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Replicating table 1 from Rouder and Morey (2012)
No homo CC Latitude north lat_from_o tpar meantemp hitemp lotemp diftemp Isosd dpop_30
1 1 595 27 0 35 1 17.8 30 1 29 0.218223437 13
2 1 475 27 0 35 1 17.8 30 1 29 0.218223437 13
3 1 507 27 0 35 1 17.8 30 1 29 0.218223437 13
4 1 570 27 0 35 1 17.8 30 1 29 0.218223437 13
6 1 776 4 1 4 7 24.7 26 11 15 0.212807364 13
7 1 506.333 4 1 4 7 24.7 26 11 15 0.212807364 13
8 1 622.5 4 1 4 7 24.7 26 11 15 0.212807364 13
5 1 500 7 1 1 7 22.2 25 6 19 0.212807364 13
15 1 775 40 1 32 4 5.8 31 -1 32 0.25577606 16
16 1 650 40 1 32 4 5.8 31 -1 32 0.25577606 16
17 1 600 40 1 32 4 5.8 31 -1 32 0.25577606 16
9 1 782.5 4 1 4 7 24.7 26 11 15 0.246603596 16
10 1 616 4 1 4 7 24.7 26 11 15 0.246603596 16
67 1 850 38 1 30 3 6.9 31 -10 41 0.232941294 17
12 1 597 4 0 12 7 22.3 31 13 18 0.232941294 17
14 1 674 4 0 12 7 22.3 31 13 18 0.252773704 17
13 1 825.4 4 1 4 7 24.7 26 11 15 0.252773704 17
18 1 639.2 4 0 12 7 22.3 31 13 18 0.221164939 17
11 1 855 8 0 16 3 25.8 31 23 8 0.222701943 19
107 1 1000 32.05 1 24.05 3 6.9 31 -10 41 0.222701943 19
19 1 662.286 4 0 12 7 22.3 31 13 18 0.222701943 19
21 1 904.5 3.9008 1 4.0992 7 24.7 26 11 15 0.260943995 19
22 1 825.667 4 1 4 7 24.7 26 11 15 0.264428076 19
27 1 856 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
29 1 792.571 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
30 1 900 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
31 1 951 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
32 1 1020 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
37 1 868.6 7.5778 0 15.5778 3 25.8 31 23 8 0.298084327 28
24 1 1070.5 4 0 12 7 22.3 31 13 18 0.309443896 28
25 1 779 34.2 1 26.2 3 6.9 31 -10 41 0.301799443 29
26 1 800 14.8333 1 6.8333 7 25.5 27 13 14 0.299464168 29
28 1 940 7.3667 0 15.3667 3 25.8 31 23 8 0.29634621 30
38 1 1185 41.55 1 33.55 1 13.4 30 5 25 0.357515549 31
39 1 732.33 4 0 12 7 22.3 31 13 18 0.390312661 31
218 1 1006 7.3833 0 15.3833 3 25.8 31 23 8 0.36580401 32
40 1 1300 35.4158 1 27.4158 3 22.5 29 9 20 0.382977102 33
108 1 1000 7.24 0 15.24 3 25.8 31 23 8 0.368289722 38
42 1 1250 10.6333 1 2.6333 7 22.2 25 6 19 0.368289722 38
47 1 1056.333 7.3833 0 15.3833 3 25.8 31 23 8 0.411476483 38
76 1 1390 43 1 35 1 13.3 28 6 22 0.411476483 38
77 1 1125 43 1 35 1 13.3 28 6 22 0.411476483 38
78 1 1153.333 43 1 35 1 13.3 28 6 22 0.411476483 38
57 1 911 35 1 27 3 17.1 28 8 20 0.338519963 40
56 1 1138.667 42.8167 1 34.8167 1 10.7 25 1 24 0.338519963 40
71 1 1100 32.817 1 24.817 3 6.9 31 -10 41 0.324690513 42
70 1 1216.667 32 0 40 1 17.8 30 1 29 0.324690513 42
68 1 1310 14 0 22 7 21.4 31 9 22 0.324690513 42
69 1 1100 3 0 11 7 22.3 31 13 18 0.324690513 42
75 1 1266.556 40.365 1 32.365 1 15.4 33 6 27 0.396802573 43
