# Analysis of mallard data illustrating basic RMark features
# How to fit a nest level continous covariate (Robel height
# 2019-05-01 CJS Initial code
# This is the mallard data that ships with RMark
library(ggplot2)
## Registered S3 methods overwritten by 'ggplot2':
## method from
## [.quosures rlang
## c.quosures rlang
## print.quosures rlang
library(readxl)
library(RMark)
## This is RMark 2.2.6
## Documentation available at http://www.phidot.org/software/mark/rmark/RMarkDocumentation.zip
# The dataframe must contain the following fields with the following names
#
# FirstFound: day the nest was first found
# LastPresent: last day that a chick was present in the nest
# LastChecked: last day the nest was checked
# Fate: fate of the nest; 0=hatch an
# Freq: number of nests with this data
#
# Also contains the following fields
# Robel - Measurement of Robel pole of visibility of nest
# PpnGrass - proportion of grassland cover on the 10.4 km2 study site t
# AgeFound - Age of nest when found
# AgeDay1 - Age of nest on day 1 of study (can be negative)
# Habitat - N=Native; P=Planted; W=Wetland; R=roadside right of way
#
# In this example, the multiple visits to a nest have been collapsed
# to a single record for each nest.
# In more complex examples, you may have multple records per nest
# as shown in the mallard example.
#
malldata <- readxl::read_excel(file.path("..","mallard.xlsx"),
sheet="mallard")
head(malldata)
## # A tibble: 6 x 10
## FirstFound LastPresent LastChecked Fate Freq Robel PpnGrass AgeFound
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 73 89 89 0 1 6 0.800 13
## 2 63 90 90 0 1 3.75 0.668 5
## 3 70 70 76 1 1 3.75 0.800 13
## 4 63 81 85 1 1 3.12 0.668 6
## 5 61 61 66 1 1 4.5 0.668 4
## 6 57 57 61 1 1 4.25 0.668 1
## # ... with 2 more variables: AgeDay1 <dbl>, Habitat <chr>
malldata <- as.data.frame(malldata)
# what are the parameters of the model
# There is only one parameter, the daily survival probality (S)
setup.parameters("Nest", check=TRUE)
## [1] "S"
# 1. Process the data.
# The nocc variable the number of sampling occasions in the data
mall.proc <- process.data(malldata, model="Nest",
nocc=max(malldata$LastChecked))
mall.proc
## $data
## FirstFound LastPresent LastChecked Fate freq Robel PpnGrass AgeFound
## 1 73 89 89 0 1 6.000 0.8002 13
## 2 63 90 90 0 1 3.750 0.6684 5
## 3 70 70 76 1 1 3.750 0.8002 13
## 4 63 81 85 1 1 3.125 0.6684 6
## 5 61 61 66 1 1 4.500 0.6684 4
## 6 57 57 61 1 1 4.250 0.6684 1
## 7 67 88 88 0 1 8.000 0.6684 12
## 8 58 87 87 0 1 5.875 0.4651 3
## 9 74 86 86 0 1 4.500 0.8002 20
## 10 65 65 70 1 1 3.625 0.8002 11
## 11 63 88 88 0 1 5.250 0.8666 10
## 12 61 66 70 1 1 3.625 0.6684 8
## 13 63 84 84 0 1 3.750 0.8002 11
## 14 74 74 78 1 1 5.625 0.8002 22
## 15 56 56 63 1 1 4.875 0.6684 4
## 16 57 87 87 0 1 3.500 0.6684 5
## 17 74 86 86 0 1 3.375 0.8002 22
## 18 68 87 87 0 1 