icens, ncens = ncens,     ddistnam = ddistname, pdistnam = pdistname, hessian = TRUE,     method = meth, lower = lower, upper = upper, ...): non-finite finite-difference value [2]>
Error in fitdistcens(cens_data_tble, model, start = start, ...) : 
  the function mle failed to estimate the parameters, 
        with the error code 100
<simpleError in optim(par = vstart, fn = fnobjcens, fix.arg = fix.arg, gr = gradient,     rcens = rcens, lcens = lcens, icens = icens, ncens = ncens,     ddistnam = ddistname, pdistnam = pdistname, hessian = TRUE,     method = meth, lower = lower, upper = upper, ...): non-finite finite-difference value [2]>
Error in fitdistcens(cens_data_tble, model, start = start_params(cens_data_tble,  : 
  the function mle failed to estimate the parameters, 
        with the error code 100
Error in fitdist(cens_data_tble[, 2], model, start = start, ...) : 
  the function mle failed to estimate the parameters, 
                with the error code 1

<simpleError in optim(par = vstart, fn = fnobjcens, fix.arg = fix.arg, gr = gradient,     rcens = rcens, lcens = lcens, icens = icens, ncens = ncens,     ddistnam = ddistname, pdistnam = pdistname, hessian = TRUE,     method = meth, lower = lower, upper = upper, ...): non-finite finite-difference value [2]>
Error in fitdistcens(cens_data_tble, model, start = start, ...) : 
  the function mle failed to estimate the parameters, 
        with the error code 100
result
       ID    model        AIC       par1       par2       par3         se1
1    73_0    hnorm 1530.80560  5.2670324         NA         NA 0.208822528
2    73_0      exp 1563.70262  0.2374460         NA         NA 0.013304602
3    73_0    lnorm 1555.85827  1.1354557  0.8428757         NA 0.048072168
4    73_0    gamma 1533.05495  1.6305942  0.3855333         NA 0.131432776
5    73_0  weibull 1530.98858  1.3423463  4.6042573         NA 0.062484170
6    73_0 invgauss 1559.18562  4.2410389  4.6609548         NA 0.226649615
7    73_0    logis 1647.38554  3.8909332  1.7743866         NA 0.175184102
8    73_0 invgamma 1600.88662  1.6604441  3.7678829         NA 0.130296466
9    73_0 gengamma 1532.70991  1.5705188  0.7274812 1.11856834 0.092995355
10   75_0    hnorm 1266.46463  5.8823017         NA         NA 0.262129280
11   75_0      exp 1294.10823  0.2118871         NA         NA 0.013345864
12   75_0    lnorm 1273.67374  1.2716292  0.8046662         NA 0.051362719
13   75_0    gamma 1258.70264  1.7916327  0.3782812         NA 0.158980659
14   75_0  weibull 1259.63111  1.3924367  5.1963624         NA 0.070139456
15   75_0 invgauss 1278.53659  4.7459771  5.7039123         NA 0.272824232
16   75_0    logis 1339.58670  4.3347955  1.8746783         NA 0.205226093
17   75_0 invgamma 1311.98984  1.7428625  4.5892120         NA 0.152317546
18   75_0 gengamma 1260.62837  1.5754181  0.7398792 0.80032607 0.087770126
19   75_1    hnorm  713.51269  4.6564538         NA         NA 0.263788197
20   75_1      exp  736.33735  0.2629533         NA         NA 0.021046162
21   75_1    lnorm  717.33810  1.0826085  0.7626413         NA 0.062145603
22   75_1    gamma  709.64566  1.9464015  0.5090396         NA 0.223371844
23   75_1  weibull  709.68581  1.4674164  4.2264478         NA 0.095840275
24   75_1 invgauss  717.47726  3.8316349  5.3201363         NA 0.260524891
25   75_1    logis  756.87401  3.5504621  1.4884598         NA 0.209408290
26   75_1 invgamma  735.12953  1.9710233  4.4631912         NA 0.222058642
27   75_1 gengamma  711.43701  1.3897357  0.6990100 0.85168137 0.119597740
28   77_0    hnorm 1154.48392  4.3189682         NA         NA 0.189154205
29   77_0      exp 1170.56727  0.2958300         NA         NA 0.018308036
30   77_0    lnorm 1172.24716  0.9136948  0.8476576         NA 0.053957937
31   77_0    gamma 1153.47637  1.5389935  0.4527302         NA 0.144150573
32   77_0  weibull 1152.43070  1.2840403  3.6674980         NA 0.066871751
33   77_0 invgauss 1175.67548  3.4199350  3.7724441         NA 0.201501391
34   77_0    logis 1245.45180  3.1060397  1.4155404         NA 0.152701665
35   77_0 invgamma 1207.42812  1.7151041  3.1804392         NA 0.154014252
36   77_0 gengamma 1154.41987  1.3075839  0.7766100 1.02186949 0.093101704
37   78_2    hnorm 3046.93081  6.6139223         NA         NA 0.194226822
38   78_2      exp 3145.06731  0.1828970         NA         NA 0.007591670
39   78_2    lnorm 3127.12893  1.4231437  0.8233190         NA 0.034550219
40   78_2    gamma 3055.21223  1.8269137  0.3331472         NA 0.106648843
41   78_2  weibull 3041.32405  1.4712434  6.0466580         NA 0.050532206
42   78_2 invgauss 3151.26809  5.4934780  6.2368731         NA 0.214050922
43   78_2    logis 3195.05558  5.1742481  2.1248106         NA 0.155477644
44   78_2 invgamma 3252.73439  1.5886692  4.7076346         NA 0.090684976
45   78_2 gengamma 3036.20618  1.9264567  0.6177754 1.39254074 0.054855243
46   79_0    hnorm   14.83316  1.7220761         NA         NA 0.560050751
47   79_0      exp   15.86294  0.6931392         NA         NA 0.316223283
48   79_0    lnorm   17.55289  0.2481839  0.6295283         NA 0.319697138
49   79_0    gamma   17.06156  2.4670119  1.6372269         NA 2.266231981
50   79_0  weibull   16.74642  1.7948854  1.6851557         NA 0.882744058
51   79_0 invgauss   17.51835  1.5308945  3.5241013         NA 0.467599238
52   79_0    logis   17.59237  1.5001619  0.5195343         NA 0.439082725
53   79_0 invgamma   18.02673  3.1401792  3.5126521         NA 2.576368089
54   85_1    hnorm  731.12743  3.9224275         NA         NA 0.211393536
55   85_1      exp  744.54229  0.3232280         NA         NA 0.024610423
