Constructing and visualising experimental designs .monash-blue2[with the edibble R-package]

.info-box.w-50.bg-white[
These slides are viewed best by Chrome or Firefox and occasionally need to be refreshed if elements did not load properly. Please note this web version takes a while to load. See <a href="edibble.pdf">here for the PDF </a>. 
]

---

background-size: cover
class: title-slide
count: false

# .monash-blue[Constructing and visualising experimental designs .monash-blue2[with the `edibble` R-package]]

.bottom_abs.width100[

Presenter: *Emi Tanaka*

Department of Econometrics and Business Statistics, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Monash University, Melbourne, Australia

emi.tanaka@monash.edu

<a href="https://twitter.com/statsgen" style="color:black"> @statsgen</a>

20 May 2021 @ Qld DAF Biometry workshop

]

---

.footnote.black.f4[
 Slides at <a href="https://emitanaka.org/slides/DAF2021/edibble" style="color:#6F7C4D!important;">emitanaka.org/slides/DAF2021/edibble</a>
]

---

.f1.tl[
 .menu-font[today's menu]]

.h-80.overflow-scroll.menu[
.f2.pa3.tl.w-90[

.lh-solid[
Overview of comparative experiments .fr[8.30]  
.monash-gray10.f4[fundamental experimental components]]

.lh-solid[
Constructing experimental designs with .yellow[`edibble`]  .fr[8.40]  
.monash-gray10.f4[`start_design`, `set_context`, `set_units`, `set_trts`, `set_rcrds`, `expect_rcrds`, `nested_in`, `allocate_trts`, `randomise_trts`, `serve_table`, `export_design`]]

.lh-solid[
Visualising experimental designs with .yellow[`deggust`]  .fr[9.50]  
.monash-gray10.f4[`autoplot`]]

.lh-solid[
Designing experiments using a web app with .yellow[`edibbleGUI`]  .fr[10.05]  
.monash-gray10.f4[For the non-coders]
]

---

.f1.tl[
The R-packages: .yellow[`edibble`], .yellow[`deggust`] and .yellow[`edibbleGUI`] are all in active development so many more additions .f3[(and possibly breaking changes)] are envisioned!]

.tl.work-box.w-70[
All code are available are online:

* https://github.com/emitanaka/edibble
* https://github.com/emitanaka/deggust
* https://github.com/emitanaka/edibbleGUI

Not an R user? It's never too late to learn! You can join the community of R learners, e.g. [R for data science](https://www.rfordatasci.com/).
]

---

# 🥗

## Overview of 
# comparative experiments

---

# A minimal comparative experiment

.flex[
.w-70[
.info-box[
There are **three components** that are *necessary* to run a *comparative* experiment:
  
* a set of experimental units `$(\Omega)$`,
* a set of treatments `$(\mathcal{T})$`, and
* allocation of treatments to experimental units `$(D:\Omega\rightarrow\mathcal{T})$`
  
{{content}}

]]
.w-30[
.pl3[
.info-box[
**Experimental unit** is the smallest unit that the treatment can be independently applied to.
 
**Observational unit** is the unit in which the response is measured on.
]]
]
]

.footnote.black[
Bailey (2008) Design of comparative experiments
 
]

and for the analysis of experiment, you additionally require the:

* response measure on observational units `$(\boldsymbol{Y})$`.

---

# Blocking units

.info-box.w-70[
**Blocks**, also called **cluster**,  are units that group some other units (e.g. experimental unit) such that the units within the same block (cluster) are alike (homogeneous).

]

* Essentially **blocks are a unit factor** which nest another unit factor within it.

.w-70[
* An experimental unit, observational unit and blocking unit are all just simply referred to as "unit" in edibble.
]

---

# `edibble` implementing the "grammar of experimental design"

.info-box[
The **grammar of experimental design** is a framework that functionally maps the fundamental components of an experiment to an object oriented system to build and modify the experimental design.  
]

* In `edibble`, the design is built step-by-step with each step modularised to an individual function. 
--

* The three main components of `edibble` are:
   1. units, 
   1. treatments, and 
   1. allocation of treatments to units

* An optional component is records that capture any measurement taken on units (e.g. responses).

---

# 🍲
# Constructing experimental designs with .yellow[edibble]

.f2.animate__animated.animate__flash.red.b.animate__delay-1s[
 This package is still experimental!
]

---
class: middle center

```r
remotes::install_github("emitanaka/edibble")

library(edibble)
```
]

.f2.animate__animated.animate__flash.red.b[
 Rapid development phase &mdash; use with caution 
]

---

# `edibble::start_design()`

* Begin with `start_design()`

```r
library(edibble)
start_design()
```

* This doesn't do much except create a new **edibble design** object.
* An edibble design contains an **edibble graph** (and later **edibble table**)

* You can give it a name to your design &mdash; think of it as the title of your experiment

```r
start_design("My diet experiment")
```
<img src="images//des-start-name.svg" width="100%" style="display: block; margin: auto;" />

---

# `edibble::set_context()`

* Set small notes that remind you the context of the experiment

```r
start_design("My diet experiment") %>% 
  set_context(aim = "Understand relation between diet and weight gain",
              experimenter = "Taylor Alwyn {.email tswift@fakemail.com}",
              "More details in {.file details.txt}")
```

* Context data is preserved in the object, displayed when object is printed and can be exported

.absolute.right-1.bottom--20.w-40[
.idea-box[
Persistent reminder of experimental context so information is not lost in your email or elsewhere!
]]

---

# `edibble::set_units()` .f4[Part 1]

* A .monash-blue["**unit**"] in edibble is any entity, physical or otherwise, that pertain to the experiment.
--

* A _single integer is a shorthand for the number of levels_.

```r
start_design("My diet experiment") %>% 
* set_units(subject = 20)
```
<img src="images//des-subject.svg" width="100%" style="display: block; margin: auto;" />

* Above specify there are **20 subjects** for the experiment.
--

<ul>
<li>Under the hood, there is an edibble graph that contains:</li>

<ul class="fa-ul">
 <li>a node corresponding to the variable subject and</li>
 <li>20 other nodes corresponding to the levels associated with subject.</li>
</ul>
</ul>

---

# An edibble graph

The full graph:
.f4[

```r
set.seed(1)
library(edibble)
g <- start_design() %>% 
 set_units(subject = 20)
plot(g, view = "all")
```

<img src="images/des-plot-all-1.png" width="360" style="display: block; margin: auto;" />
]
]
.w-30.br[

```r
# default
plot(g, view = "high")
```

<img src="images/des-plot-high-1.png" width="216" style="display: block; margin: auto;" />
]

]
.w-30[
.f4[

```r
plot(g, view = "low", 
     layout = igraph::layout_as_tree, 
     asp = 10)
```

<img src="images/des-plot-low-1.png" width="288" style="display: block; margin: auto;" />
]
]

]

---

# An edibble table

```r
start_design("My diet experiment") %>% 
 set_units(subject = 20) %>% 
* serve_table()
```
.overflow-scroll.h-60[
<img src="images//des-table.svg" width="100%" style="display: block; margin: auto;" />
]

---

# `edibble::set_units()` .f4[Part 2]

* A *string vector* is a short hand for the names of the levels.

```r
start_design("My diet experiment") %>% 
* set_units(subject = c("Bettie", "Javid", "Yohan", "Marco", "Joani",
* "Tynika", "Lakendrick", "Stephanos", "Lavonda", "Benny",
* "Daniell", "Juanito", "Kele", "Delance", "Shekelia",
* "Meghan", "Lynzie", "Viraaj", "Jeffrey", "Sunni"))
```
<img src="images//des-level-name.svg" width="100%" style="display: block; margin: auto;" />

---

# Seeing the level names in edibble table

```r
start_design("My diet experiment") %>%
 set_units(subject = c("Bettie", "Javid", "Yohan", "Marco", "Joani", 
 "Tynika", "Lakendrick", "Stephanos", "Lavonda", "Benny", 
 "Daniell", "Juanito", "Kele", "Delance", "Shekelia", 
 "Meghan", "Lynzie", "Viraaj", "Jeffrey", "Sunni")) %>% 
* serve_table()
```
.overflow-scroll.h-40[
<img src="images//des-table-name.svg" width="100%" style="display: block; margin: auto;" />
]

---

# `edibble::set_units()` .f4[Part 3]

* _The argument name can be anything!_
* So user may use names that match the experimental context.
--

```r
start_design("My diet experiment") %>% 
* set_units(fly = 20)
```
<img src="images//des-fly.svg" width="100%" style="display: block; margin: auto;" />
* Above reads that there are **20 flies** in this diet experiment.
--

```r
start_design("My diet experiment") %>% 
* set_units(pig = 20)
```
* Now it reads that there are **20 pigs** in this diet experiment.

