Height residuals sim

Background

library(purrr)
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

library(ggplot2)


n <- 10000
dat <- tibble(
    pgs1 = rnorm(n, 0, sqrt(0.3)),
    pgs2 = rnorm(n, 0, sqrt(0.1)),
    pgs3 = rnorm(n, 0, sqrt(0.3)),
    envir = rnorm(n, 0, sqrt(0.3)),
    stoch = rnorm(n, 0, sqrt(0.1)),
    height_pgs = pgs1,
    height_bv = pgs1 + pgs2 + pgs3,
    height_residual = pgs2 + pgs3 + envir + stoch,
    height = height_pgs + height_residual,
    chd_liability = height * 0.1 + envir * 0.2 + rnorm(n),
    chd = rbinom(n, 1, plogis(chd_liability))
)

fixed_effects_meta_analysis <- function(beta_vec, se_vec) {
    w <- 1 / se_vec^2
    beta <- sum(beta_vec * w) / sum(w)
    se <- sqrt(1 / sum(w))
    pval <- pnorm(abs(beta / se), lower.tail = FALSE)
    Qj <- w * (beta-beta_vec)^2
    Q <- sum(Qj)
    Qdf <- length(beta_vec)-1
    # Qjpval <- pchisq(Qj, 1, lower.tail=FALSE)
    Qpval <- pchisq(Q, Qdf, lower.tail=FALSE)
    return(list(beta=beta, se=se, Q=Q, Qpval=Qpval))
}

analysis <- function(dat) {
    fit1 <- glm(chd ~ height, family = binomial, data=dat) %>% summary
    fit2 <- glm(chd ~ height_pgs, family = binomial, data=dat) %>% summary
    fit3 <- glm(chd ~ height_residual, family = binomial, data=dat) %>% summary
    print(fit1$coef[2,1])
    print(fit2$coef[2,1])
    print(fit3$coef[2,1])

    qstat <- fixed_effects_meta_analysis(c(fit2$coefficients[2,1], fit3$coefficients[2,1]), c(fit2$coefficients[2,2], fit3$coefficients[2,2]))
    qstat$b_pgs <- fit2$coefficients[2,1]
    qstat$se_pgs <- fit2$coefficients[2,2]
    qstat$b_residual <- fit3$coefficients[2,1]
    qstat$se_residual <- fit3$coefficients[2,2]
    return(qstat)
}

analysis(dat)

[1] 0.147609
[1] 0.02825637
[1] 0.1912006

$beta
[1] 0.1463785

$se
[1] 0.0191414

$Q
[1] 14.45028

$Qpval
[1] 0.0001439086

$b_pgs
[1] 0.02825637

$se_pgs
[1] 0.03649614

$b_residual
[1] 0.1912006

$se_residual
[1] 0.02248162

sim <- function(n, b_height, b_envir, nsim=1) {
    args <- list(n=n, b_height=b_height, b_envir=b_envir, nsim=nsim) %>% as_tibble()
    dat <- tibble(
        pgs1 = rnorm(n, 0, sqrt(0.3)),
        pgs2 = rnorm(n, 0, sqrt(0.1)),
        pgs3 = rnorm(n, 0, sqrt(0.3)),
        envir = rnorm(n, 0, sqrt(0.3)),
        stoch = rnorm(n, 0, sqrt(0.1)),
        height_pgs = pgs1,
        height_bv = pgs1 + pgs2 + pgs3,
        height_residual = pgs2 + pgs3 + envir + stoch,
        height = height_pgs + height_residual,
        chd_liability = height * b_height + envir * b_envir + rnorm(n),
        chd = rbinom(n, 1, plogis(chd_liability))
    )

    analysis(dat) %>% as_tibble() %>% bind_cols(args)
}

sim(10000, 0.1, 0.5)

[1] 0.1997528
[1] 0.130806
[1] 0.2255813

# A tibble: 1 × 12
   beta     se     Q  Qpval b_pgs se_pgs b_residual se_residual     n b_height
  <dbl>  <dbl> <dbl>  <dbl> <dbl>  <dbl>      <dbl>       <dbl> <dbl>    <dbl>
1 0.199 0.0194  4.87 0.0273 0.131 0.0363      0.226      0.0229 10000      0.1
# ℹ 2 more variables: b_envir <dbl>, nsim <dbl>

param <- expand.grid(
    n = 1000,
    b_height = c(0, 1),
    b_envir = seq(0, 1, 0.1),
    nsim = 1:100
)