56   85_1    lnorm  727.87457  0.8765957  0.7592257         NA 0.059362432
57   85_1    gamma  721.71819  1.8454724  0.5917099         NA 0.210983652
58   85_1  weibull  723.95076  1.3749184  3.4107758         NA 0.083857622
59   85_1 invgauss  729.46785  3.1323950  4.4126513         NA 0.201222265
60   85_1    logis  772.11455  2.8722279  1.2100609         NA 0.160896075
61   85_1 invgamma  746.07460  2.0722270  3.8977887         NA 0.229415494
62   85_1 gengamma  723.56359  1.1042957  0.7434504 0.64516097 0.102188725
63   85_2    hnorm 4354.02345  5.8448366         NA         NA 0.140219055
64   85_2      exp 4440.92061  0.2142905         NA         NA 0.007266362
65   85_2    lnorm 4454.46718  1.2301652  0.8679806         NA 0.029914455
66   85_2    gamma 4362.56917  1.5889002  0.3393762         NA 0.077536344
67   85_2  weibull 4352.65941  1.3319530  5.0853252         NA 0.037379803
68   85_2 invgauss 4482.50203  4.6979934  4.7706691         NA 0.158089927
69   85_2    logis 4630.75167  4.3386426  1.9138172         NA 0.113579145
70   85_2 invgamma 4619.41046  1.5251798  3.6897006         NA 0.072114229
71   85_2 gengamma 4352.36537  1.6845414  0.7287975 1.16159040 0.046208322
72   87_0    hnorm 2503.79534  7.6047246         NA         NA 0.252735336
73   87_0      exp 2590.00982  0.1573617         NA         NA 0.007392674
74   87_0    lnorm 2578.61752  1.5782654  0.8248604         NA 0.039086904
75   87_0    gamma 2511.99814  1.8811249  0.2953787         NA 0.122864194
76   87_0  weibull 2496.96837  1.5173888  7.0468414         NA 0.058961971
77   87_0 invgauss 2604.62135  6.3774694  7.1027257         NA 0.283906960
78   87_0    logis 2601.28315  6.0749106  2.3988895         NA 0.198717254
79   87_0 invgamma 2692.59967  1.5242413  5.1844036         NA 0.097569355
80   87_0 gengamma 2489.29664  2.1062651  0.5786449 1.50122029 0.057437468
81   87_1    hnorm 4905.10445  7.2162328         NA         NA 0.169701800
82   87_1      exp 5105.92649  0.1632436         NA         NA 0.005426232
83   87_1    lnorm 5134.47298  1.5495997  0.8349219         NA 0.028023947
84   87_1    gamma 4950.23018  1.8998148  0.3092386         NA 0.089669063
85   87_1  weibull 4896.22329  1.5758125  6.7990263         NA 0.044455519
86   87_1 invgauss 5210.56941  6.1530944  6.6769370         NA 0.196320365
87   87_1    logis 5030.87876  6.0087778  2.2085551         NA 0.130136482
88   87_1 invgamma 5411.28983  1.4486647  4.6995465         NA 0.065959691
89   87_1 gengamma 4850.76142  2.0847454  0.5446348 1.61348967 0.029466389
90   87_2    hnorm 2516.89447  4.6935381         NA         NA 0.141663698
91   87_2      exp 2569.11285  0.2676448         NA         NA 0.011415256
92   87_2    lnorm 2508.99452  1.0477988  0.7810924         NA 0.033959472
93   87_2    gamma 2491.09674  1.8078784  0.4813122         NA 0.111347164
94   87_2  weibull 2496.63888  1.3798747  4.1156320         NA 0.047296475
95   87_2 invgauss 2511.86140  3.7663710  4.9251640         NA 0.140556947
96   87_2    logis 2680.31432  3.4189352  1.5026720         NA 0.111728479
97   87_2 invgamma 2568.42236  1.9286590  4.2017863         NA 0.116382767
98   87_2 gengamma 2492.64091  1.2874927  0.7539517 0.64842787 0.062885393
99   88_0    hnorm  503.56417  3.3185885         NA         NA 0.207358134
100  88_0      exp  514.20774  0.3813670         NA         NA 0.033650928
101  88_0    lnorm  498.07141  0.7269621  0.7289169         NA 0.066541296
102  88_0    gamma  497.09058  1.8989584  0.7162828         NA 0.258116046
103  88_0  weibull  499.35848  1.3833647  2.9022651         NA 0.099763476
104  88_0 invgauss  498.38191  2.6648072  4.1483344         NA 0.188871197
105  88_0    logis  538.33168  2.3952979  1.0198089         NA 0.155727422
106  88_0 invgamma  506.75946  2.3306543  3.9009661         NA 0.305746998
107  88_0 gengamma  498.30700  0.8765649  0.7376402 0.44541340 0.129928529
108  88_1    hnorm  631.99543  3.4971210         NA         NA 0.197435815
109  88_1      exp  637.89035  0.3701054         NA         NA 0.029518856
110  88_1    lnorm  630.01183  0.7128489  0.7969808         NA 0.065996373
111  88_1    gamma  626.82952  1.6062558  0.5892781         NA 0.199138392
112  88_1  weibull  628.02511  1.2798848  2.9403236         NA 0.085592610
113  88_1 invgauss  629.79778  2.7454661  3.5016135         NA 0.194032404
114  88_1    logis  688.63966  2.4444387  1.1349098         NA 0.157107412
115  88_1 invgamma  641.66312  2.0232205  3.2367013         NA 0.240144148
116  88_1 gengamma  628.53541  0.9385477  0.8006707 0.62020914 0.135404074
117  89_1    hnorm 2406.64126  6.7528483         NA         NA 0.224016131
118  89_1      exp 2375.45389  0.2017406         NA         NA 0.009463167
119  89_1    lnorm 2402.35380  1.1712851  1.0055974         NA 0.048196724
120  89_1    gamma 2373.23815  1.1516838  0.2320660         NA 0.077767967
121  89_1  weibull 2373.26332  1.0850098  5.1181009         NA 0.042293623
122  89_1 invgauss 2412.58970  4.9876143  3.5287883         NA 0.277949039
123  89_1    logis 2632.08142  4.3161100  2.3671299         NA 0.191894899
124  89_1 invgamma 2473.13372  1.2764551  2.7267200         NA 0.083350747
125  89_1 gengamma 2375.20833  1.6154394  0.9268213 0.96075654 0.088381462
126  90_0    hnorm 1413.69021  4.6059305         NA         NA 0.184812145
127  90_0      exp 1455.02807  0.2676296         NA         NA 0.015172293
128  90_0    lnorm 1416.81321  1.0697293  0.7551657         NA 0.043607860
129  90_0    gamma 1400.95418  1.9498892  0.5188528         NA 0.160443437
130  90_0  weibull 1402.53955  1.4504372  4.1464021         NA 0.066390806