---

# `edibble::set_units()` .f4[Part 4]

* You can add "block" units, or any other types of "units".

```r
start_design("My diet experiment") %>% 
* set_units(pen = 10,
* pig = 50)
```
<img src="images//des-pen-pig.svg" width="100%" style="display: block; margin: auto;" />
* Above reads that there are **10 pens** and **50 pigs**.

* What do you think happens if we `serve_table()` on this? What's your expectation of the output?

---

# Relationship between variables

.info-box.w-60[
We say that an edibble graph is **reconcilable** to an edibble table if for every variable, each level of the variable has a single linkage with level of another variable.

]
--

* Below edibble graph cannot be *reconciled* to an edibble table

```r
start_design("My diet experiment") %>% 
  set_units(pen = 10, 
            pig = 50) %>% 
  serve_table() 
```

---

# `edibble::nested_in()` .f4[Part 1]

* But the units must be related in someway.

```r
start_design("My diet experiment") %>% 
 set_units(pen = 10, 
* pig = nested_in(pen, 5))
```
<img src="images//des-nest.svg" width="100%" style="display: block; margin: auto;" />
* Above reads that there are **10 pens** and **5 pigs** in each pen.

---

# The edibble table with nesting structure

```r
start_design("My diet experiment") %>% 
 set_units(pen = 10, 
 pig = nested_in(pen, 5)) %>% 
* serve_table()
```
.overflow-scroll.h---300[
<img src="images//des-nest-table.svg" width="100%" style="display: block; margin: auto;" />
]

---

# `edibble::nested_in()` .f4[Part 2]

* More than one level of nesting:

```r
start_design("My diet experiment") %>% 
 set_units(pen = 10, 
* pig = nested_in(pen, 5),
* time = nested_in(pig, 3)) %>%
 serve_table()
```
.overflow-scroll.h---150[
<img src="images//des-nest-further-table.svg" width="100%" style="display: block; margin: auto;" />
]
* Above reads that there are **10 pens**, **5 pigs** in each pen, and **3 time points** observed for each pig.

---

# `edibble::nested_in()` .f4[Part 3]

* Syntactic sugar for unbalanced unit structure. Again, the units don't need to be physical objects

```r
start_design("My diet experiment") %>% 
 set_units(pen = 10, 
* pig = nested_in(pen, 1:2 ~ 5,
* 3 ~ 4,
* . ~ 2),
 time = nested_in(pig, 3)) 
```
<img src="images//des-unstructured.svg" width="100%" style="display: block; margin: auto;" />
* Above reads that there are **10 pens**, **5 pigs** in pens 1 & 2, **4 pigs** in pen 3, and **2 pigs** in the remaining pens (so a total of `$2\times 5 + 4 + 2 \times 7 = 28$` pigs), and **3 time points** observed for each pig.

---

# `edibble::nested_in()` .f4[Part 4]

* You can refer units by its label instead of level:

```r
start_design("My diet experiment") %>% 
 set_units(pen = c("A", "B", "C", "D", "E", "F", "G", "H", "I", "J"), 
* pig = nested_in(pen, c("A", "B") ~ 5,
* "C" ~ 4,
* . ~ 2),
 time = nested_in(pig, 3)) 
```
<img src="images//des-unstructured-named.svg" width="100%" style="display: block; margin: auto;" />

---

# `edibble::set_trts()` .f4[Part 1]

* Treatment factors are like "units" but some distinguishable attributes added to the object if you use `set_trts`.

```r
start_design("My diet experiment") %>% 
* set_trts(diet = c("NF", "HCD", "HFD", "HPD"))
```
<img src="images//des-trts.svg" width="100%" style="display: block; margin: auto;" />
--

* Below looks the same as above but also encodes another (long) label as well. .f4[Note: long label not used yet downstream.]

```r
start_design("My diet experiment") %>% 
* set_trts(diet = c(  "normal food" = "NF",
*                "high-carbon diet" = "HCD",
*                   "high fat diet" = "HFD",
*               "high protein diet" = "HPD"))
```

---

# `edibble::set_trts()` .f4[Part 2]

* You can set the treatment first then units or vice-versa.

```r
start_design("My diet experiment") %>% 
 set_units(pen = 10) %>% 
 set_trts(diet = c("NF", "HCD", "HFD", "HPD")) 
```
<img src="images//des-diet-exp.svg" width="100%" style="display: block; margin: auto;" />

```r
start_design("My diet experiment") %>% 
 set_trts(diet = c("NF", "HCD", "HFD", "HPD")) %>% 
 set_units(pen = 10)
```
<img src="images//des-diet-exp2.svg" width="100%" style="display: block; margin: auto;" />

---

# `edibble::set_trts()` .f4[Part 3]

* Factorial treatments

```r
start_design("My diet experiment") %>% 
* set_trts(type = c("carb", "fat", "protein"),
* level = c("high", "low"))
```
<img src="images//des-factorial.svg" width="100%" style="display: block; margin: auto;" />

---

# Setting variables later

* You can break the unit or treatment factors to another function later in the pipeline:

```r
start_design("My diet experiment") %>% 
 set_trts(type = c("carb", "fat", "protein")) %>% 
 set_units(pen = 10) %>% 
 set_trts(level = c("high", "low")) %>% 
 set_units(pig = nested_in(pen, 5)) %>% 
 set_units(time = nested_in(pig, 3))
```
<img src="images//des-break-functions.svg" width="100%" style="display: block; margin: auto;" />

---

# `edibble::add_trts()` .f4[Part 1]

* Add specific treatment levels if the treatment is not factorial.
* Each matching factor levels should be unique.

```r
start_design("My diet experiment") %>% 
 add_trts(diet = c("carb", "carb", "protein", "fat"),
 breed = c("standard", "new", "standard", "standard"))
```
<img src="images//des-add.svg" width="100%" style="display: block; margin: auto;" />

---

# `edibble::add_trts()` .f4[Part 2]

* Add specific treatment levels if the treatment is not factorial.
* Each matching factor levels should be unique.

```r
start_design("My diet experiment") %>% 
 set_trts(diet = c("carb", "protein", "fat"),
 breed = c("standard", "new")) %>% 
 add_trts(diet = c("carb", "carb"),
 breed = c("standard", "standard"))
```
<img src="images//des-add2.svg" width="100%" style="display: block; margin: auto;" />

---

# Revisiting the pig study

```r
library(edibble)
des <- start_design("My diet experiment") %>% 
 set_trts(diet = c("carb", "protein", "fat"),
 breed = c("standard", "new")) %>% 
 set_units(pen = 10,
 pig = nested_in(pen, 5))
```

---

# `edibble::allocate_trts()` .f4[Part 1]

```r
des %>% 
* allocate_trts( ~ pen)
```

* Above is the same as below.

```r
des %>% 
* allocate_trts(diet:breed ~ pen)
```

* If treatment is not specified, factorial combination is assumed.

* But you can assign a treatment factor to another unit factor instead.

```r
des %>% 
* allocate_trts(diet ~ pen,
*               breed ~ pig)
```

* Above is like the classic split-plot design where `diet` is allocated to `pen` and `breed` is allocated to `pig`.

.idea-box.w-60[
Here, the experimental unit is easy to identify. 
]
</div>

---

# `edibble::allocate_trts()` .f4[Part 2]

```r
des %>% 
* allocate_trts(diet ~ pen,
* breed ~ pig) %>%
 serve_table()
```
.overflow-scroll.h-50[
<img src="images//des-allocate-asciicast.svg" width="100%" style="display: block; margin: auto;" />
]

.absolute.right-1.bottom-3[
.info-box.w-70[
Do you notice anything about the treatment order?  
{{content}}
]
]

Yup, it's systematically ordered!

---

# `edibble::randomise_trts()`

```r
*set.seed(1)
des %>% 
 allocate_trts(diet ~ pen,
 breed ~ pig) %>% 
* randomise_trts() %>%
 serve_table() 
```
.overflow-scroll.h-50[
<img src="images//des-randomise-aciicast.svg" width="100%" style="display: block; margin: auto;" />
]

---

# Mix and match with other tools

* A lot of recent research efforts in experimental design are in developing algorithms to find the optimal design.
--

* `edibble` doesn't aim to be the best at randomisation and never will.
* Rather, the hope is that this step is replaced by others' great work!