param 

        n b_height b_envir nsim
1    1000        0     0.0    1
2    1000        1     0.0    1
3    1000        0     0.1    1
4    1000        1     0.1    1
5    1000        0     0.2    1
6    1000        1     0.2    1
7    1000        0     0.3    1
8    1000        1     0.3    1
9    1000        0     0.4    1
10   1000        1     0.4    1
11   1000        0     0.5    1
12   1000        1     0.5    1
13   1000        0     0.6    1
14   1000        1     0.6    1
15   1000        0     0.7    1
16   1000        1     0.7    1
17   1000        0     0.8    1
18   1000        1     0.8    1
19   1000        0     0.9    1
20   1000        1     0.9    1
21   1000        0     1.0    1
22   1000        1     1.0    1
23   1000        0     0.0    2
24   1000        1     0.0    2
25   1000        0     0.1    2
26   1000        1     0.1    2
27   1000        0     0.2    2
28   1000        1     0.2    2
29   1000        0     0.3    2
30   1000        1     0.3    2
31   1000        0     0.4    2
32   1000        1     0.4    2
33   1000        0     0.5    2
34   1000        1     0.5    2
35   1000        0     0.6    2
36   1000        1     0.6    2
37   1000        0     0.7    2
38   1000        1     0.7    2
39   1000        0     0.8    2
40   1000        1     0.8    2
41   1000        0     0.9    2
42   1000        1     0.9    2
43   1000        0     1.0    2
44   1000        1     1.0    2
45   1000        0     0.0    3
46   1000        1     0.0    3
47   1000        0     0.1    3
48   1000        1     0.1    3
49   1000        0     0.2    3
50   1000        1     0.2    3
51   1000        0     0.3    3
52   1000        1     0.3    3
53   1000        0     0.4    3
54   1000        1     0.4    3
55   1000        0     0.5    3
56   1000        1     0.5    3
57   1000        0     0.6    3
58   1000        1     0.6    3
59   1000        0     0.7    3
60   1000        1     0.7    3
61   1000        0     0.8    3
62   1000        1     0.8    3
63   1000        0     0.9    3
64   1000        1     0.9    3
65   1000        0     1.0    3
66   1000        1     1.0    3
67   1000        0     0.0    4
68   1000        1     0.0    4
69   1000        0     0.1    4
70   1000        1     0.1    4
71   1000        0     0.2    4
72   1000        1     0.2    4
73   1000        0     0.3    4
74   1000        1     0.3    4
75   1000        0     0.4    4
76   1000        1     0.4    4
77   1000        0     0.5    4
78   1000        1     0.5    4
79   1000        0     0.6    4
80   1000        1     0.6    4
81   1000        0     0.7    4
82   1000        1     0.7    4
83   1000        0     0.8    4
84   1000        1     0.8    4
85   1000        0     0.9    4
86   1000        1     0.9    4
87   1000        0     1.0    4
88   1000        1     1.0    4
89   1000        0     0.0    5
90   1000        1     0.0    5
91   1000        0     0.1    5
92   1000        1     0.1    5
93   1000        0     0.2    5
94   1000        1     0.2    5
95   1000        0     0.3    5
96   1000        1     0.3    5
97   1000        0     0.4    5
98   1000        1     0.4    5
99   1000        0     0.5    5
100  1000        1     0.5    5
101  1000        0     0.6    5
102  1000        1     0.6    5
103  1000        0     0.7    5
104  1000        1     0.7    5
105  1000        0     0.8    5
106  1000        1     0.8    5
107  1000        0     0.9    5
108  1000        1     0.9    5
109  1000        0     1.0    5
110  1000        1     1.0    5
111  1000        0     0.0    6
112  1000        1     0.0    6
113  1000        0     0.1    6
114  1000        1     0.1    6
115  1000        0     0.2    6
116  1000        1     0.2    6
117  1000        0     0.3    6
118  1000        1     0.3    6
119  1000        0     0.4    6
120  1000        1     0.4    6
121  1000        0     0.5    6
122  1000        1     0.5    6
123  1000        0     0.6    6
124  1000        1     0.6    6
125  1000        0     0.7    6
126  1000        1     0.7    6
127  1000        0     0.8    6
128  1000        1     0.8    6
129  1000        0     0.9    6
130  1000        1     0.9    6
131  1000        0     1.0    6
132  1000        1     1.0    6
133  1000        0     0.0    7
134  1000        1     0.0    7
135  1000        0     0.1    7
136  1000        1     0.1    7
137  1000        0     0.2    7
138  1000        1     0.2    7
139  1000        0     0.3    7
140  1000        1     0.3    7
141  1000        0     0.4    7
142  1000        1     0.4    7
143  1000        0     0.5    7
144  1000        1     0.5    7
145  1000        0     0.6    7
146  1000        1     0.6    7
147  1000        0     0.7    7
148  1000        1     0.7    7
149  1000        0     0.8    7
150  1000        1     0.8    7
151  1000        0     0.9    7
152  1000        1     0.9    7
153  1000        0     1.0    7
154  1000        1     1.0    7
155  1000        0     0.0    8
156  1000        1     0.0    8
157  1000        0     0.1    8
158  1000        1     0.1    8
159  1000        0     0.2    8
160  1000        1     0.2    8
161  1000        0     0.3    8
162  1000        1     0.3    8
163  1000        0     0.4    8
164  1000        1     0.4    8
165  1000        0     0.5    8
166  1000        1     0.5    8
167  1000        0     0.6    8
168  1000        1     0.6    8
169  1000        0     0.7    8
170  1000        1     0.7    8
171  1000        0     0.8    8
172  1000        1     0.8    8
173  1000        0     0.9    8
174  1000        1     0.9    8
175  1000        0     1.0    8
176  1000        1     1.0    8
177  1000        0     0.0    9
178  1000        1     0.0    9
179  1000        0     0.1    9
180  1000        1     0.1    9
181  1000        0     0.2    9
182  1000        1     0.2    9
183  1000        0     0.3    9
184  1000        1     0.3    9
185  1000        0     0.4    9
186  1000        1     0.4    9
187  1000        0     0.5    9
188  1000        1     0.5    9
189  1000        0     0.6    9
190  1000        1     0.6    9