131  90_0 invgauss 1421.17470  3.7679457  5.3276233         NA 0.179819181
132  90_0    logis 1490.91010  3.4390995  1.4292062         NA 0.140492530
133  90_0 invgamma 1456.95258  2.0050114  4.5119900         NA 0.161547552
134  90_0 gengamma 1402.88945  1.3406103  0.7107653 0.76284388 0.076781418
135  90_1    hnorm  127.80058  3.4429940         NA         NA 0.433390916
136  90_1      exp  125.81210  0.3953127         NA         NA 0.070337532
137  90_1    lnorm  130.90189  0.4470315  1.0844161         NA 0.212922474
138  90_1    gamma  127.63514  0.8778881  0.3484867         NA 0.276194476
139  90_1  weibull  127.76905  0.9641848  2.4875905         NA 0.171208814
140  90_1 invgauss  130.85989  2.5746310  1.6865461         NA 0.564810150
141  90_1    logis  149.23943  2.2462939  1.3052331         NA 0.408678635
142  90_1 invgamma  134.53019  1.3269110  1.4777013         NA 0.377138771
143  91_2    hnorm 3389.95525  6.7658907         NA         NA 0.189161220
144  91_2      exp 3445.10637  0.1863552         NA         NA 0.007365288
145  91_2    lnorm 3521.76574  1.3111584  0.9716389         NA 0.039087066
146  91_2    gamma 3423.08379  1.3373590  0.2486607         NA 0.076507939
147  91_2  weibull 3411.51827  1.2377636  5.7396327         NA 0.042088161
148  91_2 invgauss 3556.11901  5.3983976  4.1990234         NA 0.241747800
149  91_2    logis 3646.80711  5.0094588  2.3383819         NA 0.163084836
150  91_2 invgamma 3672.91525  1.2503176  3.0256371         NA 0.068443728
151  91_2 gengamma 3389.31039  1.9958910  0.6802506 1.70706425 0.055953545
152  93_0    hnorm 1028.47719  5.2006061         NA         NA 0.250984406
153  93_0      exp 1043.15657  0.2447320         NA         NA 0.016693210
154  93_0    lnorm 1050.85199  1.0734728  0.8925654         NA 0.062233784
155  93_0    gamma 1032.59734  1.4502332  0.3535389         NA 0.145279350
156  93_0  weibull 1030.91416  1.2593140  4.4050036         NA 0.072679614
157  93_0 invgauss 1054.42448  4.1200027  3.9869572         NA 0.285532140
158  93_0    logis 1118.26991  3.7318186  1.7834626         NA 0.213268651
159  93_0 invgamma 1083.69104  1.5346292  3.2005757         NA 0.148184481
160  93_0 gengamma 1031.95302  1.5857862  0.7520879 1.27259535 0.118267743
161  95_0    hnorm  642.25865  4.3260645         NA         NA 0.254285091
162  95_0      exp  641.01133  0.3058986         NA         NA 0.025414894
163  95_0    lnorm  642.24906  0.8530255  0.8702175         NA 0.074649392
164  95_0    gamma  636.45283  1.4013587  0.4265086         NA 0.177288543
165  95_0  weibull  636.96475  1.1966832  3.4888715         NA 0.083100460
166  95_0 invgauss  643.60798  3.3091662  3.4053797         NA 0.270936490
167  95_0    logis  700.04115  2.9147223  1.4244254         NA 0.204031538
168  95_0 invgamma  658.14252  1.6991297  2.9691256         NA 0.206316805
169  95_0 gengamma  638.39670  1.1606068  0.8520061 0.77401440 0.141358793
170  98_0    hnorm 2074.09805 10.0952694         NA         NA 0.386884114
171  98_0      exp 2191.32576  0.1097374         NA         NA 0.005945103
172  98_0    lnorm 2069.63547  2.0584828  0.6247282         NA 0.033973773
173  98_0    gamma 2000.69634  3.3580967  0.3680144         NA 0.252294053
174  98_0  weibull 1966.99379  2.1956490 10.2615600         NA 0.095863861
175  98_0 invgauss 2105.11072  9.1269851 18.5918087         NA 0.346592275
176  98_0    logis 1978.55109  9.0849252  2.4803804         NA 0.236165721
177  98_0 invgamma 2186.78091  2.2021134 13.5512067         NA 0.163924941
178  98_0 gengamma 1962.85725  2.3950095  0.4239582 1.31165273 0.036203484
179  99_0    hnorm 1251.19367  5.7069982         NA         NA 0.254355663
180  99_0      exp 1269.35522  0.2225530         NA         NA 0.014020394
181  99_0    lnorm 1291.71326  1.1440372  0.9424203         NA 0.060672705
182  99_0    gamma 1261.29878  1.3558754  0.3008511         NA 0.125418371
183  99_0  weibull 1257.92548  1.2320710  4.8104141         NA 0.066778111
184  99_0 invgauss 1299.20833  4.5273743  3.8463231         NA 0.309198784
185  99_0    logis 1358.41424  4.1493808  1.9821272         NA 0.219892733
186  99_0 invgamma 1339.28917  1.3698891  2.9313040         NA 0.121360314
187  99_0 gengamma 1254.03995  1.7933582  0.7040002 1.61320847 0.100951893
188 100_0    hnorm  208.34117  2.8516928         NA         NA 0.267479682
189 100_0      exp  215.09571  0.4364277         NA         NA 0.057761326
190 100_0    lnorm  209.68575  0.6041551  0.7210309         NA 0.099634954
191 100_0    gamma  208.62198  1.9355007  0.8327602         NA 0.406552143
192 100_0  weibull  208.90514  1.4276129  2.5542871         NA 0.162226963
193 100_0 invgauss  209.16416  2.3396175  3.8041283         NA 0.243715567
194 100_0    logis  227.13026  2.1323049  0.9098716         NA 0.211935156
195 100_0 invgamma  212.68120  2.4303818  3.6394255         NA 0.486074122
196 100_0 gengamma  210.61427  0.8246610  0.7224616 0.66411003 0.234275754
197 101_0    hnorm  602.67375  4.0014761         NA         NA 0.238676167
198 101_0      exp  624.22399  0.3051182         NA         NA 0.025704111
199 101_0    lnorm  598.55615  0.9722046  0.7006145         NA 0.060295387
200 101_0    gamma  592.84616  2.1998319  0.6659656         NA 0.273252306
201 101_0  weibull  594.91431  1.5222412  3.6660316         NA 0.101816765
202 101_0 invgauss  600.51498  3.3110917  5.5815670         NA 0.215262309
203 101_0    logis  625.54876  3.0590793  1.1811405         NA 0.172990821
204 101_0 invgamma  614.79721  2.3106725  4.8935321         NA 0.280843602
205 101_0 gengamma  594.82608  1.1830518  0.6772137 0.63878812 0.101784196
206 104_0    hnorm 3987.89170  6.7494942         NA         NA 0.173894874