* Data: 400 varieties in two blocks of 20 columns and 40 rows

.f4.flex[
.w-50[

```r
rc <- start_design("od") %>% 
 set_units(Rep = 2,
 Row = nested_in(Rep, 40),
 Plot = nested_in(Row, 20)) %>% 
 set_trts(Variety = 400) %>% 
 allocate_trts(Variety ~ Plot) %>% 
 serve_table() %>% 
 dplyr::mutate(across(Rep:Variety, as.factor))
```
]
.w-50[
.overflow-scroll.h---150.f4[

```r
od::od(fixed = ~ 1, 
       random = ~ Variety + Rep:Row,
       permute = ~ Variety, swap = ~ Rep,
       search = 'random',
       data = rc, maxit = 1000)
```

```
## Thu May 20 08:57:12 2021
## Initial A-value = 0.144458 (400 A-equations; rank C 400)
## Final A-value after 1000 iterations: 0.144227
```

```
## $permutation
## [1] 718 564 253 4 346 396 637 265 70 10 11 755 225 14 471 694 218 18 202 20 95 393 590 649 392 294 27 93 29 30 120 32 580 16 542 674 538 38 102 203 296 343 241 44 45 540 332 706 555 268 340 546 53 593 69 402 147 726 176 60 214 62 704 64 175 587 67 632 286 169 530 639 171 767 322 675 77 683
## [79] 723 762 145 305 111 152 506 86 426 484 772 90 562 76 585 252 21 96 97 272 797 638 526 761 103 133 105 591 248 232 109 624 83 297 113 114 115 116 117 550 25 708 489 122 561 777 604 451 659 748 791 130 131 132 104 134 749 717 500 138 139 219 427 142 770 144 81 162 199 148 149 686 151 84 303 154 255 251
## [157] 727 656 159 642 275 125 163 164 165 166 167 168 703 557 514 333 695 709 65 87 517 518 126 180 181 664 183 413 462 186 273 458 552 190 191 192 193 194 753 196 732 423 179 200 201 92 88 204 485 689 501 185 209 210 211 779 386 61 549 216 217 17 763 410 221 257 35 224 740 784 2 228 229 230 464 769 737 714
## [235] 395 236 378 40 188 240 756 594 243 283 66 246 247 107 249 250 156 94 610 254 488 157 222 601 259 711 338 262 263 264 8 266 697 529 796 293 389 494 187 274 161 276 277 278 127 700 281 282 454 284 285 420 497 288 289 311 291 292 374 173 295 741 320 298 172 300 301 653 419 304 82 752 520 575 525 42 581 312
## [313] 54 314 324 13 486 408 406 7 416 75 323 315 189 326 512 48 317 330 331 663 5 576 335 336 553 261 339 51 626 342 310 344 177 52 347 348 208 670 267 352 353 354 705 356 445 358 510 360 361 586 363 364 49 150 367 399 369 370 371 91 373 684 577 696 377 521 379 583 381 108 524 754 385 693 205 437 271 498
## [391] 391 738 596 112 136 350 629 398 239 313 401 799 74 404 428 788 407 318 409 220 688 412 184 414 231 321 545 418 460 280 470 422 198 424 425 548 123 129 628 430 615 432 387 733 435 436 388 438 439 440 441 442 443 444 609 533 447 736 101 678 722 452 453 362 455 800 476 368 775 212 599 349 463 366 158 466 467 468
## [469] 469 655 570 472 473 522 620 457 648 551 479 41 121 482 483 238 433 329 79 155 774 490 760 647 160 390 692 680 287 325 528 245 207 502 503 504 137 26 507 508 6 359 511 327 306 634 582 719 383 178 153 99 141 474 523 573 309 449 527 662 739 765 531 532 702 795 376 536 235 37 539 46 541 55 543 237 537 793
## [547] 85 59 39 611 421 405 337 554 223 556 170 776 493 712 547 57 563 345 771 58 357 731 569 560 571 792 446 574 384 334 78 578 579 496 290 515 380 584 213 244 505 588 589 728 745 592 666 47 595 22 597 598 461 316 411 602 603 146 605 600 758 499 43 3 118 612 613 480 431 616 781 627 619 475 682 725 623 110
## [625] 382 341 618 429 397 630 631 660 633 607 635 495 394 100 72 640 641 534 643 50 645 710 773 477 715 375 665 652 302 36 269 566 351 658 567 68 661 608 465 182 651 568 667 668 669 71 415 672 673 654 509 676 677 450 679 33 790 128 519 270 448 671 73 258 206 690 328 636 279 34 417 535 750 798 699 365 701 227
## [703] 9 63 355 691 707 31 174 400 260 15 713 234 19 143 606 1 516 720 721 308 487 724 622 242 256 23 233 730 646 197 456 734 735 729 685 119 644 544 614 742 743 744 106 746 747 621 135 657 751 513 559 372 12 403 757 140 759 491 215 80 687 764 299 766 28 768 625 716 565 89 226 481 459 558 124 778 478 780
## [781] 617 782 783 492 785 786 787 319 789 681 98 572 24 794 195 650 307 698 56 434 1000 802 803 938 1490 806 886 1216 1188 810 1236 1313 1268 1565 815 1233 1112 1010 983 1183 821 1174 823 824 1416 1427 1456 1312 829 1035 1142 1343 1524 877 1584 947 1295 838 1408 840 1336 1141 1351 884 1553 1307 1005 1391 1326 850 851 1458 1437 1557 855 856 857 858
## [859] 1244 1445 1108 1369 863 1014 1249 866 867 868 869 859 871 1459 901 1039 1109 1347 834 878 882 880 881 945 963 1163 1139 1030 1175 1201 832 904 891 1314 1267 1080 895 896 897 1096 1140 1585 1600 1383 903 890 1250 1211 907 908 845 910 1463 912 913 914 930 916 889 1442 1110 872 921 1095 923 1011 1448 926 1538 1440 989 994 1531 932 1577 1090 935 1061
## [937] 1567 920 1213 1015 1088 1504 873 1483 1117 902 836 1530 949 950 1059 952 953 954 955 1092 918 818 959 1055 1275 1473 1229 1062 965 966 1306 968 1566 1158 971 981 1207 1025 975 976 1570 1409 1356 1187 1328 982 1338 984 985 1551 987 988 929 990 991 1203 1526 915 842 956 997 998 1182 801
## [ reached getOption("max.print") -- omitted 600 entries ]
## 
## $criterion
## [1] 0.1442267
## 
## $design
## Rep Row Plot Variety
## 1 Rep1 Row1 Plot1 Variety318
## 2 Rep1 Row1 Plot2 Variety164
## 3 Rep1 Row1 Plot3 Variety253
## 4 Rep1 Row1 Plot4 Variety4
## 5 Rep1 Row1 Plot5 Variety346
## 6 Rep1 Row1 Plot6 Variety396
## 7 Rep1 Row1 Plot7 Variety237
## 8 Rep1 Row1 Plot8 Variety265
## 9 Rep1 Row1 Plot9 Variety70
## 10 Rep1 Row1 Plot10 Variety10
## 11 Rep1 Row1 Plot11 Variety11
## 12 Rep1 Row1 Plot12 Variety355
## 13 Rep1 Row1 Plot13 Variety225
## 14 Rep1 Row1 Plot14 Variety14
## 15 Rep1 Row1 Plot15 Variety71
## 16 Rep1 Row1 Plot16 Variety294
## 17 Rep1 Row1 Plot17 Variety218
## 18 Rep1 Row1 Plot18 Variety18
## 19 Rep1 Row1 Plot19 Variety202
## 20 Rep1 Row1 Plot20 Variety20
## 21 Rep1 Row2 Plot21 Variety95
## 22 Rep1 Row2 Plot22 Variety393
## 23 Rep1 Row2 Plot23 Variety190
## 24 Rep1 Row2 Plot24 Variety249
## 25 Rep1 Row2 Plot25 Variety392
## 26 Rep1 Row2 Plot26 Variety294
## 27 Rep1 Row2 Plot27 Variety27
## 28 Rep1 Row2 Plot28 Variety93
## 29 Rep1 Row2 Plot29 Variety29
## 30 Rep1 Row2 Plot30 Variety30
## 31 Rep1 Row2 Plot31 Variety120
## 32 Rep1 Row2 Plot32 Variety32
## 33 Rep1 Row2 Plot33 Variety180
## 34 Rep1 Row2 Plot34 Variety16
## 35 Rep1 Row2 Plot35 Variety142
## 36 Rep1 Row2 Plot36 Variety274
## 37 Rep1 Row2 Plot37 Variety138
## 38 Rep1 Row2 Plot38 Variety38
## 39 Rep1 Row2 Plot39 Variety102
## 40 Rep1 Row2 Plot40 Variety203
## 41 Rep1 Row3 Plot41 Variety296
## 42 Rep1 Row3 Plot42 Variety343
## 43 Rep1 Row3 Plot43 Variety241
## 44 Rep1 Row3 Plot44 Variety44
## 45 Rep1 Row3 Plot45 Variety45
## 46 Rep1 Row3 Plot46 Variety140
## 47 Rep1 Row3 Plot47 Variety332
## 48 Rep1 Row3 Plot48 Variety306
## 49 Rep1 Row3 Plot49 Variety155
## 50 Rep1 Row3 Plot50 Variety268
## 51 Rep1 Row3 Plot51 Variety340
## 52 Rep1 Row3 Plot52 Variety146
## 53 Rep1 Row3 Plot53 Variety53
## 54 Rep1 Row3 Plot54 Variety193
## 55 Rep1 Row3 Plot55 Variety69
## 56 Rep1 Row3 Plot56 Variety2
## 57 Rep1 Row3 Plot57 Variety147
## 58 Rep1 Row3 Plot58 Variety326
## 59 Rep1 Row3 Plot59 Variety176
## 60 Rep1 Row3 Plot60 Variety60
## 61 Rep1 Row4 Plot61 Variety214
## 62 Rep1 Row4 Plot62 Variety62
## 63 Rep1 Row4 Plot63 Variety304
## 64 Rep1 Row4 Plot64 Variety64
## 65 Rep1 Row4 Plot65 Variety175
## 66 Rep1 Row4 Plot66 Variety187
## 67 Rep1 Row4 Plot67 Variety67
## 68 Rep1 Row4 Plot68 Variety232
## 69 Rep1 Row4 Plot69 Variety286
## 70 Rep1 Row4 Plot70 Variety169
## 71 Rep1 Row4 Plot71 Variety130
## 72 Rep1 Row4 Plot72 Variety239
## 73 Rep1 Row4 Plot73 Variety171
## 74 Rep1 Row4 Plot74 Variety367
## 75 Rep1 Row4 Plot75 Variety322
## 76 Rep1 Row4 Plot76 Variety275
## 77 Rep1 Row4 Plot77 Variety77
## 78 Rep1 Row4 Plot78 Variety283
## 79 Rep1 Row4 Plot79 Variety323
## 80 Rep1 Row4 Plot80 Variety362
## 81 Rep1 Row5 Plot81 Variety145
## 82 Rep1 Row5 Plot82 Variety305
## 83 Rep1 Row5 Plot83 Variety111
## 84 Rep1 Row5 