191  1000        0     0.7    9
192  1000        1     0.7    9
193  1000        0     0.8    9
194  1000        1     0.8    9
195  1000        0     0.9    9
196  1000        1     0.9    9
197  1000        0     1.0    9
198  1000        1     1.0    9
199  1000        0     0.0   10
200  1000        1     0.0   10
201  1000        0     0.1   10
202  1000        1     0.1   10
203  1000        0     0.2   10
204  1000        1     0.2   10
205  1000        0     0.3   10
206  1000        1     0.3   10
207  1000        0     0.4   10
208  1000        1     0.4   10
209  1000        0     0.5   10
210  1000        1     0.5   10
211  1000        0     0.6   10
212  1000        1     0.6   10
213  1000        0     0.7   10
214  1000        1     0.7   10
215  1000        0     0.8   10
216  1000        1     0.8   10
217  1000        0     0.9   10
218  1000        1     0.9   10
219  1000        0     1.0   10
220  1000        1     1.0   10
221  1000        0     0.0   11
222  1000        1     0.0   11
223  1000        0     0.1   11
224  1000        1     0.1   11
225  1000        0     0.2   11
226  1000        1     0.2   11
227  1000        0     0.3   11
228  1000        1     0.3   11
229  1000        0     0.4   11
230  1000        1     0.4   11
231  1000        0     0.5   11
232  1000        1     0.5   11
233  1000        0     0.6   11
234  1000        1     0.6   11
235  1000        0     0.7   11
236  1000        1     0.7   11
237  1000        0     0.8   11
238  1000        1     0.8   11
239  1000        0     0.9   11
240  1000        1     0.9   11
241  1000        0     1.0   11
242  1000        1     1.0   11
243  1000        0     0.0   12
244  1000        1     0.0   12
245  1000        0     0.1   12
246  1000        1     0.1   12
247  1000        0     0.2   12
248  1000        1     0.2   12
249  1000        0     0.3   12
250  1000        1     0.3   12
251  1000        0     0.4   12
252  1000        1     0.4   12
253  1000        0     0.5   12
254  1000        1     0.5   12
255  1000        0     0.6   12
256  1000        1     0.6   12
257  1000        0     0.7   12
258  1000        1     0.7   12
259  1000        0     0.8   12
260  1000        1     0.8   12
261  1000        0     0.9   12
262  1000        1     0.9   12
263  1000        0     1.0   12
264  1000        1     1.0   12
265  1000        0     0.0   13
266  1000        1     0.0   13
267  1000        0     0.1   13
268  1000        1     0.1   13
269  1000        0     0.2   13
270  1000        1     0.2   13
271  1000        0     0.3   13
272  1000        1     0.3   13
273  1000        0     0.4   13
274  1000        1     0.4   13
275  1000        0     0.5   13
276  1000        1     0.5   13
277  1000        0     0.6   13
278  1000        1     0.6   13
279  1000        0     0.7   13
280  1000        1     0.7   13
281  1000        0     0.8   13
282  1000        1     0.8   13
283  1000        0     0.9   13
284  1000        1     0.9   13
285  1000        0     1.0   13
286  1000        1     1.0   13
287  1000        0     0.0   14
288  1000        1     0.0   14
289  1000        0     0.1   14
290  1000        1     0.1   14
291  1000        0     0.2   14
292  1000        1     0.2   14
293  1000        0     0.3   14
294  1000        1     0.3   14
295  1000        0     0.4   14
296  1000        1     0.4   14
297  1000        0     0.5   14
298  1000        1     0.5   14
299  1000        0     0.6   14
300  1000        1     0.6   14
301  1000        0     0.7   14
302  1000        1     0.7   14
303  1000        0     0.8   14
304  1000        1     0.8   14
305  1000        0     0.9   14
306  1000        1     0.9   14
307  1000        0     1.0   14
308  1000        1     1.0   14
309  1000        0     0.0   15
310  1000        1     0.0   15
311  1000        0     0.1   15
312  1000        1     0.1   15
313  1000        0     0.2   15
314  1000        1     0.2   15
315  1000        0     0.3   15
316  1000        1     0.3   15
317  1000        0     0.4   15
318  1000        1     0.4   15
319  1000        0     0.5   15
320  1000        1     0.5   15
321  1000        0     0.6   15
322  1000        1     0.6   15
323  1000        0     0.7   15
324  1000        1     0.7   15
325  1000        0     0.8   15
326  1000        1     0.8   15
327  1000        0     0.9   15
328  1000        1     0.9   15
329  1000        0     1.0   15
330  1000        1     1.0   15
331  1000        0     0.0   16
332  1000        1     0.0   16
333  1000        0     0.1   16
334  1000        1     0.1   16
335  1000        0     0.2   16
336  1000        1     0.2   16
337  1000        0     0.3   16
338  1000        1     0.3   16
339  1000        0     0.4   16
340  1000        1     0.4   16
341  1000        0     0.5   16
342  1000        1     0.5   16
343  1000        0     0.6   16
344  1000        1     0.6   16
345  1000        0     0.7   16
346  1000        1     0.7   16
347  1000        0     0.8   16
348  1000        1     0.8   16
349  1000        0     0.9   16
350  1000        1     0.9   16
351  1000        0     1.0   16
352  1000        1     1.0   16
353  1000        0     0.0   17
354  1000        1     0.0   17
355  1000        0     0.1   17
356  1000        1     0.1   17
357  1000        0     0.2   17
358  1000        1     0.2   17
359  1000        0     0.3   17
360  1000        1     0.3   17
361  1000        0     0.4   17
362  1000        1     0.4   17
363  1000        0     0.5   17
364  1000        1     0.5   17
365  1000        0     0.6   17
366  1000        1     0.6   17
367  1000        0     0.7   17
368  1000        1     0.7   17
369  1000        0     0.8   17
370  1000        1     0.8   17
371  1000        0     0.9   17
372  1000        1     0.9   17
373  1000        0     1.0   17
374  1000        1     1.0   17
375  1000        0     0.0   18
376  1000        1     0.0   18
377  1000        0     0.1   18
378  1000        1     0.1   18
379  1000        0     0.2   18
380  1000        1     0.2   18
381  1000        0     0.3   18
382  1000        1     0.3   18