102 1 1305 32 1 24 3 17.1 28 8 20 0.417255655 47
72 1 1432 49.2983 1 41.2983 0 8.4 24 -3 27 0.417255655 47
73 1 1111.192 47 1 39 0 8.4 24 -3 27 0.417255655 47
79 1 1249.333 23.3 1 15.3 5 23.7 41 7 34 0.417255655 47
95 1 1280 30 0 38 1 17.8 30 1 29 0.410862309 48
103 1 1400 32 1 24 3 17.1 28 8 20 0.406021609 49
20 1 1000 7.5778 0 15.5778 3 25.8 31 23 8 0.417855328 51
81 1 1012.5 31.7167 1 23.7167 3 6.9 31 -10 41 0.417855328 51
23 1 850 7.5778 0 15.5778 3 25.8 31 23 8 0.425454367 58
58 1 1030 38 1 30 3 6.9 31 -10 41 0.425454367 58
59 1 937.5 38 1 30 3 6.9 31 -10 41 0.425454367 58
60 1 1220 38 1 30 3 6.9 31 -10 41 0.425454367 58
61 1 1225 38 1 30 3 6.9 31 -10 41 0.425454367 58
62 1 1015 38 1 30 3 6.9 31 -10 41 0.425454367 58
63 1 1030 38 1 30 3 6.9 31 -10 41 0.425454367 58
82 1 1160 25.7 1 17.7 3 6.9 31 -10 41 0.432039854 59
83 1 1450 50.9833 1 42.9833 0 8.4 24 -3 27 0.425318887 60
89 1 900 7.3833 0 15.3833 3 25.8 31 23 8 0.414916251 61
84 1 1121.429 7 0 15 7 22.3 31 13 18 0.414916251 61
85 1 1266.167 7 0 15 7 22.3 31 13 18 0.414916251 61
86 1 1115.714 7 0 15 7 22.3 31 13 18 0.414916251 61
87 1 1135 7 0 15 7 22.3 31 13 18 0.414916251 61
88 1 1109 7 0 15 7 22.3 31 13 18 0.414916251 61
140 1 1090 7 0 15 7 22.3 31 13 18 0.414916251 61
100 1 1432.5 7 1 1 7 22.2 25 6 19 0.408297587 61
90 1 1316.667 42.05 1 34.05 3 6.9 31 -10 41 0.405555998 62
91 1 1334.571 47.617 1 39.617 0 9.8 28 -4 32 0.407075204 63
92 1 1200 50.3 1 42.3 0 10.7 25 1 24 0.40956105 64
93 1 1420 45.95 1 37.95 0 10.7 25 1 24 0.406054306 65
225 1 1450 12 1 4 7 22.2 25 6 19 0.406054306 65
94 1 1065 46.583 1 38.583 0 10.7 25 1 24 0.401801067 66
97 1 1550 13.15 1 5.15 7 26.8 42 15 27 0.384918654 66
96 1 1375 3.25 1 4.75 7 24.7 26 11 15 0.384918654 66
64 1 1305 52 1 44 0 8.4 22 2 20 0.384918654 67
80 1 1400 3.25 1 4.75 7 24.7 26 11 15 0.385 67
239 1 1390 42.05 1 34.05 3 6.9 31 -10 41 0.384378768 73
219 1 1250 43.5 1 35.5 1 10.7 25 1 24 0.384378768 73
98 1 1450 46.1681 1 38.1681 1 10.9 29 6 23 0.384378768 73
99 1 1200 46.1681 1 38.1681 1 10.9 29 6 23 0.384378768 73
222 1 1450 46.1681 1 38.1681 1 10.9 29 6 23 0.384378768 73
223 1 1205 46.1681 1 38.1681 1 10.9 29 6 23 0.384378768 73
101 1 1283.5 3.1667 0 11.1667 7 22.3 31 13 18 0.36220423 73
104 1 1234.333 41.9 1 33.9 1 13.4 30 5 25 0.413475128 75
105 1 1295 41.9 1 33.9 1 13.4 30 5 25 0.413475128 75
106 1 1270.5 35 1 27 4 19.2 31 5 26 0.413475128 75
224 1 1450 32 1 24 4 19.2 31 5 26 0.413475128 75
109 1 995 14.6667 1 6.6667 7 22.2 25 6 19 0.413475128 75
33 1 1300 32 1 24 4 19.2 31 5 26 0.407602948 75
34 1 1554.5 32 1 24 4 19.2 31 5 26 0.407602948 75
35 1 1499.5 32 1 24 4 19.2 31 5 26 0.407602948 75
36 1 1587.333 32 1 24 4 19.2 31 5 26 0.407602948 75
142 1 1280 32 1 24 4 19.2 31 5 26 0.407602948 75
167 1 1531 32 1 24 4 19.2 31 5 26 0.407602948 75