Plot84 Variety152
## 85 Rep1 Row5 Plot85 Variety106
## 86 Rep1 Row5 Plot86 Variety86
## 87 Rep1 Row5 Plot87 Variety26
## 88 Rep1 Row5 Plot88 Variety84
## 89 Rep1 Row5 Plot89 Variety372
## 90 Rep1 Row5 Plot90 Variety90
## 91 Rep1 Row5 Plot91 Variety162
## 92 Rep1 Row5 Plot92 Variety76
## 93 Rep1 Row5 Plot93 Variety185
## 94 Rep1 Row5 Plot94 Variety252
## 95 Rep1 Row5 Plot95 Variety21
## 96 Rep1 Row5 Plot96 Variety96
## 97 Rep1 Row5 Plot97 Variety97
## 98 Rep1 Row5 Plot98 Variety272
## 99 Rep1 Row5 Plot99 Variety397
## 100 Rep1 Row5 Plot100 Variety238
## 101 Rep1 Row6 Plot101 Variety126
## 102 Rep1 Row6 Plot102 Variety361
## 103 Rep1 Row6 Plot103 Variety103
## 104 Rep1 Row6 Plot104 Variety133
## 105 Rep1 Row6 Plot105 Variety105
## 106 Rep1 Row6 Plot106 Variety191
## 107 Rep1 Row6 Plot107 Variety248
## 108 Rep1 Row6 Plot108 Variety232
## 109 Rep1 Row6 Plot109 Variety109
## 110 Rep1 Row6 Plot110 Variety224
## 111 Rep1 Row6 Plot111 Variety83
## 112 Rep1 Row6 Plot112 Variety297
## 113 Rep1 Row6 Plot113 Variety113
## 114 Rep1 Row6 Plot114 Variety114
## 115 Rep1 Row6 Plot115 Variety115
## 116 Rep1 Row6 Plot116 Variety116
## 117 Rep1 Row6 Plot117 Variety117
## 118 Rep1 Row6 Plot118 Variety150
## 119 Rep1 Row6 Plot119 Variety25
## 120 Rep1 Row6 Plot120 Variety308
## 121 Rep1 Row7 Plot121 Variety89
## 122 Rep1 Row7 Plot122 Variety122
## 123 Rep1 Row7 Plot123 Variety161
## 124 Rep1 Row7 Plot124 Variety377
## 125 Rep1 Row7 Plot125 Variety204
## 126 Rep1 Row7 Plot126 Variety51
## 127 Rep1 Row7 Plot127 Variety259
## 128 Rep1 Row7 Plot128 Variety348
## 129 Rep1 Row7 Plot129 Variety391
## 130 Rep1 Row7 Plot130 Variety130
## 131 Rep1 Row7 Plot131 Variety131
## 132 Rep1 Row7 Plot132 Variety132
## 133 Rep1 Row7 Plot133 Variety104
## 134 Rep1 Row7 Plot134 Variety134
## 135 Rep1 Row7 Plot135 Variety349
## 136 Rep1 Row7 Plot136 Variety317
## 137 Rep1 Row7 Plot137 Variety100
## 138 Rep1 Row7 Plot138 Variety138
## 139 Rep1 Row7 Plot139 Variety139
## 140 Rep1 Row7 Plot140 Variety219
## 141 Rep1 Row8 Plot141 Variety27
## 142 Rep1 Row8 Plot142 Variety142
## 143 Rep1 Row8 Plot143 Variety370
## 144 Rep1 Row8 Plot144 Variety144
## 145 Rep1 Row8 Plot145 Variety81
## 146 Rep1 Row8 Plot146 Variety162
## 147 Rep1 Row8 Plot147 Variety199
## 148 Rep1 Row8 Plot148 Variety148
## 149 Rep1 Row8 Plot149 Variety149
## 150 Rep1 Row8 Plot150 Variety286
## 151 Rep1 Row8 Plot151 Variety151
## 152 Rep1 Row8 Plot152 Variety84
## 153 Rep1 Row8 Plot153 Variety303
## 154 Rep1 Row8 Plot154 Variety154
## 155 Rep1 Row8 Plot155 Variety255
## 156 Rep1 Row8 Plot156 Variety251
## 157 Rep1 Row8 Plot157 Variety327
## 158 Rep1 Row8 Plot158 Variety256
## 159 Rep1 Row8 Plot159 Variety159
## 160 Rep1 Row8 Plot160 Variety242
## 161 Rep1 Row9 Plot161 Variety275
## 162 Rep1 Row9 Plot162 Variety125
## 163 Rep1 Row9 Plot163 Variety163
## 164 Rep1 Row9 Plot164 Variety164
## 165 Rep1 Row9 Plot165 Variety165
## 166 Rep1 Row9 Plot166 Variety166
## 167 Rep1 Row9 Plot167 Variety167
## 168 Rep1 Row9 Plot168 Variety168
## 169 Rep1 Row9 Plot169 Variety303
## 170 Rep1 Row9 Plot170 Variety157
## 171 Rep1 Row9 Plot171 Variety114
## 172 Rep1 Row9 Plot172 Variety333
## 173 Rep1 Row9 Plot173 Variety295
## 174 Rep1 Row9 Plot174 Variety309
## 175 Rep1 Row9 Plot175 Variety65
## 176 Rep1 Row9 Plot176 Variety87
## 177 Rep1 Row9 Plot177 Variety117
## 178 Rep1 Row9 Plot178 Variety118
## 179 Rep1 Row9 Plot179 Variety126
## 180 Rep1 Row9 Plot180 Variety180
## 181 Rep1 Row10 Plot181 Variety181
## 182 Rep1 Row10 Plot182 Variety264
## 183 Rep1 Row10 Plot183 Variety183
## 184 Rep1 Row10 Plot184 Variety13
## 185 Rep1 Row10 Plot185 Variety62
## 186 Rep1 Row10 Plot186 Variety186
## 187 Rep1 Row10 Plot187 Variety273
## 188 Rep1 Row10 Plot188 Variety58
## 189 Rep1 Row10 Plot189 Variety152
## 190 Rep1 Row10 Plot190 Variety190
## 191 Rep1 Row10 Plot191 Variety191
## 192 Rep1 Row10 Plot192 Variety192
## 193 Rep1 Row10 Plot193 Variety193
## 194 Rep1 Row10 Plot194 Variety194
## 195 Rep1 Row10 Plot195 Variety353
## 196 Rep1 Row10 Plot196 Variety196
## 197 Rep1 Row10 Plot197 Variety332
## 198 Rep1 Row10 Plot198 Variety23
## 199 Rep1 Row10 Plot199 Variety179
## 200 Rep1 Row10 Plot200 Variety200
## 201 Rep1 Row11 Plot201 Variety201
## 202 Rep1 Row11 Plot202 Variety92
## 203 Rep1 Row11 Plot203 Variety88
## 204 Rep1 Row11 Plot204 Variety204
## 205 Rep1 Row11 Plot205 Variety85
## 206 Rep1 Row11 Plot206 Variety289
## 207 Rep1 Row11 Plot207 Variety101
## 208 Rep1 Row11 Plot208 Variety185
## 209 Rep1 Row11 Plot209 Variety209
## 210 Rep1 Row11 Plot210 Variety210
## 211 Rep1 Row11 Plot211 Variety211
## 212 Rep1 Row11 Plot212 Variety379
## 213 Rep1 Row11 Plot213 Variety386
## 214 Rep1 Row11 Plot214 Variety61
## 215 Rep1 Row11 Plot215 Variety149
## 216 Rep1 Row11 Plot216 Variety216
## 217 Rep1 Row11 Plot217 Variety217
## 218 Rep1 Row11 Plot218 Variety17
## 219 Rep1 Row11 Plot219 Variety363
## 220 Rep1 Row11 Plot220 Variety10
## 221 Rep1 Row12 Plot221 Variety221
## 222 Rep1 Row12 Plot222 Variety257
## 223 Rep1 Row12 Plot223 Variety35
## 224 Rep1 Row12 Plot224 Variety224
## 225 Rep1 Row12 Plot225 Variety340
## 226 Rep1 Row12 Plot226 Variety384
## 227 Rep1 Row12 Plot227 Variety2
## 228 Rep1 Row12 Plot228 Variety228
## 229 Rep1 Row12 Plot229 Variety229
## 230 Rep1 Row12 Plot230 Variety230
## 231 Rep1 Row12 Plot231 Variety64
## 232 Rep1 Row12 Plot232 Variety369
## 233 Rep1 Row12 Plot233 Variety337
## 234 Rep1 Row12 Plot234 Variety314
## 235 Rep1 Row12 Plot235 Variety395
## 236 Rep1 Row12 Plot236 Variety236
## 237 Rep1 Row12 Plot237 Variety378
## 238 Rep1 Row12 Plot238 Variety40
## 239 Rep1 Row12 Plot239 Variety188
## 240 Rep1 Row12 Plot240 Variety240
## 241 Rep1 Row13 Plot241 Variety356
## 242 Rep1 Row13 Plot242 Variety194
## 243 Rep1 Row13 Plot243 Variety243
## 244 Rep1 Row13 Plot244 Variety283
## 245 Rep1 Row13 Plot245 Variety66
## 246 Rep1 Row13 Plot246 Variety246
## 247 Rep1 Row13 Plot247 Variety247
## 248 Rep1 Row13 Plot248 Variety107
## 249 Rep1 Row13 Plot249 Variety249
## 250 Rep1 Row13 Plot250 Variety250
## [ reached 'max' / getOption("max.print") -- omitted 1350 rows ]
## 
## $call
## od::od(fixed = ~1, random = ~Variety + Rep:Row, permute = ~Variety, 
## swap = ~Rep, search = "random", maxit = 1000, data = rc)
## 
## $formulae
## $formulae$fixed
## ~1
## attr(,"variables")
## list()
## attr(,"factors")
## integer(0)
## attr(,"term.labels")
## character(0)
## attr(,"order")
## integer(0)
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 0
## attr(,".Environment")
## <environment: R_GlobalEnv>
## attr(,"specials")
## list()
## 
## $formulae$random
## ~Variety + Rep:Row
## attr(,"variables")
## list(Variety, Rep, Row)
## attr(,"factors")
## Variety Rep:Row
## Variety 1 0
## Rep 0 2
## Row 0 2
## attr(,"term.labels")
## [1] "Variety" "Rep:Row"
## attr(,"specials")
## list()
## attr(,"order")
## [1] 1 2
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 0
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## $formulae$residual
## ~NULL
## attr(,"variables")
## list()
## attr(,"factors")
## integer(0)
## attr(,"term.labels")
## character(0)
## attr(,"order")
## integer(0)
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 0
## attr(,".Environment")
## <environment: 0x7fe37aa57660>
## attr(,"specials")
## list()
## 
## $formulae$permute
## ~Variety
## attr(,"variables")
## list(Variety)
## attr(,"factors")
## Variety
## Variety 1
## attr(,"term.labels")
## [1] "Variety"
## attr(,"specials")
## list()
## attr(,"order")
## [1] 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 0
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## $formulae$swap