383  1000        0     0.4   18
384  1000        1     0.4   18
385  1000        0     0.5   18
386  1000        1     0.5   18
387  1000        0     0.6   18
388  1000        1     0.6   18
389  1000        0     0.7   18
390  1000        1     0.7   18
391  1000        0     0.8   18
392  1000        1     0.8   18
393  1000        0     0.9   18
394  1000        1     0.9   18
395  1000        0     1.0   18
396  1000        1     1.0   18
397  1000        0     0.0   19
398  1000        1     0.0   19
399  1000        0     0.1   19
400  1000        1     0.1   19
401  1000        0     0.2   19
402  1000        1     0.2   19
403  1000        0     0.3   19
404  1000        1     0.3   19
405  1000        0     0.4   19
406  1000        1     0.4   19
407  1000        0     0.5   19
408  1000        1     0.5   19
409  1000        0     0.6   19
410  1000        1     0.6   19
411  1000        0     0.7   19
412  1000        1     0.7   19
413  1000        0     0.8   19
414  1000        1     0.8   19
415  1000        0     0.9   19
416  1000        1     0.9   19
417  1000        0     1.0   19
418  1000        1     1.0   19
419  1000        0     0.0   20
420  1000        1     0.0   20
421  1000        0     0.1   20
422  1000        1     0.1   20
423  1000        0     0.2   20
424  1000        1     0.2   20
425  1000        0     0.3   20
426  1000        1     0.3   20
427  1000        0     0.4   20
428  1000        1     0.4   20
429  1000        0     0.5   20
430  1000        1     0.5   20
431  1000        0     0.6   20
432  1000        1     0.6   20
433  1000        0     0.7   20
434  1000        1     0.7   20
435  1000        0     0.8   20
436  1000        1     0.8   20
437  1000        0     0.9   20
438  1000        1     0.9   20
439  1000        0     1.0   20
440  1000        1     1.0   20
441  1000        0     0.0   21
442  1000        1     0.0   21
443  1000        0     0.1   21
444  1000        1     0.1   21
445  1000        0     0.2   21
446  1000        1     0.2   21
447  1000        0     0.3   21
448  1000        1     0.3   21
449  1000        0     0.4   21
450  1000        1     0.4   21
451  1000        0     0.5   21
452  1000        1     0.5   21
453  1000        0     0.6   21
454  1000        1     0.6   21
455  1000        0     0.7   21
456  1000        1     0.7   21
457  1000        0     0.8   21
458  1000        1     0.8   21
459  1000        0     0.9   21
460  1000        1     0.9   21
461  1000        0     1.0   21
462  1000        1     1.0   21
463  1000        0     0.0   22
464  1000        1     0.0   22
465  1000        0     0.1   22
466  1000        1     0.1   22
467  1000        0     0.2   22
468  1000        1     0.2   22
469  1000        0     0.3   22
470  1000        1     0.3   22
471  1000        0     0.4   22
472  1000        1     0.4   22
473  1000        0     0.5   22
474  1000        1     0.5   22
475  1000        0     0.6   22
476  1000        1     0.6   22
477  1000        0     0.7   22
478  1000        1     0.7   22
479  1000        0     0.8   22
480  1000        1     0.8   22
481  1000        0     0.9   22
482  1000        1     0.9   22
483  1000        0     1.0   22
484  1000        1     1.0   22
485  1000        0     0.0   23
486  1000        1     0.0   23
487  1000        0     0.1   23
488  1000        1     0.1   23
489  1000        0     0.2   23
490  1000        1     0.2   23
491  1000        0     0.3   23
492  1000        1     0.3   23
493  1000        0     0.4   23
494  1000        1     0.4   23
495  1000        0     0.5   23
496  1000        1     0.5   23
497  1000        0     0.6   23
498  1000        1     0.6   23
499  1000        0     0.7   23
500  1000        1     0.7   23
501  1000        0     0.8   23
502  1000        1     0.8   23
503  1000        0     0.9   23
504  1000        1     0.9   23
505  1000        0     1.0   23
506  1000        1     1.0   23
507  1000        0     0.0   24
508  1000        1     0.0   24
509  1000        0     0.1   24
510  1000        1     0.1   24
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1756 1000        1     0.8   80
1757 1000        0     0.9   80
1758 1000        1     0.9   80
1759 1000        0     1.0   80
1760 1000        1     1.0   80
1761 1000        0     0.0   81
1762 1000        1     0.0   81
1763 1000        0     0.1   81
1764 1000        1     0.1   81
1765 1000        0     0.2   81
1766 1000        1     0.2   81
1767 1000        0     0.3   81
1768 1000        1     0.3   81
1769 1000        0     0.4   81
1770 1000        1     0.4   81
1771 1000        0     0.5   81
1772 1000        1     0.5   81
1773 1000        0     0.6   81
1774 1000        1     0.6   81
1775 1000        0     0.7   81
1776 1000        1     0.7   81
1777 1000        0     0.8   81
1778 1000        1     0.8   81
1779 1000        0     0.9   81
1780 1000        1     0.9   81
1781 1000        0     1.0   81
1782 1000        1     1.0   81
1783 1000        0     0.0   82
1784 1000        1     0.0   82
1785 1000        0     0.1   82
1786 1000        1     0.1   82
1787 1000        0     0.2   82
1788 1000        1     0.2   82
1789 1000        0     0.3   82
1790 1000        1     0.3   82
1791 1000        0     0.4   82
1792 1000        1     0.4   82
1793 1000        0     0.5   82
1794 1000        1     0.5   82
1795 1000        0     0.6   82
1796 1000        1     0.6   82
1797 1000        0     0.7   82
1798 1000        1     0.7   82
1799 1000        0     0.8   82
1800 1000        1     0.8   82
1801 1000        0     0.9   82
1802 1000        1     0.9   82
1803 1000        0     1.0   82
1804 1000        1     1.0   82
1805 1000        0     0.0   83
1806 1000        1     0.0   83
1807 1000        0     0.1   83
1808 1000        1     0.1   83
1809 1000        0     0.2   83
1810 1000        1     0.2   83
1811 1000        0     0.3   83
1812 1000        1     0.3   83
1813 1000        0     0.4   83
1814 1000        1     0.4   83
1815 1000        0     0.5   83
1816 1000        1     0.5   83
1817 1000        0     0.6   83