4.875 0.8002 16
## 19 56 56 63 1 1 3.875 0.6684 4
## 20 66 66 73 1 1 3.375 0.8002 15
## 21 81 84 84 0 1 5.750 0.8002 30
## 22 63 63 68 1 1 5.250 0.8666 13
## 23 56 56 63 1 1 5.875 0.6684 7
## 24 56 63 69 1 1 5.750 0.6684 7
## 25 74 84 84 0 1 4.125 0.8002 25
## 26 55 64 69 1 1 5.875 0.4651 7
## 27 56 80 80 0 1 5.000 0.6684 8
## 28 56 56 63 1 1 2.250 0.6684 8
## 29 50 60 64 1 1 3.750 0.7281 2
## 30 58 58 63 1 1 3.375 0.6684 10
## 31 58 73 77 1 1 1.875 0.8666 10
## 32 57 80 80 0 1 2.250 0.8666 9
## 33 63 63 68 1 1 4.625 0.8002 16
## 34 60 79 79 0 1 6.125 0.6684 13
## 35 61 61 66 1 1 4.750 0.6684 14
## 36 56 69 74 1 1 4.125 0.6684 9
## 37 65 81 81 0 1 5.000 0.8002 18
## 38 57 68 73 1 1 3.000 0.4651 11
## 39 73 76 76 0 1 4.875 0.8002 27
## 40 54 64 68 1 1 5.000 0.4651 8
## 41 75 79 79 0 1 3.750 0.8002 29
## 42 55 55 59 1 1 3.000 0.6684 9
## 43 50 56 60 1 1 5.500 0.7281 4
## 44 58 58 64 1 1 5.625 0.8666 12
## 45 62 80 80 0 1 4.875 0.6684 16
## 46 54 74 74 0 1 4.625 0.4651 9
## 47 61 66 70 1 1 3.250 0.8666 16
## 48 73 76 76 0 1 6.000 0.8002 28
## 49 52 52 57 1 1 4.250 0.7281 7
## 50 53 75 75 0 1 4.750 0.7281 9
## 51 52 61 66 1 1 3.375 0.7281 8
## 52 63 78 78 0 1 4.750 0.8666 19
## 53 63 77 77 0 1 3.625 0.8002 19
## 54 70 70 76 1 1 4.375 0.8002 26
## 55 73 79 79 0 1 3.750 0.8002 29
## 56 59 77 77 0 1 4.125 0.8666 15
## 57 50 50 56 1 1 3.625 0.7281 7
## 58 63 73 73 0 1 2.750 0.8666 20
## 59 63 73 73 0 1 3.500 0.8002 20
## 60 49 49 55 1 1 3.750 0.4651 6
## 61 56 63 69 1 1 6.250 0.6684 14
## 62 47 53 59 1 1 5.250 0.4651 5
## 63 44 44 48 1 1 4.125 0.4651 2
## 64 55 74 74 0 1 5.125 0.4651 14
## 65 45 56 61 1 1 4.750 0.4651 4
## 66 47 53 59 1 1 6.875 0.4651 7
## 67 61 61 66 1 1 4.500 0.6684 21
## 68 61 61 66 1 1 4.625 0.6684 21
## 69 67 70 70 0 1 5.625 0.6684 27
## 70 55 68 68 0 1 4.375 0.4651 15
## 71 43 46 50 1 1 4.750 0.8666 3
## 72 47 67 67 0 1 3.875 0.8666 7
## 73 64 73 73 0 1 3.500 0.8002 24
## 74 50 60 64 1 1 1.875 0.7281 11
## 75 63 63 68 1 1 2.500 0.8002 24
## 76 54 68 74 1 1 4.625 0.4651 15
## 77 64 64 69 1 1 3.500 0.8002 25
## 78 43 70 70 0 1 4.625 0.5079 4
## 79 42 46 46 0 1 5.750 0.4651 4
## 80 60 60 65 1 1 3.750 0.8666 22
## 81 43 46 46 0 1 3.875 0.8666 5
## 82 61 69 69 0 1 4.750 0.6684 23
## 83 61 66 70 1 1 4.125 0.6684 23
## 84 68 72 72 0 1 4.875 0.8002 30
## 85 52 65 69 1 1 4.125 0.7281 14
## 86 47 71 71 0 1 3.625 0.8666 9
## 87 65 70 72 1 1 4.375 0.8002 28
## 88 43 43 49 1 1 4.000 0.4651 6
## 89 41 46 46 0 1 2.375 0.3344 4
## 90 43 46 50 1 1 5.125 0.8666 6
## 91 56 72 72 0 1 5.500 0.6684 19
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## 94 62 70 70 0 1 4.500 0.8666 25