## ~Rep
## attr(,"variables")
## list(Rep)
## attr(,"factors")
## Rep
## Rep 1
## attr(,"term.labels")
## [1] "Rep"
## attr(,"specials")
## list()
## attr(,"order")
## [1] 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 0
## attr(,".Environment")
## <environment: R_GlobalEnv>
## 
## 
## $mf
## Rep Row Variety units ..resolve
## 1: Rep1 Row1 Variety1 1 1
## 2: Rep1 Row1 Variety2 2 1
## 3: Rep1 Row1 Variety3 3 1
## 4: Rep1 Row1 Variety4 4 1
## 5: Rep1 Row1 Variety5 5 1
## --- 
## 1596: Rep2 Row80 Variety396 1596 1
## 1597: Rep2 Row80 Variety397 1597 1
## 1598: Rep2 Row80 Variety398 1598 1
## 1599: Rep2 Row80 Variety399 1599 1
## 1600: Rep2 Row80 Variety400 1600 1
## 
## $R.param
## $R.param$units
## $R.param$units$variance
## $R.param$units$variance$size
## [1] 1600
## 
## $R.param$units$variance$model
## units!scale 
## "idv" 
## 
## $R.param$units$variance$initial
## units!R 
## 1 
## attr(,"Tgamma")
## [1] "V"
## attr(,"Bound")
## [1] ""
## 
## 
## $R.param$units$units
## $R.param$units$units$facnam
## [1] "units"
## 
## $R.param$units$units$model
## units 
## "id" 
## 
## $R.param$units$units$levels
## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45" "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56" 
## [57] "57" "58" "59" "60" "61" "62" "63" "64" "65" "66" "67" "68" "69" "70" "71" "72" "73" "74" "75" "76" "77" "78" "79" "80" "81" "82" "83" "84" "85" "86" "87" "88" "89" "90" "91" "92" "93" "94" "95" "96" "97" "98" "99" "100" "101" "102" "103" "104" "105" "106" "107" "108" "109" "110" "111" "112" 
## [113] "113" "114" "115" "116" "117" "118" "119" "120" "121" "122" "123" "124" "125" "126" "127" "128" "129" "130" "131" "132" "133" "134" "135" "136" "137" "138" "139" "140" "141" "142" "143" "144" "145" "146" "147" "148" "149" "150" "151" "152" "153" "154" "155" "156" "157" "158" "159" "160" "161" "162" "163" "164" "165" "166" "167" "168" 
## [169] "169" "170" "171" "172" "173" "174" "175" "176" "177" "178" "179" "180" "181" "182" "183" "184" "185" "186" "187" "188" "189" "190" "191" "192" "193" "194" "195" "196" "197" "198" "199" "200" "201" "202" "203" "204" "205" "206" "207" "208" "209" "210" "211" "212" "213" "214" "215" "216" "217" "218" "219" "220" "221" "222" "223" "224" 
## [225] "225" "226" "227" "228" "229" "230" "231" "232" "233" "234" "235" "236" "237" "238" "239" "240" "241" "242" "243" "244" "245" "246" "247" "248" "249" "250" "251" "252" "253" "254" "255" "256" "257" "258" "259" "260" "261" "262" "263" "264" "265" "266" "267" "268" "269" "270" "271" "272" "273" "274" "275" "276" "277" "278" "279" "280" 
## [281] "281" "282" "283" "284" "285" "286" "287" "288" "289" "290" "291" "292" "293" "294" "295" "296" "297" "298" "299" "300" "301" "302" "303" "304" "305" "306" "307" "308" "309" "310" "311" "312" "313" "314" "315" "316" "317" "318" "319" "320" "321" "322" "323" "324" "325" "326" "327" "328" "329" "330" "331" "332" "333" "334" "335" "336" 
## [337] "337" "338" "339" "340" "341" "342" "343" "344" "345" "346" "347" "348" "349" "350" "351" "352" "353" "354" "355" "356" "357" "358" "359" "360" "361" "362" "363" "364" "365" "366" "367" "368" "369" "370" "371" "372" "373" "374" "375" "376" "377" "378" "379" "380" "381" "382" "383" "384" "385" "386" "387" "388" "389" "390" "391" "392" 
## [393] "393" "394" "395" "396" "397" "398" "399" "400" "401" "402" "403" "404" "405" "406" "407" "408" "409" "410" "411" "412" "413" "414" "415" "416" "417" "418" "419" "420" "421" "422" "423" "424" "425" "426" "427" "428" "429" "430" "431" "432" "433" "434" "435" "436" "437" "438" "439" "440" "441" "442" "443" "444" "445" "446" "447" "448" 
## [449] "449" "450" "451" "452" "453" "454" "455" "456" "457" "458" "459" "460" "461" "462" "463" "464" "465" "466" "467" "468" "469" "470" "471" "472" "473" "474" "475" "476" "477" "478" "479" "480" "481" "482" "483" "484" "485" "486" "487" "488" "489" "490" "491" "492" "493" "494" "495" "496" "497" "498" "499" "500" "501" "502" "503" "504" 
## [505] "505" "506" "507" "508" "509" "510" "511" "512" "513" "514" "515" "516" "517" "518" "519" "520" "521" "522" "523" "524" "525" "526" "527" "528" "529" "530" "531" "532" "533" "534" "535" "536" "537" "538" "539" "540" "541" "542" "543" "544" "545" "546" "547" "548" "549" "550" "551" "552" "553" "554" "555" "556" "557" "558" "559" "560" 
## [561] "561" "562" "563" "564" "565" "566" "567" "568" "569" "570" "571" "572" "573" "574" "575" "576" "577" "578" "579" "580" "581" "582" "583" "584" "585" "586" "587" "588" "589" "590" "591" "592" "593" "594" "595" "596" "597" "598" "599" "600" "601" "602" "603" "604" "605" "606" "607" "608" "609" "610" "611" "612" "613" "614" "615" "616" 
## [617] "617" "618" "619" "620" "621" "622" "623" "624" "625" "626" "627" "628" "629" "630" "631" "632" "633" "634" "635" "636" "637" "638" "639" "640" "641" "642" "643" "644" "645" "646" "647" "648" "649" "650" "651" "652" "653" "654" "655" "656" "657" "658" "659" "660" "661" "662" "663" "664" "665" "666" "667" "668" "669" "670" "671" "672" 
## [673] "673" "674" "675" "676" "677" "678" "679" "680" "681" "682" "683" "684" "685" "686" "687" "688" "689" "690" "691" "692" "693" "694" "695" "696" "697" "698" "699" "700" "701" "702" "703" "704" "705" "706" "707" "708" "709" "710" "711" "712" "713" "714" "715" "716" "717" "718" "719" "720" "721" "722" "723" "724" "725" "726" "727" "728" 
## [729] "729" "730" "731" "732" "733" "734" "735" "736" "737" "738" "739" "740" "741" "742" "743" "744" "745" "746" "747" "748" "749" "750" "751" "752" "753" "754" "755" "756" "757" "758" "759" "760" "761" "762" "763" "764" "765" "766" "767" "768" "769" "770" "771" "772" "773" "774" "775" "776" "777" "778" "779" "780" "781" "782" "783" "784" 
## [785] "785" "786" "787" "788" "789" "790" "791" "792" "793" "794" "795" "796" "797" "798" "799" "800" "801" "802" "803" "804" "805" "806" "807" "808" "809" "810" "811" "812" "813" "814" "815" "816" "817" "818" "819" "820" "821" "822" "823" "824" "825" "826" "827" "828" "829" "830" "831" "832" "833" "834" "835" "836" "837" "838" "839" "840" 
## [841] "841" "842" "843" "844" "845" "846" "847" "848" "849" "850" "851" "852" "853" "854" "855" "856" "857" "858" "859" "860" "861" "862" "863" "864" "865" "866" "867" "868" "869" "870" "871" "872" "873" "874" "875" "876" "877" "878" "879" "880" "881" "882" "883" "884" "885" "886" "887" "888" "889" "890" "891" "892" "893" "894" "895" "896" 
## [897] "897" "898" "899" "900" "901" "902" "903" "904" "905" "906" "907" "908" "909" "910" "911" "912" "913" "914" "915" "916" "917" "918" "919" "920" "921" "922" "923" "924" "925" "926" "927" "928" "929" "930" "931" "932" "933" "934" "935" "936" "937" "938" "939" "940" "941" "942" "943" "944" "945" "946" "947" "948" "949" "950" "951" "952" 
## [953] "953" "954" "955" "956" "957" "958" "959" "960" "961" "962" "963" "964" "965" "966" "967" "968" "969" "970" "971" "972" "973" "974" "975" "976" "977" "978" "979" "980" "981" "982" "983" "984" "985" "986" "987" "988" "989" "990" "991" "992" "993" "994" "995" "996" "997" "998" "999" "1000"
## [ reached getOption("max.print") -- omitted 600 entries ]
## 
## $R.param$units$units$uniq
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