168 1 1535 32 1 24 4 19.2 31 5 26 0.407602948 75
229 1 1510 29 0 37 1 17.8 30 1 29 0.40409947 76
41 1 1650.2 45 1 37 1 10.7 25 1 24 0.402105157 77
220 1 1362 50.5 1 42.5 0 10.7 25 1 24 0.396490598 80
43 1 1226.75 35 1 27 3 13.3 28 6 22 0.396490598 80
44 1 1581 41 1 33 1 12.1 32 -15 47 0.396490598 80
169 1 1550 42 1 34 1 13.4 30 5 25 0.394052574 81
45 1 1551 41.2 1 33.2 1 13.4 30 5 25 0.394052574 82
46 1 1745 33 1 25 4 19.2 31 5 26 0.388439222 82
54 1 1457.5 50.8 1 42.8 0 9.6 23 -1 24 0.388439222 90
55 1 1487.4 50.8 1 42.8 0 9.6 23 -1 24 0.388439222 90
48 1 1337.75 52 1 44 0 8.4 24 -3 27 0.388439222 90
51 1 1345.25 44 1 36 1 10.7 25 1 24 0.388439222 90
144 1 1310 44 1 36 1 10.7 25 1 24 0.388439222 90
221 1 1400 35 1 27 3 13.3 28 6 22 0.388439222 90
50 1 1626 42.7333 1 34.7333 1 10.7 25 1 24 0.388439222 90
49 1 1320 49.0167 1 41.0167 0 6.8 26 -3 29 0.388439222 90
52 1 1650 36 1 28 4 21.4 41 7 34 0.388439222 90
53 1 1550 36 1 28 4 21.4 41 7 34 0.388439222 90
237 1 1480 24.5 1 16.5 3 6.9 31 -10 41 0.383797175 93
66 1 1486.2 44.9833 1 36.9833 1 10.7 25 1 24 0.383797175 93
65 1 1400 40.8167 1 32.8167 4 19.2 31 5 26 0.383797175 93
162 1 1500 50.5 1 42.5 0 7.5 25 -5 30 0.377070104 95
178 1 1620 50.5 1 42.5 0 7.5 25 -5 30 0.377070104 95
74 1 1235 10.0333 0 18.0333 7 22.3 31 13 18 0.377070104 95
153 1 1420 27 1 19 5 22.1 36 8 28 0.377247824 95
176 1 1600 45 1 37 1 10.7 25 1 24 0.378345024 97
231 1 1590 45 1 37 1 10.7 25 1 24 0.378345024 97
230 1 1570 45 1 37 1 10.7 25 1 24 0.378345024 101
148 1 1375 44 1 36 1 10.7 25 1 24 0.378345024 101
175 1 1580 44 1 36 1 10.7 25 1 24 0.378345024 101
181 1 1775 44 1 36 1 10.7 25 1 24 0.378345024 101
232 1 1538 49 1 41 0 7.5 25 -5 30 0.38 105
233 1 1481 49 1 41 0 7.5 25 -5 30 0.38 105
234 1 1378 49 1 41 0 7.5 25 -5 30 0.38 105
235 1 1547 49 1 41 0 7.5 25 -5 30 0.38 105
166 1 1531 52 1 44 0 8.4 24 -3 27 0.38 106
157 1 1452 50.5 1 42.5 0 7.5 25 -5 30 0.379526652 110
163 1 1518 50.5 1 42.5 0 7.5 25 -5 30 0.379526652 110
171 1 1555 50.5 1 42.5 0 7.5 25 -5 30 0.379526652 110
177 1 1608 50.5 1 42.5 0 7.5 25 -5 30 0.379526652 110
145 1 1322 49 1 41 0 7.5 25 -5 30 0.379526652 115
165 1 1522 49 1 41 0 7.5 25 -5 30 0.378345024 115
226 1 1600 49 1 41 0 7.5 25 -5 30 0.378345024 115
227 1 1500 49 1 41 0 7.5 25 -5 30 0.378345024 115
228 1 1304 49 1 41 0 7.5 25 -5 30 0.378345024 115
238 1 1464 56 1 48 1 -5.1 23 -16 39 0.384102389 116
150 1 1380 45 1 37 1 10.7 25 1 24 0.39131532 117
236 1 1605 51.5 1 43.5 1 -5.1 23 -16 39 0.39131532 118
182 1 1880 44 1 36 1 13.4 30 5 25 0.39131532 119
159 1 1490 44 1 36 1 13.4 30 5 25 0.387277852 120
139 1 1090 26.5 1 18.5 2 11.1 30 -2 32 0.397247483 126
141 1 1170 26.5 1 18.5 2 11.1 30 -2 32 0.397247483 126
151 1 1390 26.5 1 18.5 2 11.1 30 -2 32 0.397247483 126
143 1 1290 38 1 30 3 6.9 31 -10 41 0.397247483 126