207 104_0      exp 3917.40115  0.2043716         NA         NA 0.007445685
208 104_0    lnorm 3949.34844  1.1378882  1.0213516         NA 0.038050245
209 104_0    gamma 3915.81047  1.1050120  0.2256128         NA 0.057676143
210 104_0  weibull 3916.34490  1.0551574  5.0037903         NA 0.031933717
211 104_0 invgauss 3956.39504  4.9222558  3.3495073         NA 0.217238794
212 104_0    logis 4385.37183  4.2303139  2.4083279         NA 0.151912730
213 104_0 invgamma 4047.58285  1.2699648  2.6185271         NA 0.064249033
214 104_0 gengamma 3917.41174  1.5464011  0.9657413 0.86335757 0.076024814
215 105_0    hnorm 1748.68363  3.8993514         NA         NA 0.135599866
216 105_0      exp 1799.62488  0.3178830         NA         NA 0.015613557
217 105_0    lnorm 1776.27198  0.8880789  0.7799354         NA 0.039359768
218 105_0    gamma 1747.63135  1.7981408  0.5671938         NA 0.133952654
219 105_0  weibull 1744.78015  1.4050750  3.4753995         NA 0.058115898
220 105_0 invgauss 1780.66928  3.1864124  4.2750467         NA 0.135253949
221 105_0    logis 1868.01971  2.9234004  1.2439192         NA 0.106763098
222 105_0 invgamma 1828.66578  1.9626282  3.6858121         NA 0.140659533
223 105_0 gengamma 1746.71170  1.2620166  0.7064396 1.04740184 0.071100487
224 106_0    hnorm  680.96551  6.3281652         NA         NA 0.390278320
225 106_0      exp  644.04461  0.2394041         NA         NA 0.020886884
226 106_0    lnorm  644.41140  0.8800214  1.1018863         NA 0.100065701
227 106_0    gamma  644.75941  0.8644730  0.2073995         NA 0.112909169
228 106_0  weibull  644.12628  0.9051415  3.9677193         NA 0.067017236
229 106_0 invgauss  644.90963  4.2101155  2.3605804         NA 0.490099893
230 106_0    logis  759.61548  3.3155272  2.2242110         NA 0.326708131
231 106_0 invgamma  656.09025  1.2351717  1.9878564         NA 0.155327018
232 106_0 gengamma  644.53368  1.1390566  1.1264888 0.52882397 0.216466130
233 107_0    hnorm  801.80911  4.8746427         NA         NA 0.262978883
234 107_0      exp  783.70680  0.2848220         NA         NA 0.021727617
235 107_0    lnorm  802.82923  0.7139231  1.1596380         NA 0.094417838
236 107_0    gamma  783.44373  0.8334343  0.2382387         NA 0.103196099
237 107_0  weibull  784.56520  0.9273500  3.3892504         NA 0.066823560
238 107_0 invgauss  804.83472  3.5494815  1.9122132         NA 0.368241145
239 107_0    logis  910.38511  3.0661486  1.8466923         NA 0.246363258
240 107_0 invgamma  827.46894  1.1336422  1.5068482         NA 0.129733750
241 107_0 gengamma  777.75283  1.7401369  0.8236298 2.26415493 0.170559186
242 107_2    hnorm 1086.10558  4.8985882         NA         NA 0.227216678
243 107_2      exp 1061.54498  0.2834719         NA         NA 0.018593010
244 107_2    lnorm 1034.83070  0.9323673  0.8222411         NA 0.055216988
245 107_2    gamma 1048.63827  1.4704259  0.4149979         NA 0.140001675
246 107_2  weibull 1054.77947  1.1707968  3.7512571         NA 0.059404702
247 107_2 invgauss 1036.39748  3.5591040  4.0043471         NA 0.220105673
248 107_2    logis 1170.31550  2.9791613  1.5343391         NA 0.169559447
249 107_2 invgamma 1046.74692  1.9078344  3.7144429         NA 0.179088016
250 107_2 gengamma 1036.80396  0.9456040  0.8249566 0.03550689 0.099541484
251 108_0    hnorm 3239.06732  6.4421310         NA         NA 0.182576710
252 108_0      exp 3319.92541  0.1915112         NA         NA 0.007671950
253 108_0    lnorm 3329.16611  1.3504783  0.8623238         NA 0.034999733
254 108_0    gamma 3253.96785  1.6479936  0.3146089         NA 0.093885161
255 108_0  weibull 3242.88337  1.3762874  5.7186580         NA 0.045804407
256 108_0 invgauss 3355.43247  5.2501724  5.3742311         NA 0.207863501
257 108_0    logis 3433.98558  4.8786969  2.1182562         NA 0.149136693
258 108_0 invgamma 3461.40276  1.5008780  4.0610115         NA 0.083054060
259 108_0 gengamma 3239.24185  1.8564565  0.6758718 1.32637966 0.055343367
260 109_0    hnorm  985.80177  5.4519083         NA         NA 0.271331789
261 109_0      exp  995.33514  0.2359062         NA         NA 0.016595493
262 109_0    lnorm 1006.05072  1.0757768  0.9366910         NA 0.067400331
263 109_0    gamma  990.10932  1.3300945  0.3128541         NA 0.136305992
264 109_0  weibull  988.78626  1.2011911  4.5152254         NA 0.072142600
265 109_0 invgauss 1007.50890  4.2719399  3.6816970         NA 0.323619325
266 109_0    logis 1084.52437  3.8398708  1.9478778         NA 0.241242000
267 109_0 invgamma 1034.31580  1.4333519  2.9190477         NA 0.141585491
268 109_0 gengamma  988.41157  1.7736910  0.6983398 1.70628572 0.223675682
269 118_0    hnorm  203.64892  3.4824357         NA         NA 0.347180724
270 118_0      exp  211.81154  0.3492715         NA         NA 0.049156357
271 118_0    lnorm  205.55393  0.8296223  0.7161233         NA 0.103629572
272 118_0    gamma  203.55567  2.0929360  0.7238931         NA 0.442608045
273 118_0  weibull  203.53857  1.5174049  3.2061414         NA 0.178625470
274 118_0 invgauss  205.34059  2.9012580  4.7412230         NA 0.320277445
275 118_0    logis  217.72179  2.6902964  1.0956236         NA 0.272167531
276 118_0 invgamma  209.85353  2.3035521  4.2356323         NA 0.471711353
277 118_0 gengamma  205.47628  1.1173135  0.6736985 0.85511907 0.217675318
278 119_0    hnorm  158.20206  7.1458548         NA         NA 0.939827488
279 119_0      exp  158.42950  0.1834794         NA         NA 0.034118058
280 119_0    lnorm  164.54442  1.2314662  1.0912705         NA 0.207885633
281 119_0    gamma  160.38053  1.0621646  0.1947974         NA 0.287811309