## [79] 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
## [157] 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234
## [235] 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312
## [313] 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390
## [391] 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
## [469] 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546
## [547] 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624
## [625] 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702
## [703] 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780
## [781] 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858
## [859] 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936
## [937] 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000
## [ reached getOption("max.print") -- omitted 600 entries ]
## 
## $R.param$units$units$initial
## units!units 
## NA 
## attr(,"set")
## [1] FALSE
## attr(,"Tgamma")
## character(0)
## 
## 
## 
## attr(,"conditioning.factor")
## [1] "units"
## 
## $G.param
## $G.param$Variety
## $G.param$Variety$variance
## $G.param$Variety$variance$size
## [1] 400
## 
## $G.param$Variety$variance$model
## scale 
## "idv" 
## 
## $G.param$Variety$variance$initial
## Variety 
## 0.1 
## attr(,"Tgamma")
## [1] "V"
## attr(,"Bound")
## [1] ""
## 
## 
## $G.param$Variety$Variety
## $G.param$Variety$Variety$facnam
## [1] "Variety"
## 
## $G.param$Variety$Variety$model
## Variety 
## "id" 
## 
## $G.param$Variety$Variety$levels
## [1] "Variety1" "Variety10" "Variety100" "Variety101" "Variety102" "Variety103" "Variety104" "Variety105" "Variety106" "Variety107" "Variety108" "Variety109" "Variety11" "Variety110" "Variety111" "Variety112" "Variety113" "Variety114" "Variety115" "Variety116" "Variety117" "Variety118" "Variety119" "Variety12" "Variety120" "Variety121" "Variety122" "Variety123" "Variety124" "Variety125"
## [31] "Variety126" "Variety127" "Variety128" "Variety129" "Variety13" "Variety130" "Variety131" "Variety132" "Variety133" "Variety134" "Variety135" "Variety136" "Variety137" "Variety138" "Variety139" "Variety14" "Variety140" "Variety141" "Variety142" "Variety143" "Variety144" "Variety145" "Variety146" "Variety147" "Variety148" "Variety149" "Variety15" "Variety150" "Variety151" "Variety152"
## [61] "Variety153" "Variety154" "Variety155" "Variety156" "Variety157" "Variety158" "Variety159" "Variety16" "Variety160" "Variety161" "Variety162" "Variety163" "Variety164" "Variety165" "Variety166" "Variety167" "Variety168" "Variety169" "Variety17" "Variety170" "Variety171" "Variety172" "Variety173" "Variety174" "Variety175" "Variety176" "Variety177" "Variety178" "Variety179" "Variety18" 
## [91] "Variety180" "Variety181" "Variety182" "Variety183" "Variety184" "Variety185" "Variety186" "Variety187" "Variety188" "Variety189" "Variety19" "Variety190" "Variety191" "Variety192" "Variety193" "Variety194" "Variety195" "Variety196" "Variety197" "Variety198" "Variety199" "Variety2" "Variety20" "Variety200" "Variety201" "Variety202" "Variety203" "Variety204" "Variety205" "Variety206"
## [121] "Variety207" "Variety208" "Variety209" "Variety21" "Variety210" "Variety211" "Variety212" "Variety213" "Variety214" "Variety215" "Variety216" "Variety217" "Variety218" "Variety219" "Variety22" "Variety220" "Variety221" "Variety222" "Variety223" "Variety224" "Variety225" "Variety226" "Variety227" "Variety228" "Variety229" "Variety23" "Variety230" "Variety231" "Variety232" "Variety233"
## [151] "Variety234" "Variety235" "Variety236" "Variety237" "Variety238" "Variety239" "Variety24" "Variety240" "Variety241" "Variety242" "Variety243" "Variety244" "Variety245" "Variety246" "Variety247" "Variety248" "Variety249" "Variety25" "Variety250" "Variety251" "Variety252" "Variety253" "Variety254" "Variety255" "Variety256" "Variety257" "Variety258" "Variety259" "Variety26" "Variety260"
## [181] "Variety261" "Variety262" "Variety263" "Variety264" "Variety265" "Variety266" "Variety267" "Variety268" "Variety269" "Variety27" "Variety270" "Variety271" "Variety272" "Variety273" "Variety274" "Variety275" "Variety276" "Variety277" "Variety278" "Variety279" "Variety28" "Variety280" "Variety281" "Variety282" "Variety283" "Variety284" "Variety285" "Variety286" "Variety287" "Variety288"
## [211] "Variety289" "Variety29" "Variety290" "Variety291" "Variety292" "Variety293" "Variety294" "Variety295" "Variety296" "Variety297" "Variety298" "Variety299" "Variety3" "Variety30" "Variety300" "Variety301" "Variety302" "Variety303" "Variety304" "Variety305" "Variety306" "Variety307" "Variety308" "Variety309" "Variety31" "Variety310" "Variety311" "Variety312" "Variety313" "Variety314"
## [241] "Variety315" "Variety316" "Variety317" "Variety318" "Variety319" "Variety32" "Variety320" "Variety321" "Variety322" "Variety323" "Variety324" "Variety325" "Variety326" "Variety327" "Variety328" "Variety329" "Variety33" "Variety330" "Variety331" "Variety332" "Variety333" "Variety334" "Variety335" "Variety336" "Variety337" "Variety338" "Variety339" "Variety34" "Variety340" "Variety341"
## [271] "Variety342" "Variety343" "Variety344" "Variety345" "Variety346" "Variety347" "Variety348" "Variety349" "Variety35" "Variety350" "Variety351" "Variety352" "Variety353" "Variety354" "Variety355" "Variety356" "Variety357" "Variety358" "Variety359" "Variety36" "Variety360" "Variety361" "Variety362" "Variety363" "Variety364" "Variety365" "Variety366" "Variety367" "Variety368" "Variety369"
## [301] "Variety37" "Variety370" "Variety371" "Variety372" "Variety373" "Variety374" "Variety375" "Variety376" "Variety377" "Variety378" "Variety379" "Variety38" "Variety380" "Variety381" "Variety382" "Variety383" "Variety384" "Variety385" "Variety386" "Variety387" "Variety388" "Variety389" "Variety39" "Variety390" "Variety391" "Variety392" "Variety393" "Variety394" "Variety395" "Variety396"
## [331] "Variety397" "Variety398" "Variety399" "Variety4" "Variety40" "Variety400" "Variety41" "Variety42" "Variety43" "Variety44" "Variety45" "Variety46" "Variety47" "Variety48" "Variety49" "Variety5" "Variety50" "Variety51" "Variety52" "Variety53" "Variety54" "Variety55" "Variety56" "Variety57" "Variety58" "Variety59" "Variety6" "Variety60" "Variety61" "Variety62" 
## [361] "Variety63" "Variety64" "Variety65" "Variety66" "Variety67" "Variety68" "Variety69" "Variety7" "Variety70" "Variety71" "Variety72" "Variety73" "Variety74" "Variety75" "Variety76" "Variety77" "Variety78" "Variety79" "Variety8" "Variety80" "Variety81" "Variety82" "Variety83" "Variety84" "Variety85" "Variety86" "Variety87" "Variety88" "Variety89" "Variety9" 
## [391] "Variety90" "Variety91" "Variety92" "Variety93" "Variety94" "Variety95" "Variety96" "Variety97" "Variety98" "Variety99" 
## 
## $G.param$Variety$Variety$initial
## Variety!Variety 
## NA 
## attr(,"set")
## [1] FALSE
## attr(,"Tgamma")
## character(0)
## 
## 
## 
## $G.param$`Rep:Row`
## $G.param$`Rep:Row`$variance
## $G.param$`Rep:Row`$variance$size
## [1] 160
## 
## $G.param$`Rep:Row`$variance$model
## scale 
## "idv" 
## 
## $G.param$`Rep:Row`$variance$initial
## Rep:Row 
## 0.1 
## attr(,"Tgamma")
## [1] "V"
## attr(,"Bound")
## [1] ""
## 
## 
## $G.param$`Rep:Row`$Rep
## $G.param$`Rep:Row`$Rep$facnam
## [1] "Rep"
## 
## $G.param$`Rep:Row`$Rep$model
## Rep 
## "id" 
## 
## $G.param$`Rep:Row`$Rep$levels
## [1] "Rep1" "Rep2"
## 
## $G.param$`Rep:Row`$Rep$initial
## Rep:Row!Rep 
## NA 
## attr(,"set")
## [1] FALSE
## attr(,"Tgamma")
## character(0)
## 
## 
## $G.param$`Rep:Row`$Row
## $G.param$`Rep:Row`$Row$facnam
## [1] "Row"
## 
## $G.param$`Rep:Row`$Row$model
## Row 
## "id" 
## 
## $G.param$`Rep:Row`$Row$levels
## [1] "Row1" "Row10" "Row11" "Row12" "Row13" "Row14" "Row15" "Row16" "Row17" "Row18" "Row19" "Row2" "Row20" "Row21" "Row22" "Row23" "Row24" "Row25" "Row26" "Row27" "Row28" "Row29" "Row3" "Row30" "Row31" "Row32" "Row33" "Row34" "Row35" "Row36" "Row37" "Row38" "Row39" "Row4" "Row40" "Row41" "Row42" "Row43" "Row44" "Row45" "Row46" "Row47" "Row48" "Row49" "Row5" "Row50" "Row51" "Row52" "Row53"
## [50] "Row54" "Row55" "Row56" "Row57" "Row58" "Row59" "Row6" "Row60" "Row61" "Row62" "Row63" "Row64" "Row65" "Row66" "Row67" "Row68" "Row69" "Row7" "Row70" "Row71" "Row72" "Row73" "Row74" "Row75" "Row76" "Row77" "Row78" "Row79" "Row8" "Row80" "Row9" 
## 
## $G.param$`Rep:Row`$Row$initial
## Rep:Row!Row 
## NA 
## attr(,"set")
## [1] FALSE
## attr(,"Tgamma")
## character(0)
## 
## 
## 
## 
## attr(,"class")
## [1] "od"
```