149 1 1380 38 1 30 3 6.9 31 -10 41 0.397247483 126
161 1 1500 38 1 30 3 6.9 31 -10 41 0.397247483 126
146 1 1354 45 1 37 1 10.7 25 1 24 0.392478942 127
147 1 1370 51 1 43 0 8.4 24 -3 27 0.39644267 132
160 1 1500 51 1 43 0 8.4 24 -3 27 0.39644267 132
156 1 1434 45 1 37 1 10.7 25 1 24 0.39644267 132
180 1 1700 45 1 37 1 10.7 25 1 24 0.39644267 132
170 1 1555 44 1 36 1 10.7 25 1 24 0.39644267 132
152 1 1414 44 1 36 1 13.4 30 5 25 0.394097668 136
154 1 1424 44 1 36 1 13.4 30 5 25 0.394097668 136
164 1 1520 44 1 36 1 13.4 30 5 25 0.394097668 136
179 1 1661 44 1 36 1 13.4 30 5 25 0.394097668 136
158 1 1484 38 1 30 1 13.4 30 5 25 0.389503389 140
172 1 1560 38 1 30 1 13.4 30 5 25 0.389503389 140
173 1 1565 38 1 30 1 13.4 30 5 25 0.389503389 140
174 1 1569 38 1 30 1 13.4 30 5 25 0.389503389 140
155 1 1430 45 1 37 1 10.7 25 1 24 0.389503389 141
---
title: "Replicate Table 1 of Rouder and Morey (2012)"
author: "Richard D. Morey"
date: "24/08/2021"
output: html_document
editor_options:
chunk_output_type: console
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
library(dplyr)
library(gt)
library(ggplot2)
library(colorspace)
```
```{r functions}
## Regression functions as they were in 2012
dinvgamma = function (x, shape, scale = 1)
{
if (shape <= 0 | scale <= 0) {
stop("Shape or scale parameter negative in dinvgamma().\n")
}
alpha <- shape
beta <- scale
log.density <- alpha * log(beta) - lgamma(alpha) - (alpha +
1) * log(x) - (beta/x)
return(exp(log.density))
}
integrand.regression=function(g,N,p,R2)
{
a=.5*((N-p-1)*log(1+g)-(N-1)*log(1+g*(1-R2)))
exp(a)*dinvgamma(g,shape=.5,scale=N/2)
}
linearReg.Quad=function(N,p,R2) {
h=integrate(integrand.regression,lower=0,upper=Inf,N=N,p=p,R2=R2)
return(h$value)
}
```
```{r readdata}
## Read from public gist
data_files = gistr::gist('https://gist.github.com/richarddmorey/1bca5c91a5a16a100a07644f9be6d7bf')
# I extracted these values using mathpix because I do not
# have the original .tex file
data_files$files[['table1.tsv']]$content %>%
textConnection() %>%
read.delim(.,
sep = '\t',
header = TRUE) -> tab1
data_files$files[['Bailey_Geary_2009.csv']]$content %>%
textConnection() %>%
read.csv(.,
header = TRUE) %>%
rename(
Density = dpop_30,
Parasites = tpar,
Local = diftemp,
Global = Isosd,
Capacity = CC
) %>%
select(Density, Parasites, Local, Global, Capacity ) -> b_g
```
## Table as published
```{r tab1.1}
tab1 %>%
gt(rowname_col = 'abbr') %>%
cols_label(
R2 = '\\(R^2\\)',
Bm0 = '\\(B_{m0}\\)',
Bmf = '\\(B_{mf}\\)'
) %>%
fmt_scientific(c('Bm0','Bmf')) %>%
tab_header(title = 'TABLE 1',
subtitle = 'Bayes Factor Analysis of Hominid Cranial Capacity (Data From Bailey & Geary, 2009)') %>%
tab_source_note(
source_note = html('<i>Note</i>. Local = local climate; Global = global temperature; Parasites = parasite load; Density
= population density.')