1818 1000        1     0.6   83
1819 1000        0     0.7   83
1820 1000        1     0.7   83
1821 1000        0     0.8   83
1822 1000        1     0.8   83
1823 1000        0     0.9   83
1824 1000        1     0.9   83
1825 1000        0     1.0   83
1826 1000        1     1.0   83
1827 1000        0     0.0   84
1828 1000        1     0.0   84
1829 1000        0     0.1   84
1830 1000        1     0.1   84
1831 1000        0     0.2   84
1832 1000        1     0.2   84
1833 1000        0     0.3   84
1834 1000        1     0.3   84
1835 1000        0     0.4   84
1836 1000        1     0.4   84
1837 1000        0     0.5   84
1838 1000        1     0.5   84
1839 1000        0     0.6   84
1840 1000        1     0.6   84
1841 1000        0     0.7   84
1842 1000        1     0.7   84
1843 1000        0     0.8   84
1844 1000        1     0.8   84
1845 1000        0     0.9   84
1846 1000        1     0.9   84
1847 1000        0     1.0   84
1848 1000        1     1.0   84
1849 1000        0     0.0   85
1850 1000        1     0.0   85
1851 1000        0     0.1   85
1852 1000        1     0.1   85
1853 1000        0     0.2   85
1854 1000        1     0.2   85
1855 1000        0     0.3   85
1856 1000        1     0.3   85
1857 1000        0     0.4   85
1858 1000        1     0.4   85
1859 1000        0     0.5   85
1860 1000        1     0.5   85
1861 1000        0     0.6   85
1862 1000        1     0.6   85
1863 1000        0     0.7   85
1864 1000        1     0.7   85
1865 1000        0     0.8   85
1866 1000        1     0.8   85
1867 1000        0     0.9   85
1868 1000        1     0.9   85
1869 1000        0     1.0   85
1870 1000        1     1.0   85
1871 1000        0     0.0   86
1872 1000        1     0.0   86
1873 1000        0     0.1   86
1874 1000        1     0.1   86
1875 1000        0     0.2   86
1876 1000        1     0.2   86
1877 1000        0     0.3   86
1878 1000        1     0.3   86
1879 1000        0     0.4   86
1880 1000        1     0.4   86
1881 1000        0     0.5   86
1882 1000        1     0.5   86
1883 1000        0     0.6   86
1884 1000        1     0.6   86
1885 1000        0     0.7   86
1886 1000        1     0.7   86
1887 1000        0     0.8   86
1888 1000        1     0.8   86
1889 1000        0     0.9   86
1890 1000        1     0.9   86
1891 1000        0     1.0   86
1892 1000        1     1.0   86
1893 1000        0     0.0   87
1894 1000        1     0.0   87
1895 1000        0     0.1   87
1896 1000        1     0.1   87
1897 1000        0     0.2   87
1898 1000        1     0.2   87
1899 1000        0     0.3   87
1900 1000        1     0.3   87
1901 1000        0     0.4   87
1902 1000        1     0.4   87
1903 1000        0     0.5   87
1904 1000        1     0.5   87
1905 1000        0     0.6   87
1906 1000        1     0.6   87
1907 1000        0     0.7   87
1908 1000        1     0.7   87
1909 1000        0     0.8   87
1910 1000        1     0.8   87
1911 1000        0     0.9   87
1912 1000        1     0.9   87
1913 1000        0     1.0   87
1914 1000        1     1.0   87
1915 1000        0     0.0   88
1916 1000        1     0.0   88
1917 1000        0     0.1   88
1918 1000        1     0.1   88
1919 1000        0     0.2   88
1920 1000        1     0.2   88
1921 1000        0     0.3   88
1922 1000        1     0.3   88
1923 1000        0     0.4   88
1924 1000        1     0.4   88
1925 1000        0     0.5   88
1926 1000        1     0.5   88
1927 1000        0     0.6   88
1928 1000        1     0.6   88
1929 1000        0     0.7   88
1930 1000        1     0.7   88
1931 1000        0     0.8   88
1932 1000        1     0.8   88
1933 1000        0     0.9   88
1934 1000        1     0.9   88
1935 1000        0     1.0   88
1936 1000        1     1.0   88
1937 1000        0     0.0   89
1938 1000        1     0.0   89
1939 1000        0     0.1   89
1940 1000        1     0.1   89
1941 1000        0     0.2   89
1942 1000        1     0.2   89
1943 1000        0     0.3   89
1944 1000        1     0.3   89
1945 1000        0     0.4   89
1946 1000        1     0.4   89
1947 1000        0     0.5   89
1948 1000        1     0.5   89
1949 1000        0     0.6   89
1950 1000        1     0.6   89
1951 1000        0     0.7   89
1952 1000        1     0.7   89
1953 1000        0     0.8   89
1954 1000        1     0.8   89
1955 1000        0     0.9   89
1956 1000        1     0.9   89
1957 1000        0     1.0   89
1958 1000        1     1.0   89
1959 1000        0     0.0   90
1960 1000        1     0.0   90
1961 1000        0     0.1   90
1962 1000        1     0.1   90
1963 1000        0     0.2   90
1964 1000        1     0.2   90
1965 1000        0     0.3   90
1966 1000        1     0.3   90
1967 1000        0     0.4   90
1968 1000        1     0.4   90
1969 1000        0     0.5   90
1970 1000        1     0.5   90
1971 1000        0     0.6   90
1972 1000        1     0.6   90
1973 1000        0     0.7   90
1974 1000        1     0.7   90
1975 1000        0     0.8   90
1976 1000        1     0.8   90
1977 1000        0     0.9   90
1978 1000        1     0.9   90
1979 1000        0     1.0   90
1980 1000        1     1.0   90
1981 1000        0     0.0   91
1982 1000        1     0.0   91
1983 1000        0     0.1   91
1984 1000        1     0.1   91
1985 1000        0     0.2   91
1986 1000        1     0.2   91
1987 1000        0     0.3   91
1988 1000        1     0.3   91
1989 1000        0     0.4   91
1990 1000        1     0.4   91
1991 1000        0     0.5   91
1992 1000        1     0.5   91
1993 1000        0     0.6   91
1994 1000        1     0.6   91
1995 1000        0     0.7   91
1996 1000        1     0.7   91
1997 1000        0     0.8   91
1998 1000        1     0.8   91
1999 1000        0     0.9   91
2000 1000        1     0.9   91
2001 1000        0     1.0   91
2002 1000        1     1.0   91
2003 1000        0     0.0   92
2004 1000        1     0.0   92
2005 1000        0     0.1   92
2006 1000        1     0.1   92
2007 1000        0     0.2   92
2008 1000        1     0.2   92