]

]]

---

# `edibble::make_classical`

* Still want the "named" experimental design?

```r
make_classical("crd", t = 5, n = 20)
```
.overflow-scroll.h---400[
<img src="images//des-classical.svg" width="100%" style="display: block; margin: auto;" />
]

---

# `edibble::set_rcrds()`

* Please note this API will likely change ([](https://github.com/emitanaka/edibble/issues/26))

```r
des %>% 
  allocate_trts(diet ~ pen,
                breed ~ pig) %>% 
  randomise_trts() %>% 
* set_rcrds(pen = avg_temp,
*           pig = c(diseased, inital_weight, final_weight)) %>%
  serve_table()
```

.overflow-scroll.h---200[
<img src="images//des-rcrds.svg" width="100%" style="display: block; margin: auto;" />
]
--

.idea-box.w-60[
* The __*intention*__ of __*which metric*__ to capture __*on what*__ is clearly specified.
* What is an observational unit is more obvious.
]
</div>

---

# `edibble::expect_rcrds()`

```r
df <- des %>% 
 allocate_trts(diet ~ pen,
 breed ~ pig) %>% 
 randomise_trts() %>% 
 set_rcrds(pig = c(diseased, inital_weight, final_weight),
 pen = avg_temp) %>% 
* expect_rcrds(diseased = to_be_factor(levels = c("yes", "no", "unknown")),
* inital_weight = to_be_numeric(with_value(">=", 0)),
* final_weight = to_be_numeric(with_value(">=", 0))) %>%
 serve_table()
```

* This encodes data validation rules in the edibble object.

* But why bother do this?

---

# `edibble::export_design()`

```r
export_design(df, file = "design.xlsx")
```
.flex[
.w-50[
<img src="images/data-export-pig.png" width="90%" class="ba">

]
.w-50[
<img src="images/data-export-pen.png" width="90%" class="ba">

]
]

---

# `edibble::fill_rcrds` or `edibble::simulate_rcrds`

* This is in my plans to implement [](https://github.com/emitanaka/edibble/issues/23)
* `fill_rcrds` is a simple, quick way to simulate dummy data
* `simulate_rcrds` is a more flexible, proper simulation of data

**Other plans**

* Diagnosis of the design (e.g. skeleton ANOVA [](https://github.com/emitanaka/edibble/issues/20), design anatomy and efficiency calculation [](https://github.com/emitanaka/edibble/issues/21), Hasse diagram...)
* Suggest model for analysis [](https://github.com/emitanaka/edibble/issues/7)
* Warning to user for unreplicated experiments [](https://github.com/emitanaka/edibble/issues/36)

---

# 🍨
# Visualising experimental designs with .yellow[deggust]

.f2.animate__animated.animate__flash.red.b.animate__delay-1s[
 This package is still nuclear-level experimental!
]

---

library(deggust) 
```
]

.f2.animate__animated.animate__flash.red.b[
 Rapid development phase &mdash; use with caution 
]

.think-box.tl[
The **origin of the name**:
* **deggust** as in degustation 
* **de** = design of experiments 
* **gg** = ggplot object
]

---

# Back to the pig design

```r
set.seed(1)
df1 <- start_design("My diet experiment") %>% 
 set_trts(diet = c("carb", "protein", "fat")) %>% 
 set_units(pig = 50) %>% 
 allocate_trts(~ pig) %>% 
 randomise_trts() %>% 
 serve_table() 
```

---

# Visualising designs with `ggplot2`

```r
library(ggplot2)
df1 %>% 
  # make it normal data frame
  as_data_frame() %>% 
  # plot using ggplot
  ggplot(aes(pig, "1", fill = diet)) +
    geom_tile(color = "black")
```

* Slightly painful if you want to *quickly* visualise your design.

---

# `deggust::autoplot()` .f4[Part 1]

* Just `autoplot` it!