282 119_0  weibull  160.24207  1.0749555  5.5986498         NA 0.175686202
283 119_0 invgauss  165.77340  5.4843957  3.2357461         NA 1.327039706
284 119_0    logis  175.72063  4.9380821  2.6426074         NA 0.866486800
285 119_0 invgamma  170.67629  1.0877697  2.2816739         NA 0.280334837
286 119_0 gengamma  160.39279  2.2336363  0.6272254 2.46752375 0.389684198
287 125_0    hnorm 1534.59464  4.0806054         NA         NA 0.153047842
288 125_0      exp 1577.39568  0.3041302         NA         NA 0.016113138
289 125_0    lnorm 1562.39306  0.9226283  0.7959515         NA 0.043267881
290 125_0    gamma 1536.16416  1.7521186  0.5290406         NA 0.139687663
291 125_0  weibull 1533.12642  1.3910295  3.6242742         NA 0.062140077
292 125_0 invgauss 1565.93340  3.3266516  4.2568798         NA 0.155888809
293 125_0    logis 1642.70461  3.0632314  1.3179709         NA 0.122356151
294 125_0 invgamma 1608.92007  1.8838035  3.6145106         NA 0.144560306
295 125_0 gengamma 1534.82245  1.3243076  0.7062166 1.10682576 0.077650583
296 128_1    hnorm 4471.27673  5.1285905         NA         NA 0.118176049
297 128_1      exp 4389.93059  0.2681493         NA         NA 0.008744306
298 128_1    lnorm 4415.89235  0.9337331  0.9369790         NA 0.031498362
299 128_1    gamma 4374.03999  1.2369992  0.3307430         NA 0.060567687
300 128_1  weibull 4376.87084  1.1142426  3.8914609         NA 0.030107816
301 128_1 invgauss 4431.23458  3.7666763  3.2133349         NA 0.132892092
302 128_1    logis 4845.95430  3.2750356  1.6906377         NA 0.094571256
303 128_1 invgamma 4536.05603  1.4876423  2.6897829         NA 0.069943981
304 128_1 gengamma 4374.84540  1.2674743  0.9127868 0.78235320 0.056245161
305 131_0    hnorm  238.71892  3.7131332         NA         NA 0.346835462
306 131_0      exp  237.96283  0.3574163         NA         NA 0.047180891
307 131_0    lnorm  243.37916  0.6313429  0.9674197         NA 0.135089262
308 131_0    gamma  239.67275  1.1241267  0.4006482         NA 0.240466315
309 131_0  weibull  239.49706  1.0880380  2.8948756         NA 0.131860406
310 131_0 invgauss  242.86639  2.8420477  2.3717026         NA 0.410159226
311 131_0    logis  272.95212  2.4995971  1.3763649         NA 0.320805219
312 131_0 invgamma  248.60149  1.5266664  2.0983904         NA 0.304937974
313 131_0 gengamma  237.21995  2.0302936  0.2393278 7.74987734 0.286522286
314 133_0    hnorm  155.55114  4.6198641         NA         NA 0.562425408
315 133_0      exp  160.47687  0.2651077         NA         NA 0.045598201
316 133_0    lnorm  154.07497  1.0973166  0.7093776         NA 0.124120397
317 133_0    gamma  154.02285  2.1679610  0.5716874         NA 0.526223752
318 133_0  weibull  154.92339  1.5096071  4.2173721         NA 0.203741391
319 133_0 invgauss  153.85982  3.7961040  6.1666910         NA 0.513106722
320 133_0    logis  164.93451  3.4725511  1.4231825         NA 0.426662648
321 133_0 invgamma  156.59749  2.2685882  5.3994100         NA 0.549342917
322 133_0 gengamma  155.71217  1.2203364  0.7027501 0.35803631 0.236419214
323 134_0    hnorm  307.99006  4.2956617         NA         NA 0.364677459
324 134_0      exp  314.00068  0.2937611         NA         NA 0.035237139
325 134_0    lnorm  301.14332  0.9862677  0.7219355         NA 0.088425548
326 134_0    gamma  301.40920  2.0472757  0.5975521         NA 0.352758070
327 134_0  weibull  303.92666  1.4240380  3.7792371         NA 0.130435236
328 134_0 invgauss  301.13139  3.4324492  5.3315048         NA 0.330909858
329 134_0    logis  321.86594  3.1612197  1.2849411         NA 0.268463652
330 134_0 invgamma  306.51578  2.2224878  4.7172383         NA 0.378284571
331 134_0 gengamma  302.37502  1.1033311  0.7198087 0.33926105 0.156449009
332 135_0    hnorm 2062.40474  5.9274765         NA         NA 0.207234776
333 135_0      exp 2142.16531  0.2015107         NA         NA 0.009956368
334 135_0    lnorm 2095.81710  1.3611796  0.7612268         NA 0.038040915
335 135_0    gamma 2052.44134  2.0764125  0.4169178         NA 0.144899953
336 135_0  weibull 2044.16049  1.5661590  5.5372294         NA 0.063234830
337 135_0 invgauss 2109.27614  4.9875378  6.8399668         NA 0.210526793
338 135_0    logis 2137.78387  4.7207944  1.8292676         NA 0.159135251
339 135_0 invgamma 2175.15129  1.8344736  5.3604406         NA 0.125863899
340 135_0 gengamma 2044.90370  1.7691996  0.6133321 1.18335981 0.060600788
           se2         se3
1           NA          NA
2           NA          NA
3   0.03696496          NA
4   0.03515710          NA
5   0.20405702          NA
6   0.41547646          NA
7   0.08275183          NA
8   0.36331315          NA
9   0.04804562  0.22620815
10          NA          NA
11          NA          NA
12  0.03878895          NA
13  0.03781596          NA
14  0.24924684          NA
15  0.55813242          NA
16  0.09921562          NA
17  0.48436603          NA
18  0.04251064  0.19854791
19          NA          NA
20          NA          NA
21  0.04716303          NA
22  0.06488566          NA
23  0.24498194          NA
24  0.66953867          NA
25  0.09955148          NA
26  0.59907003          NA
27  0.05647364  0.29710497
28          NA          NA
29          NA          NA
30  0.04310527          NA
31  0.04755171          NA
32  0.18838774          NA
33  0.39107713          NA
34  0.07368185          NA
35  0.35586860          NA
36  0.04607035  0.21107458
37          NA          NA
38          NA          NA
39  0.02608888          NA
40  0.02189122          NA
41  0.18027835          NA
42  0.40063932          NA
43  0.07304418          NA
44  0.32875183          NA
45  0.03200087  0.15514218