## 95 55 66 66 0 1 3.750 0.4651 18
## 96 44 72 72 0 1 3.750 0.8666 7
## 97 67 68 68 0 1 9.250 0.6684 31
## 98 61 65 65 0 1 4.625 0.6684 25
## 99 62 67 67 0 1 3.500 0.6684 26
## 100 42 57 60 1 1 5.375 0.3344 6
## 101 52 52 57 1 1 2.875 0.7281 16
## 102 50 64 69 1 1 4.000 0.7281 14
## 103 48 55 60 1 1 5.875 0.7281 12
## 104 63 67 67 0 1 4.625 0.8666 27
## 105 62 67 67 0 1 5.000 0.6684 26
## 106 63 67 67 0 1 4.375 0.6684 28
## 107 43 55 60 1 1 3.375 0.5079 8
## 108 40 50 56 1 1 2.375 0.3344 5
## 109 60 60 65 1 1 5.500 0.6684 25
## 110 42 64 68 1 1 1.750 0.5079 7
## 111 59 70 70 0 1 4.500 0.6684 24
## 112 42 66 66 0 1 2.875 0.3344 7
## 113 40 40 44 1 1 4.625 0.7265 6
## 114 46 46 52 1 1 5.250 0.4651 12
## 115 58 63 63 0 1 4.875 0.8666 24
## 116 40 60 64 1 1 3.375 0.3344 6
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## 118 42 46 46 0 1 5.375 0.4651 8
## 119 40 44 50 1 1 2.875 0.3344 6
## 120 42 42 48 1 1 2.625 0.3344 9
## 121 57 66 68 1 1 4.750 0.6684 24
## 122 63 67 67 0 1 2.750 0.8666 30
## 123 40 44 50 1 1 4.625 0.7265 7
## 124 47 67 67 0 1 4.375 0.7281 14
## 125 57 57 61 1 1 4.250 0.6684 24
## 126 40 44 50 1 1 4.000 0.3344 7
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## 146 40 40 44 1 1 3.375 0.3344 9
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## 185 30 42 42 0 1 4.875 0.6587 3
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## 197 48 55 60 1 1 3.250 0.7281 23
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## 212 25 25 29 1 1 4.250 0.9671 1
## 213 36 52 58 1 1 4.500 0.3344 12
## 214 31 42 46 1 1 3.375 0.9671 7
## 215 31 58 58 0 1 4.375 0.6587 7
## 216 31 31 42 1 1 4.750 0.1876 7
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## 218 31 31 36 1 1 1.750 0.1876 7
## 219 31 46 54 1 1 4.000 0.6587 7
## 220 30 56 56 0 1 1.125 0.6587 6
## 221 25 30 35 1 1 3.375 0.6587 2
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## 223 32 34 34 0 1 4.250 0.9671 9
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## 226 30 30 41 1 1 3.250 0.6587 7
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## 228 35 41 45 1 1 4.625 0.3344 12
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## 235 31 31 36 1 1 3.500 0.6587 9
## 236 31 42 46 1 1 2.625 0.9671 9
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## 238 41 41 45 1 1 2.875 0.3344 20
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## 240 27 30 34 1 1 0.750 0.9671 6
## 241 29 29 34 1 1 3.125 0.1876 8
## 242 25 25 32 1 1 3.125 0.6587 4
## 243 31 31 36 1 1 4.000 0.6587 10
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## 249 29 34 37 1 1 3.500 0.1876 9
## 250 41 55 55 0 1 3.875 0.7265 21
## 251 40 54 54 0 1 5.625 0.7265 20
## 252 40 40 44 1 1 3.000 0.3344 20
## 253 29 51 51 0 1 2.250 0.1876 10
## 254 31 46 54 1 1 3.625 0.6587 12
## 255 27 34 40 1 1 2.375 0.9671 8
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## 257 27 30 35 1 1 4.000 0.9671 8
## 258 25 49 54 1 1 4.375 0.9671 6
## 259 23 51 51 0 1 3.125 0.9378 4
## 260 23 23 27 1 1 2.250 0.6587 4
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## 262 45 50 54 1 1 3.875 0.4651 26