2009 1000        0     0.3   92
2010 1000        1     0.3   92
2011 1000        0     0.4   92
2012 1000        1     0.4   92
2013 1000        0     0.5   92
2014 1000        1     0.5   92
2015 1000        0     0.6   92
2016 1000        1     0.6   92
2017 1000        0     0.7   92
2018 1000        1     0.7   92
2019 1000        0     0.8   92
2020 1000        1     0.8   92
2021 1000        0     0.9   92
2022 1000        1     0.9   92
2023 1000        0     1.0   92
2024 1000        1     1.0   92
2025 1000        0     0.0   93
2026 1000        1     0.0   93
2027 1000        0     0.1   93
2028 1000        1     0.1   93
2029 1000        0     0.2   93
2030 1000        1     0.2   93
2031 1000        0     0.3   93
2032 1000        1     0.3   93
2033 1000        0     0.4   93
2034 1000        1     0.4   93
2035 1000        0     0.5   93
2036 1000        1     0.5   93
2037 1000        0     0.6   93
2038 1000        1     0.6   93
2039 1000        0     0.7   93
2040 1000        1     0.7   93
2041 1000        0     0.8   93
2042 1000        1     0.8   93
2043 1000        0     0.9   93
2044 1000        1     0.9   93
2045 1000        0     1.0   93
2046 1000        1     1.0   93
2047 1000        0     0.0   94
2048 1000        1     0.0   94
2049 1000        0     0.1   94
2050 1000        1     0.1   94
2051 1000        0     0.2   94
2052 1000        1     0.2   94
2053 1000        0     0.3   94
2054 1000        1     0.3   94
2055 1000        0     0.4   94
2056 1000        1     0.4   94
2057 1000        0     0.5   94
2058 1000        1     0.5   94
2059 1000        0     0.6   94
2060 1000        1     0.6   94
2061 1000        0     0.7   94
2062 1000        1     0.7   94
2063 1000        0     0.8   94
2064 1000        1     0.8   94
2065 1000        0     0.9   94
2066 1000        1     0.9   94
2067 1000        0     1.0   94
2068 1000        1     1.0   94
2069 1000        0     0.0   95
2070 1000        1     0.0   95
2071 1000        0     0.1   95
2072 1000        1     0.1   95
2073 1000        0     0.2   95
2074 1000        1     0.2   95
2075 1000        0     0.3   95
2076 1000        1     0.3   95
2077 1000        0     0.4   95
2078 1000        1     0.4   95
2079 1000        0     0.5   95
2080 1000        1     0.5   95
2081 1000        0     0.6   95
2082 1000        1     0.6   95
2083 1000        0     0.7   95
2084 1000        1     0.7   95
2085 1000        0     0.8   95
2086 1000        1     0.8   95
2087 1000        0     0.9   95
2088 1000        1     0.9   95
2089 1000        0     1.0   95
2090 1000        1     1.0   95
2091 1000        0     0.0   96
2092 1000        1     0.0   96
2093 1000        0     0.1   96
2094 1000        1     0.1   96
2095 1000        0     0.2   96
2096 1000        1     0.2   96
2097 1000        0     0.3   96
2098 1000        1     0.3   96
2099 1000        0     0.4   96
2100 1000        1     0.4   96
2101 1000        0     0.5   96
2102 1000        1     0.5   96
2103 1000        0     0.6   96
2104 1000        1     0.6   96
2105 1000        0     0.7   96
2106 1000        1     0.7   96
2107 1000        0     0.8   96
2108 1000        1     0.8   96
2109 1000        0     0.9   96
2110 1000        1     0.9   96
2111 1000        0     1.0   96
2112 1000        1     1.0   96
2113 1000        0     0.0   97
2114 1000        1     0.0   97
2115 1000        0     0.1   97
2116 1000        1     0.1   97
2117 1000        0     0.2   97
2118 1000        1     0.2   97
2119 1000        0     0.3   97
2120 1000        1     0.3   97
2121 1000        0     0.4   97
2122 1000        1     0.4   97
2123 1000        0     0.5   97
2124 1000        1     0.5   97
2125 1000        0     0.6   97
2126 1000        1     0.6   97
2127 1000        0     0.7   97
2128 1000        1     0.7   97
2129 1000        0     0.8   97
2130 1000        1     0.8   97
2131 1000        0     0.9   97
2132 1000        1     0.9   97
2133 1000        0     1.0   97
2134 1000        1     1.0   97
2135 1000        0     0.0   98
2136 1000        1     0.0   98
2137 1000        0     0.1   98
2138 1000        1     0.1   98
2139 1000        0     0.2   98
2140 1000        1     0.2   98
2141 1000        0     0.3   98
2142 1000        1     0.3   98
2143 1000        0     0.4   98
2144 1000        1     0.4   98
2145 1000        0     0.5   98
2146 1000        1     0.5   98
2147 1000        0     0.6   98
2148 1000        1     0.6   98
2149 1000        0     0.7   98
2150 1000        1     0.7   98
2151 1000        0     0.8   98
2152 1000        1     0.8   98
2153 1000        0     0.9   98
2154 1000        1     0.9   98
2155 1000        0     1.0   98
2156 1000        1     1.0   98
2157 1000        0     0.0   99
2158 1000        1     0.0   99
2159 1000        0     0.1   99
2160 1000        1     0.1   99
2161 1000        0     0.2   99
2162 1000        1     0.2   99
2163 1000        0     0.3   99
2164 1000        1     0.3   99
2165 1000        0     0.4   99
2166 1000        1     0.4   99
2167 1000        0     0.5   99
2168 1000        1     0.5   99
2169 1000        0     0.6   99
2170 1000        1     0.6   99
2171 1000        0     0.7   99
2172 1000        1     0.7   99
2173 1000        0     0.8   99
2174 1000        1     0.8   99
2175 1000        0     0.9   99
2176 1000        1     0.9   99
2177 1000        0     1.0   99
2178 1000        1     1.0   99
2179 1000        0     0.0  100
2180 1000        1     0.0  100
2181 1000        0     0.1  100
2182 1000        1     0.1  100
2183 1000        0     0.2  100
2184 1000        1     0.2  100
2185 1000        0     0.3  100
2186 1000        1     0.3  100
2187 1000        0     0.4  100
2188 1000        1     0.4  100
2189 1000        0     0.5  100
2190 1000        1     0.5  100
2191 1000        0     0.6  100
2192 1000        1     0.6  100
2193 1000        0     0.7  100
2194 1000        1     0.7  100
2195 1000        0     0.8  100
2196 1000        1     0.8  100
2197 1000        0     0.9  100
2198 1000        1     0.9  100
2199 1000        0     1.0  100
2200 1000        1     1.0  100