```r
library(deggust)
```

```r
autoplot(df1) 
```

---

# `deggust::autoplot()` .f4[Part 2]

* It makes some decision for you of how to plot which can be customised in two ways:
   1. modify scale and theme like any ggplot objects!
   2. as arguments in the `autoplot` function

```r
autoplot(df1) 
```
]
.w-50[
<img src="images/vis-autoplot-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

# `deggust::autoplot()` .f4[Part 3]

* It makes some decision for you of how to plot which can be customised in two ways:
   1. .red[**modify scale and theme like any ggplot objects!**]
   2. as arguments in the `autoplot` function

```r
autoplot(df1) +
 # ggplot2 functions below
* theme_void() +
* scale_fill_viridis_d(option = "A")
```
]
.w-50[
<img src="images/vis-autoplot-modify-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

# `deggust::autoplot()` .f4[Part 4]

* It makes some decision for you of how to plot which can be customised in two ways:
   1. modify scale and theme like any ggplot objects!
   2. .red[**as arguments in the `autoplot` function**]

```r
autoplot(df1, 
* shape = "hexagon",
* text = TRUE,
* aspect_ratio = 0.5)
```
]
.w-50[
<img src="images/vis-autoplot-args-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

# `deggust::autoplot()` .f4[Part 5]

<img src="images/pig.png" width = "200px">
--

```r
autoplot(df1, 
* image = "images/pig.png") +
 theme_void() 
```
]
.w-50[
<img src="images/vis-autoplot-pigimage-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

# `deggust::autoplot()` .f4[Part 6]

* Nested design

```r
set.seed(2021)
start_design() %>% 
 set_units(pen = 10, 
 pig = nested_in(pen, 5)) %>% 
 set_trts(breed = c("A", "B", "C")) %>% 
 allocate_trts(breed ~ pig) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
 autoplot()
```
]
.w-50[
<img src="images/vis-nested-1.png" width="432" style="display: block; margin: auto;" />

]

---

# `deggust::autoplot()` .f4[Part 7]

* What changed here?

```r
set.seed(2021)
start_design() %>% 
 set_units(pen = 10, 
 pig = nested_in(pen, 5)) %>% 
 set_trts(breed = c("A", "B", "C")) %>% 
 allocate_trts(breed ~ pen) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
 autoplot()
```
]
.w-50[
<img src="images/vis-nested-pen-1.png" width="432" style="display: block; margin: auto;" />

]

---

# `deggust::autoplot()` .f4[Part 8]

* Factorial experiment

```r
set.seed(2021)
start_design() %>% 
 set_units(pig = 40) %>% 
 set_trts(breed = c("A", "B", "C"),
 feed = c("X", "Y", "Z")) %>% 
 allocate_trts(breed:feed ~ pig) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
 autoplot()
```
]
.w-50[
<img src="images/vis-nested-fac-1.png" width="432" style="display: block; margin: auto;" />

]

---

# `deggust::autoplot()` .f4[Part 9]

* Focus on the treatment you want:

```r
set.seed(2021)
start_design() %>% 
 set_units(pig = 40) %>% 
 set_trts(breed = c("A", "B", "C"),
 feed = c("X", "Y", "Z")) %>% 
 allocate_trts(breed:feed ~ pig) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
 autoplot(trts = "breed")
```
]
.w-50[
<img src="images/vis-nested-fac1-1.png" width="432" style="display: block; margin: auto;" />

]

---

# `deggust::autoplot()` .f4[Part 10]

* Is your design too big to fit in the plot?

```r
set.seed(2021)
start_design() %>% 
 set_units(pen = 100,
 pig = nested_in(pen, 10)) %>% 
 set_trts(breed = c("A", "B", "C")) %>% 
 allocate_trts(breed ~ pig) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
 autoplot()
```
]
.w-50[
<img src="images/vis-nested-big-1.png" width="432" style="display: block; margin: auto;" />

]

---

# `deggust::autoplot()` .f4[Part 10]

* Is your design too big to fit in the plot?
* Subset it!

```r
set.seed(2021)
start_design() %>% 
 set_units(pen = 100,
 pig = nested_in(pen, 10)) %>% 
 set_trts(breed = c("A", "B", "C")) %>% 
 allocate_trts(breed ~ pig) %>% 
 randomise_trts() %>% 
 serve_table() %>% 
* dplyr::filter(pen %in% c("pen1", "pen2", "pen3", "pen4")) %>%
 autoplot() +
 annotate("text", x = 10, y = 4.7, label = "x 25 more")
```
]
.w-50[
<img src="images/vis-nested-filter-1.png" width="432" style="display: block; margin: auto;" />

]

---

# .square[Data .circle[1]] Four-way factorial agronomic experiment in triticale

.flex.h-80.f4[

.w-60.br[

```r
library(edibble)
set.seed(1)
start_design("agridat::besag.triticale") %>% 
  set_units(row = 1:3,
            col = 1:18,
            plot =~ row:col) %>% 
  set_trts(rate = c(125, 150),
           nitro = c(100, 150),
           regulator = c("Control", "Cycocel", "Terpal"),
           gen = c("Newton", "Torrs", "Warren")) %>% 
  allocate_trts( ~ plot) %>% 
  randomise_trts()
```
]
.w-40.pl3[

]
]

.footnote.black.f5.mb1[
Data source: Julian Besag and Rob Kempton (1986). Statistical Analysis of Field Experiments Using Neighbouring Plots. Biometrics, 42, 231-251
 
]

---

# 🧆

# Designing experiments using a web app with .yellow[edibbleGUI]

.f2.animate__animated.animate__flash.red.b.animate__delay-1s[
 Totally not ready very bare bones, not enough meat for consumption
]

---

```r
remotes::install_github("emitanaka/edibbleGUI")

edibbleGUI::app()
```
]

.f2.animate__animated.animate__flash.red.b[
 Rapid development phase &mdash; use with caution 
]

---

# `edibbleGUI::app()`

]
.w-30[
* This app is bound to change. 
* The development of the app will always lag from `edibble`.

Some plans:

<ul class="fa-ul">
 <li>Show corresponding code</li>
 <li>Export design table</li>
 <li>Host app on the web</li>
 <li>Better integration with <code>edibble</code></li>
</ul>
]
]

---

# 🍹
# Future directions

---

# Experimental design is different to statistical analysis

.w-70[
* Constructing an experimental design is different to analysis: 
   * redoing an experiment is generally more expensive than redoing an analysis 
   * often there is no "data" but "information" only" 
      * taking into account experimental context is important 
      * selecting a design from a list of known designs often means that you are not adapting the design to the context

]

---

# What `edibble` does

* `tidyverse` does well for processes in (B)
* `edibble` aims to tackle (A)

---

# Designing for the *whole* experiment

.overflow-scroll.h-80.center[
<img src="images/seq-diagram-eg.png" width="80%">
]

---

# `edibble` developments
* All developments are open-source and transparent:
 * https://github.com/emitanaka/edibble
 * https://github.com/emitanaka/deggust
 * https://github.com/emitanaka/edibbleGUI
* `edibble` and its extensions `deggust` and `edibbleGUI` are currently one-person effort 
* Something not working? Feature request? Feel free to submit it in issues!
 * https://github.com/emitanaka/edibble/issues
 * https://github.com/emitanaka/deggust/issues
 * https://github.com/emitanaka/edibbleGUI/issues
--

* 🚧 `edibble` is a work-in-progress with plans to submit the CRAN version later this year
* `edibble` will continue to improve &mdash; how *fast* it improves is another story!
--

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This slide is made using the `xaringan` R-package and found at

.w-80.center[
[emitanaka.org/slides/DAF2021/edibble](https://emitanaka.org/slides/DAF2021/edibble)

]

.bottom_abs.width100[

*Emi Tanaka*

Department of Econometrics and Business Statistics, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Monash University, Melbourne, Australia

emi.tanaka@monash.edu

<a href="https://twitter.com/statsgen" style="color:black"> @statsgen</a>

]

Thank you!