46          NA          NA
47          NA          NA
48  0.29269885          NA
49  1.52246257          NA
50  0.47408212          NA
51  3.44203272          NA
52  0.20403474          NA
53  3.49246402          NA
54          NA          NA
55          NA          NA
56  0.04657813          NA
57  0.07457987          NA
58  0.20133554          NA
59  0.55197109          NA
60  0.07737419          NA
61  0.51714374          NA
62  0.04677023  0.23777597
63          NA          NA
64          NA          NA
65  0.02311644          NA
66  0.01880392          NA
67  0.13717166          NA
68  0.25782185          NA
69  0.05399171          NA
70  0.21774459          NA
71  0.02503094  0.10713912
72          NA          NA
73          NA          NA
74  0.02925577          NA
75  0.02172158          NA
76  0.23014809          NA
77  0.51092800          NA
78  0.09301558          NA
79  0.40724047          NA
80  0.03455947  0.17428449
81          NA          NA
82          NA          NA
83  0.02131751          NA
84  0.01633577          NA
85  0.15091560          NA
86  0.34491853          NA
87  0.06012294          NA
88  0.26625316          NA
89  0.01791465  0.09055254
90          NA          NA
91          NA          NA
92  0.02599841          NA
93  0.03310929          NA
94  0.13530096          NA
95  0.33343345          NA
96  0.05398582          NA
97  0.30380521          NA
98  0.02753747  0.14519248
99          NA          NA
100         NA          NA
101 0.05282021          NA
102 0.10621454          NA
103 0.19824490          NA
104 0.61487494          NA
105 0.07735657          NA
106 0.60712462          NA
107 0.05284602  0.32670323
108         NA          NA
109         NA          NA
110 0.05311654          NA
111 0.08076324          NA
112 0.19634880          NA
113 0.47864716          NA
114 0.07736072          NA
115 0.46935699          NA
116 0.05408072  0.31858117
117         NA          NA
118         NA          NA
119 0.03793000          NA
120 0.01855123          NA
121 0.23525451          NA
122 0.27052238          NA
123 0.09407164          NA
124 0.23367626          NA
125 0.04239155  0.16856071
126         NA          NA
127         NA          NA
128 0.03343266          NA
129 0.04728175          NA
130 0.17228421          NA
131 0.47938616          NA
132 0.06896055          NA
133 0.43260955          NA
134 0.03578577  0.18436440
135         NA          NA
136         NA          NA
137 0.18903195          NA
138 0.12491423          NA
139 0.50316901          NA
140 0.61580097          NA
141 0.19630039          NA
142 0.60888064          NA
143         NA          NA
144         NA          NA
145 0.03070431          NA
146 0.01648148          NA
147 0.19393209          NA
148 0.26896417          NA
149 0.07616162          NA
150 0.21714941          NA
151 0.03387011  0.15375545
152         NA          NA
153         NA          NA
154 0.04892087          NA
155 0.04037638          NA
156 0.25361566          NA
157 0.44442827          NA
158 0.10193754          NA
159 0.38945515          NA
160 0.06301221  0.28525462
161         NA          NA
162         NA          NA
163 0.06004384          NA
164 0.06100403          NA
165 0.25875939          NA
166 0.48023163          NA
167 0.10047427          NA
168 0.45256722          NA
169 0.06204964  0.30210655
170         NA          NA
171         NA          NA
172 0.02483601          NA
173 0.02967882          NA
174 0.26594323          NA
175 1.49483488          NA
176 0.11121738          NA
177 1.15168247          NA
178 0.02155646  0.13019346
179         NA          NA
180         NA          NA
181 0.04796199          NA
182 0.03201310          NA
183 0.26105037          NA
184 0.39798269          NA
185 0.10373226          NA
186 0.33585272          NA
187 0.05940893  0.26973211
188         NA          NA
189         NA          NA
190 0.08006517          NA
191 0.18882872          NA
192 0.25469269          NA
193 0.86860251          NA
194 0.10286232          NA
195 0.86647284          NA
196 0.08531420  0.62555528
197         NA          NA
198         NA          NA
199 0.04641870          NA
200 0.09024433          NA
201 0.21602545          NA
202 0.75179090          NA
203 0.08445015          NA
204 0.69500385          NA
205 0.04704184  0.25347646
206         NA          NA
207         NA          NA
208 0.02986596          NA
209 0.01404648          NA
210 0.18390753          NA
211 0.19927970          NA
212 0.07415305          NA
213 0.17413529          NA
214 0.03404707  0.14200174
215         NA          NA
216         NA          NA
217 0.03118866          NA
218 0.04659878          NA
219 0.12950964          NA
220 0.34852895          NA
221 0.05173629          NA
222 0.32017375          NA
223 0.03508750  0.17834473
224         NA          NA
225         NA          NA
226 0.08191775          NA
227 0.03303844          NA
228 0.41037194          NA
229 0.35950668          NA
230 0.16937174          NA
231 0.34218025          NA
232 0.08242011  0.37899596
233         NA          NA
234         NA          NA
235 0.08120997          NA
236 0.03507174          NA
237 0.30129210          NA
238 0.27662260          NA
239 0.11850328          NA
240 0.25222754          NA
241 0.10716097  0.48143897
242         NA          NA
243         NA          NA
244 0.04281822          NA
245 0.04505599          NA
246 0.22428638          NA
247 0.42466422          NA
248 0.08813384          NA
249 0.42129163          NA
250 0.04567253  0.21942764
251         NA          NA
252         NA          NA
253 0.02678797          NA
254 0.02034319          NA