res <- pmap(param, sim) %>% bind_rows()

[1] 0.01800818
[1] 0.1713108
[1] -0.03533014
[1] 0.908396
[1] 0.7226004
[1] 0.8336633
[1] -0.02483897
[1] -0.2079779
[1] 0.04488912
[1] 0.925955
[1] 0.8850862
[1] 0.8545807
[1] 0.1202448
[1] 0.2436984
[1] 0.08063141
[1] 0.8609787
[1] 0.7479215
[1] 0.8527188
[1] 0.04657861
[1] -0.0688618
[1] 0.08413758
[1] 0.7749491
[1] 0.5448883
[1] 0.8190131
[1] 0.1582379
[1] -0.08660318
[1] 0.2608373
[1] 0.9168313
[1] 0.7633909
[1] 0.872402
[1] 0.1245738
[1] 0.07335547
[1] 0.1397185
[1] 0.9379709
[1] 0.594076
[1] 0.9251078
[1] 0.1576102
[1] -0.1699972
[1] 0.2843288
[1] 1.053924
[1] 0.8181886
[1] 1.094401
[1] 0.06949874
[1] -0.03413526
[1] 0.1103236
[1] 1.087968
[1] 0.8316363
[1] 1.047478
[1] 0.1152077
[1] 0.002802937
[1] 0.1596038
[1] 1.125787
[1] 0.6567734
[1] 1.107982
[1] 0.3016479
[1] 0.06682807
[1] 0.3790374
[1] 0.8305476
[1] 0.8080171
[1] 0.8031609
[1] 0.3082349
[1] 0.1111273
[1] 0.3702977
[1] 1.121094
[1] 0.6522728
[1] 1.169902
[1] -0.08301374
[1] 0.0193001
[1] -0.1167894
[1] 0.9211536
[1] 0.7887588
[1] 0.8339168
[1] 0.03078572
[1] -0.02266645
[1] 0.04655282
[1] 0.8061115
[1] 0.6291685
[1] 0.7913655
[1] 0.03328735
[1] -0.05023603
[1] 0.06270138
[1] 0.8787824
[1] 0.915396
[1] 0.7880918
[1] -0.01177001
[1] 0.03006715
[1] -0.02786979
[1] 0.967293
[1] 0.6450512
[1] 1.005635
[1] 0.04265417
[1] 0.1274123
[1] 0.008853428
[1] 1.010021
[1] 0.6990006
[1] 0.9685733
[1] 0.09249367
[1] 0.00856686
[1] 0.1211151
[1] 1.007624
[1] 0.7959734
[1] 0.9282777
[1] 0.07855951
[1] 0.1065402
[1] 0.06753653
[1] 0.9774338
[1] 0.8039937
[1] 0.9739033
[1] 0.171299
[1] -0.06896754
[1] 0.2504849
[1] 1.161212
[1] 0.9572136
[1] 1.146831
[1] 0.2627389
[1] 0.1410106
[1] 0.2934927
[1] 0.9319642
[1] 0.7128393
[1] 1.029284
[1] 0.24297
[1] -0.09307614
[1] 0.3821367
[1] 0.9533576
[1] 0.6324128
[1] 0.983509
[1] 0.2295543
[1] 0.024121
[1] 0.3202023
[1] 0.9488355
[1] 0.5298595
[1] 1.030991
[1] -0.008404144
[1] 0.00748022
[1] -0.01466613
[1] 0.9911581
[1] 0.8966417
[1] 0.9120986
[1] -0.07778952
[1] -0.03061743
[1] -0.09765534
[1] 0.8657621
[1] 0.8534189
[1] 0.8023662
[1] -0.01260535
[1] 0.08167185
[1] -0.0477451
[1] 0.9600275
[1] 0.9563593
[1] 0.8578048
[1] -0.0325202
[1] -0.05463005
[1] -0.02318041
[1] 0.9900471
[1] 0.5593557
[1] 1.056664
[1] 0.110467
[1] 0.1188301
[1] 0.1011585
[1] 1.125856
[1] 0.8914722
[1] 1.016905
[1] 0.1015153
[1] -0.2336163
[1] 0.2129067
[1] 0.825734
[1] 0.5445866
[1] 0.9347913
[1] 0.1905113
[1] 0.08046974
[1] 0.2287108
[1] 1.060865
[1] 0.641314
[1] 1.074024
[1] 0.2556503
[1] -0.01877149
[1] 0.3452285
[1] 1.087922
[1] 0.905905
[1] 1.032408
[1] 0.1571488
[1] 0.08658146
[1] 0.1818787
[1] 0.9574364
[1] 0.5701556
[1] 0.9881419
[1] 0.1139777
[1] -0.1739557
[1] 0.2201816
[1] 1.061472
[1] 0.5232185
[1] 1.143872
[1] 0.2805014
[1] 0.05768243
[1] 0.3567959
[1] 1.022271
[1] 0.6969472
[1] 0.9925273
[1] 0.09477624
[1] 0.1720474
[1] 0.07477356
[1] 0.8082959
[1] 0.7302525
[1] 0.769579
[1] 0.102231
[1] -0.04715775
[1] 0.1522442
[1] 0.8957492
[1] 0.5995536
[1] 0.9064578
[1] 0.05204397
[1] -0.1031586
[1] 0.1086121
[1] 0.8330483
[1] 0.801476
[1] 0.8021612
[1] 0.1416928
[1] 0.1415601
[1] 0.1470328
[1] 0.8008592
[1] 0.7684514
[1] 0.7368972
[1] 0.06538948
[1] -0.2218764
[1] 0.1667502
[1] 0.9056199
[1] 0.7153484
[1] 0.8700194
[1] -0.0174143
[1] -0.007551621
[1] -0.02097384
[1] 1.022345
[1] 0.7492443
[1] 0.9944392
[1] 0.0320208
[1] -0.1805913
[1] 0.1105507
[1] 1.000429
[1] 0.6311309
[1] 1.069257
[1] 0.2573941
[1] 0.1228298
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[1] 1.008342
[1] 0.6883262
[1] 1.070805