)
```
## Some checking
I wanted to compare the results to the 2012 code, to see whether the differences could be accounted for by integration tweaks.
```{r}
## Do some checks
tab1 %>%
pull(Model) %>%
paste('Capacity ~',.) %>%
sapply(X = ., FUN = function(fmla){
lm(as.formula(fmla), data = b_g) %>%
summary() %>%
`$`('r.squared')
}) -> r2s
npars = stringr::str_count(tab1$Model, pattern = '\\+') + 1
tab1 %>%
pull(Model) %>%
paste('Capacity ~',.) %>%
sapply(X = ., FUN = function(fmla){
BayesFactor::lmBF(as.formula(fmla), data = b_g, rscaleCont = 1) %>%
as.vector()
}) -> bfs
names(bfs) = names(r2s)
bfs2012 = mapply(p = npars,
R2 = r2s,
MoreArgs = list(N = nrow(b_g)),
FUN = linearReg.Quad)
## These are almost exactly the same
tibble(
idx = 1:length(bfs),
bfs = bfs,
bfs2012 = bfs2012,
perc_diff = 100*(bfs - bfs2012)/bfs
) %>%
ggplot(aes(x = idx, y = perc_diff)) +
geom_point() +
scale_x_continuous(
name = 'Model index',
breaks = 1:length(bfs)
) +
scale_y_continuous(
name = 'Difference (% of BayesFactor)',
limits = c(-.001,.001)
) +
ggtitle(label = 'Difference between 2012 BF and BayesFactor') +
theme_minimal()
```
Apparently not. The differences are very small.
## Table as it should be
In the table below, I have computed the values using the `BayesFactor`
package. I have highlighted the background color of the cells based on their original table's deviation from this table; redder cells are "worse". As you can see, the $\cal{M}_13$ row seems to be the main error, but there are still minor deviations elsewhere.
```{r}
tab1 %>%
mutate(
Bm0_2021 = bfs,
Bmf_2021 = bfs / bfs[1],
err_bm0 = abs(100 * (Bm0 - Bm0_2021)/Bm0_2021),
err_bmf = abs(100 * (Bmf - Bmf_2021)/Bmf_2021)
) -> tab1_corrected
tab1_corrected %>%
gt(rowname_col = 'abbr') %>%
cols_hide(c('Bm0','Bmf','err_bm0','err_bmf')) %>%
cols_label(
R2 = '\\(R^2\\)',
Bm0_2021 = '\\(B_{m0}\\)',
Bmf_2021 = '\\(B_{mf}\\)'
) %>%
fmt_scientific(c('Bm0_2021','Bmf_2021')) %>%
tab_header(title = 'TABLE 1',
subtitle = 'Bayes Factor Analysis of Hominid Cranial Capacity (Data From Bailey & Geary, 2009)') %>%
tab_source_note(
source_note = html('<i>Note</i>. Local = local climate; Global = global temperature; Parasites = parasite load; Density
= population density.')
) -> gt_obj
# Coloring of cells
# adapted from https://stackoverflow.com/a/63945239/1129889
heat_palette <- leaflet::colorNumeric(
palette = colorRamp(c("#FFFFFF", "#FF4444"), interpolate = "spline"),
domain = c(tab1_corrected$err_bm0,
tab1_corrected$err_bmf)
)
ht_bm0 <- heat_palette(tab1_corrected$err_bm0)
ht_bmf <- heat_palette(tab1_corrected$err_bmf)
for(i in seq_along(tab1_corrected$err_bm0)) {
gt_obj <- gt_obj %>%
tab_style(
style = cell_fill(color = ht_bm0[i]),
locations = cells_body(columns = "Bm0_2021", rows = i)
)
gt_obj <- gt_obj %>%
tab_style(
style = cell_fill(color = ht_bmf[i]),
locations = cells_body(columns = "Bmf_2021", rows = i)
)
}
gt_obj
```
## Rounded \(R^2\)?
As a check, I wanted to see if the smaller differences could be due to using the rounded \(R^2\) values in the table. Maybe we wanted people to be able to type the value from the table into a calculator and get the Bayes factor from the table.