255 0.17610218          NA
256 0.33824034          NA
257 0.07047167          NA
258 0.27943348          NA
259 0.03138857  0.14211558
260         NA          NA
261         NA          NA
262 0.05286879          NA
263 0.03703391          NA
264 0.28122089          NA
265 0.42312474          NA
266 0.11489950          NA
267 0.36887488          NA
268 0.13372291  0.64672198
269         NA          NA
270         NA          NA
271 0.08055441          NA
272 0.16674615          NA
273 0.31759592          NA
274 1.08865369          NA
275 0.13002865          NA
276 1.02203122          NA
277 0.09639627  0.58280696
278         NA          NA
279         NA          NA
280 0.16622188          NA
281 0.06303031          NA
282 1.02816403          NA
283 1.00188349          NA
284 0.40854848          NA
285 0.81109462          NA
286 0.26407179  1.47971117
287         NA          NA
288         NA          NA
289 0.03415129          NA
290 0.04673619          NA
291 0.14703486          NA
292 0.37227524          NA
293 0.05875731          NA
294 0.33793453          NA
295 0.03935433  0.19478576
296         NA          NA
297         NA          NA
298 0.02534405          NA
299 0.01869039          NA
300 0.12151466          NA
301 0.17732655          NA
302 0.04675641          NA
303 0.16297196          NA
304 0.02572051  0.11020461
305         NA          NA
306         NA          NA
307 0.11345750          NA
308 0.09741833          NA
309 0.37889173          NA
310 0.57505290          NA
311 0.15334633          NA
312 0.55705621          NA
313 0.34289683 11.41698144
314         NA          NA
315         NA          NA
316 0.09259501          NA
317 0.15310048          NA
318 0.51127750          NA
319 1.63926577          NA
320 0.20689775          NA
321 1.52189903          NA
322 0.09430727  0.58690333
323         NA          NA
324         NA          NA
325 0.06685443          NA
326 0.11365844          NA
327 0.33892139          NA
328 1.00616966          NA
329 0.12884925          NA
330 0.94217921          NA
331 0.06684391  0.37338208
332         NA          NA
333         NA          NA
334 0.02861180          NA
335 0.03228532          NA
336 0.18480255          NA
337 0.52134514          NA
338 0.07491888          NA
339 0.43871945          NA
340 0.03369890  0.16641702

There they all are! The generalized gamma didn’t always converge, which is the source of the warnings and the fact that it is missing from many places.

Now lets calculate the delta-AIC within each dataset:

result <- group_by(result, ID) %>% mutate(delta_AIC = AIC - min(AIC))
print(result, n=50) 
# A tibble: 340 x 10
# Groups:   ID [38]
   ID    model    AIC  par1   par2   par3     se1     se2    se3 delta_AIC
   <fct> <fct>  <dbl> <dbl>  <dbl>  <dbl>   <dbl>   <dbl>  <dbl>     <dbl>
 1 73_0  hnorm 1531.  5.27  NA     NA     0.209   NA      NA        0     
 2 73_0  exp   1564.  0.237 NA     NA     0.0133  NA      NA       32.9   
 3 73_0  lnorm 1556.  1.14   0.843 NA     0.0481   0.0370 NA       25.1   
 4 73_0  gamma 1533.  1.63   0.386 NA     0.131    0.0352 NA        2.25  
 5 73_0  weib… 1531.  1.34   4.60  NA     0.0625   0.204  NA        0.183 
 6 73_0  invg… 1559.  4.24   4.66  NA     0.227    0.415  NA       28.4   
 7 73_0  logis 1647.  3.89   1.77  NA     0.175    0.0828 NA      117.    
 8 73_0  invg… 1601.  1.66   3.77  NA     0.130    0.363  NA       70.1   
 9 73_0  geng… 1533.  1.57   0.727  1.12  0.0930   0.0480  0.226    1.90  
10 75_0  hnorm 1266.  5.88  NA     NA     0.262   NA      NA        7.76  
11 75_0  exp   1294.  0.212 NA     NA     0.0133  NA      NA       35.4   
12 75_0  lnorm 1274.  1.27   0.805 NA     0.0514   0.0388 NA       15.0   
13 75_0  gamma 1259.  1.79   0.378 NA     0.159    0.0378 NA        0     
14 75_0  weib… 1260.  1.39   5.20  NA     0.0701   0.249  NA        0.928 
15 75_0  invg… 1279.  4.75   5.70  NA     0.273    0.558  NA       19.8   
16 75_0  logis 1340.  4.33   1.87  NA     0.205    0.0992 NA       80.9   
17 75_0  invg… 1312.  1.74   4.59  NA     0.152    0.484  NA       53.3   
18 75_0  geng… 1261.  1.58   0.740  0.801 0.0878   0.0425  0.199    1.93  
19 75_1  hnorm  714.  4.66  NA     NA     0.264   NA      NA        3.87  
20 75_1  exp    736.  0.263 NA     NA     0.0210  NA      NA       26.7   
21 75_1  lnorm  717.  1.08   0.763 NA     0.0621   0.0472 NA        7.69  
22 75_1  gamma  710.  1.95   0.509 NA     0.223    0.0649 NA        0     
23 75_1  weib…  710.  1.47   4.23  NA     0.0958   0.245  NA        0.0401
24 75_1  invg…  717.  3.83   5.32  NA     0.261    0.670  NA        7.83  
25 75_1  logis  757.  3.55   1.49  NA     0.209    0.0996 NA       47.2   
26 75_1  invg…  735.  1.97   4.46  NA     0.222    0.599  NA       25.5   
27 75_1  geng…  711.  1.39   0.699  0.851 0.120    0.0565  0.297    1.79  
28 77_0  hnorm 1154.  4.32  NA     NA     0.189   NA      NA        2.05  
29 77_0  exp   1171.  0.296 NA     NA     0.0183  NA      NA       18.1   
30 77_0  lnorm 1172.  0.914  0.848 NA     0.0540   0.0431 NA       19.8   
31 77_0  gamma 1153.  1.54   0.453 NA     0.144    0.0476 NA        1.05  
32 77_0  weib… 1152.  1.28   3.67  NA     0.0669   0.188  NA        0     
33 77_0  invg… 1176.  3.42   3.77  NA     0.202    0.391  NA       23.2   
34 77_0  logis 1245.  3.11   1.42  NA     0.153    0.0737 NA       93.0   
35 77_0  invg… 1207.  1.72   3.18  NA     0.154    0.356  NA       55.0   
36 77_0  geng… 1154.  1.31   0.776  1.02  0.0931   0.0461  0.211    1.99  
37 78_2  hnorm 3047.  6.61  NA     NA     0.194   NA      NA       10.7   
38 78_2  exp   3145.  0.183 NA     NA     0.00759 NA      NA      109.    