library(ggplot2)

res %>% 
    group_by(b_height, b_envir) %>% 
    summarise(Q = mean(Q), pow=sum(Qpval < 0.05)/n()) %>%
    ggplot(., aes(b_envir, Q)) + geom_point(aes(colour=b_height))

`summarise()` has grouped output by 'b_height'. You can override using the
`.groups` argument.

---

sessionInfo()

R version 4.4.3 (2025-02-28)
Platform: aarch64-apple-darwin20
Running under: macOS Sonoma 14.6.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Europe/London
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.5.1 dplyr_1.1.4   purrr_1.0.2  

loaded via a namespace (and not attached):
 [1] vctrs_0.6.5       cli_3.6.3         knitr_1.48        rlang_1.1.4      
 [5] xfun_0.48         generics_0.1.3    jsonlite_1.8.9    labeling_0.4.3   
 [9] glue_1.8.0        colorspace_2.1-1  htmltools_0.5.8.1 scales_1.3.0     
[13] fansi_1.0.6       rmarkdown_2.27    grid_4.4.3        munsell_0.5.1    
[17] evaluate_1.0.1    tibble_3.2.1      fastmap_1.2.0     yaml_2.3.10      
[21] lifecycle_1.0.4   compiler_4.4.3    htmlwidgets_1.6.4 pkgconfig_2.0.3  
[25] farver_2.1.2      digest_0.6.37     R6_2.5.1          tidyselect_1.2.1 
[29] utf8_1.2.4        pillar_1.9.0      magrittr_2.0.3    withr_3.0.2      
[33] tools_4.4.3       gtable_0.3.6