```{r}
bfs_r2tab = mapply(p = npars,
R2 = tab1$R2,
MoreArgs = list(N = nrow(b_g)),
FUN = linearReg.Quad)
tab1 %>%
mutate(
Bm0_rounded = bfs_r2tab,
Bmf_rounded = bfs_r2tab / bfs_r2tab[1],
err_bm0 = abs(100 * (Bm0 - Bm0_rounded)/Bm0_rounded),
err_bmf = abs(100 * (Bmf - Bmf_rounded)/Bmf_rounded)
) -> tab1_rounded
tab1_rounded %>%
gt(rowname_col = 'abbr') %>%
cols_hide(c('Bm0','Bmf','err_bm0','err_bmf')) %>%
cols_label(
R2 = '\\(R^2\\)',
Bm0_rounded = '\\(B_{m0}\\)',
Bmf_rounded = '\\(B_{mf}\\)'
) %>%
fmt_scientific(c('Bm0_rounded','Bmf_rounded')) %>%
tab_header(title = 'TABLE 1',
subtitle = 'Bayes Factor Analysis of Hominid Cranial Capacity (Data From Bailey & Geary, 2009)') %>%
tab_source_note(
source_note = html('<i>Note</i>. Local = local climate; Global = global temperature; Parasites = parasite load; Density
= population density.')
) -> gt_obj
# Coloring of cells
# adapted from https://stackoverflow.com/a/63945239/1129889
heat_palette <- leaflet::colorNumeric(
palette = colorRamp(c("#FFFFFF", "#FF4444"), interpolate = "spline"),
domain = c(tab1_rounded$err_bm0,
tab1_rounded$err_bmf)
)
ht_bm0 <- heat_palette(tab1_rounded$err_bm0)
ht_bmf <- heat_palette(tab1_rounded$err_bmf)
for(i in seq_along(tab1_rounded$err_bm0)) {
gt_obj <- gt_obj %>%
tab_style(
style = cell_fill(color = ht_bm0[i]),
locations = cells_body(columns = "Bm0_rounded", rows = i)
)
gt_obj <- gt_obj %>%
tab_style(
style = cell_fill(color = ht_bmf[i]),
locations = cells_body(columns = "Bmf_rounded", rows = i)
)
}
gt_obj
```
Using rounded $R^2$ seems to account for the smaller differences in the table.
abbr Model R2 Bm0 Bmf
\(\cal{M}_{f}\) Local+Global+Parasites+Density .7109 3.54e41 1
\(\cal{M}_{1}\) Local+Global+Parasites .567 5.56e27 1.57e-14
\(\cal{M}_{2}\) Local+Global+Density .7072 1.56e42 4.41
\(\cal{M}_{3}\) Local+Parasites+Density .6303 3.82e33 1.08e-8
\(\cal{M}_{4}\) Global+Parasites+Density .7109 4.59e42 12.97
\(\cal{M}_{5}\) Local+Global .5199 1.02e25 2.88e-17
\(\cal{M}_{6}\) Local+Parasites .2429 1.23e8 3.47e-34
\(\cal{M}_{7}\) Local+Density .6258 1.84e34 5.20e-8
\(\cal{M}_{8}\) Global+Parasites .5642 4.02e28 1.14e-13
\(\cal{M}_{9}\) Global+Density .7069 2.17e43 61.03
\(\cal{M}_{10}\) Parasites+Density .6298 4.60e34 1.30e-7
\(\cal{M}_{11}\) Local .091 220 6.21e-40
\(\cal{M}_{12}\) Global .5049 1.10e25 3.11e-17
\(\cal{M}_{13}\) Parasites .2221 1.28e8 3.62e-34
\(\cal{M}_{14}\) Density .6244 2.29e35 6.47e-7
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