39 78_2  lnorm 3127.  1.42   0.823 NA     0.0346   0.0261 NA       90.9   
40 78_2  gamma 3055.  1.83   0.333 NA     0.107    0.0219 NA       19.0   
41 78_2  weib… 3041.  1.47   6.05  NA     0.0505   0.180  NA        5.12  
42 78_2  invg… 3151.  5.49   6.24  NA     0.214    0.401  NA      115.    
43 78_2  logis 3195.  5.17   2.12  NA     0.155    0.0730 NA      159.    
44 78_2  invg… 3253.  1.59   4.71  NA     0.0907   0.329  NA      217.    
45 78_2  geng… 3036.  1.93   0.618  1.39  0.0548   0.0320  0.155    0     
46 79_0  hnorm   14.8 1.72  NA     NA     0.560   NA      NA        0     
47 79_0  exp     15.9 0.693 NA     NA     0.316   NA      NA        1.03  
48 79_0  lnorm   17.6 0.248  0.630 NA     0.320    0.293  NA        2.72  
49 79_0  gamma   17.1 2.47   1.64  NA     2.27     1.52   NA        2.23  
50 79_0  weib…   16.7 1.79   1.69  NA     0.883    0.474  NA        1.91  
# ... with 290 more rows

And plot the results:

ggplot(result, aes(x=delta_AIC, group = model)) + geom_histogram() + facet_wrap(~model, scales = "free") 
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Only the generalized gamma has consistently small delta-AIC values, suggesting that I should try harder on this. Let’s look at a particular case:

temp <- filter(disperseLer, ID == "73_0")
cens_data <- cens_dispersal_data(temp, 7)
start <- start_params(cens_data, "gengamma")
start[3] <- 0
library(flexsurv)
# dgengamma <- function(x, mu, sigma, Q) {
#   print(x)
#   print(c(mu, sigma, Q))
#   (x > 0) * flexsurv::dgengamma(x, mu, sigma, Q)
# }
fit <- try(fitdistcens(cens_data, "gengamma", start = start, silent = FALSE, lower = c(-Inf, 0, -Inf), optim.method = "L-BFGS-B", control=list(trace=0)))
<simpleError in optim(par = vstart, fn = fnobjcens, fix.arg = fix.arg, gr = gradient,     rcens = rcens, lcens = lcens, icens = icens, ncens = ncens,     ddistnam = ddistname, pdistnam = pdistname, hessian = TRUE,     method = meth, lower = lower, upper = upper, ...): L-BFGS-B needs finite values of 'fn'>
fit <- try(fitdist(cens_data[,2], "gengamma", start = start, silent = FALSE, lower = c(-Inf, 0, -Inf), optim.method = "L-BFGS-B", control=list(trace=0)))
summary(fit)
Fitting of the distribution ' gengamma ' by maximum likelihood 
Parameters : 
       estimate Std. Error
mu    1.4644461 0.07501084
sigma 0.6922186 0.03164702
Q     0.4123414 0.18156173
Loglikelihood:  -767.0602   AIC:  1540.12   BIC:  1551.425 
Correlation matrix:
              mu      sigma          Q
mu     1.0000000 -0.4631829  0.8533900
sigma -0.4631829  1.0000000 -0.4651418
Q      0.8533900 -0.4651418  1.0000000
fit$est
       mu     sigma         Q 
1.4644461 0.6922186 0.4123414 
fit <- try(fitdistcens(cens_data, "gengamma", start = as.list(fit$est), silent = FALSE, lower = c(-Inf, 0, -Inf), optim.method = "L-BFGS-B", control=list(trace=0)))
summary(fit)
Fitting of the distribution ' gengamma ' By maximum likelihood on censored data 
Parameters
       estimate Std. Error
mu    1.5703197 0.09299907
sigma 0.7275757 0.04804571
Q     1.1181647 0.22618933
Loglikelihood:  -763.355   AIC:  1532.71   BIC:  1544.015 
Correlation matrix:
              mu      sigma          Q
mu     1.0000000 -0.7393269  0.8825932
sigma -0.7393269  1.0000000 -0.7010293
Q      0.8825932 -0.7010293  1.0000000

Got it to fit almost everywhere, and still is always better than 4. Some cases where it is 2, suggesting a limiting distribution fits equally. But sometimes it’s at zero.

result2 <- filter(result, ID != "90_1", ID!="79_0")
plot(filter(result2, model == "gengamma")$delta_AIC, filter(result2, model == "weibull")$delta_AIC, xlab = "gengamma delta_AIC", ylab = "weibull delta_AIC")

plot(filter(result2, model == "gengamma")$delta_AIC, filter(result2, model == "gamma")$delta_AIC, xlab = "gengamma delta_AIC", ylab = "gamma delta_AIC")

plot(filter(result2, model == "gengamma")$delta_AIC, filter(result2, model == "lnorm")$delta_AIC, xlab = "gengamma delta_AIC", ylab = "lnorm delta_AIC")