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## 265 29 40 45 1 1 3.000 0.1876 10
## 266 26 35 41 1 1 2.500 0.9671 8
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## 281 40 49 49 0 1 2.375 0.7265 23
## 282 29 52 52 0 1 4.375 0.6587 12
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## 284 31 51 51 0 1 3.500 0.9671 15
## 285 43 50 51 1 1 4.500 0.8666 27
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## 301 40 46 46 0 1 2.625 0.3344 26
## 302 21 30 41 1 1 1.000 0.9248 7
## 303 21 25 30 1 1 3.125 0.9248 7
## 304 40 49 49 0 1 3.375 0.3344 26
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## 306 40 49 49 0 1 6.750 0.7265 26
## 307 43 44 44 0 1 3.500 0.5079 29
## 308 23 46 46 0 1 5.000 0.9378 9
## 309 22 37 42 1 1 2.750 0.9378 8
## 310 31 49 49 0 1 3.250 0.6587 17
## 311 23 46 46 0 1 3.625 0.9378 9
## 312 44 44 48 1 1 5.125 0.4651 30
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## 315 47 48 48 0 1 3.500 0.8666 34
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## AgeDay1 Habitat
## 1 -59 R
## 2 -57 P
## 3 -56 P
## 4 -56 N
## 5 -56 P
## 6 -55 P
## 7 -54 P
## 8 -54 N
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## 10 -53 N
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## 12 -52 P
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## 21 -50 N
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## 29 -47 R
## 30 -47 P
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##
## $model
## [1] "Nest"
##
## $mixtures
## [1] 1
##
## $freq
## group1
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## 400 1
## 401 1
## 402 1
## 403 1
## 404 1
## 405 1
## 406 1
## 407 1
## 408 1
## 409 1
## 410 1
## 411 1
## 412 1
## 413 1
## 414 1
## 415 1
## 416 1
## 417 1
## 418 1
## 419 1
## 420 1
## 421 1
## 422 1
## 423 1
## 424 1
## 425 1
## 426 1
## 427 1
## 428 1
## 429 1
## 430 1
## 431 1
## 432 1
## 433 1
## 434 1
## 435 1
## 436 1
## 437 1
## 438 1
## 439 1
## 440 1
## 441 1
## 442 1
## 443 1
## 444 1
## 445 1
## 446 1
## 447 1
## 448 1
## 449 1
## 450 1
## 451 1
## 452 1
## 453 1
## 454 1
## 455 1
## 456 1
## 457 1
## 458 1
## 459 1
## 460 1
## 461 1
## 462 1
## 463 1
## 464 1
## 465 1
## 466 1
## 467 1
## 468 1
## 469 1
## 470 1
## 471 1
## 472 1
## 473 1
## 474 1
## 475 1
## 476 1
## 477 1
## 478 1
## 479 1
## 480 1
## 481 1
## 482 1
## 483 1
## 484 1
## 485 1
## 486 1
## 487 1
## 488 1
## 489 1
## 490 1
## 491 1
## 492 1
## 493 1
## 494 1
## 495 1
## 496 1
## 497 1
## 498 1
## 499 1
## 500 1
## 501 1
## 502 1
## 503 1
## 504 1
## 505 1
## 506 1
## 507 1
## 508 1
## 509 1
## 510 1
## 511 1
## 512 1
## 513 1
## 514 1
## 515 1
## 516 1
## 517 1
## 518 1
## 519 1
## 520 1
## 521 1
## 522 1
## 523 1
## 524 1
## 525 1
## 526 1
## 527 1
## 528 1
## 529 1
## 530 1
## 531 1
## 532 1
## 533 1
## 534 1
## 535 1
## 536 1
## 537 1
## 538 1
## 539 1
## 540 1
## 541 1
## 542 1
## 543 1
## 544 1
## 545 1
## 546 1
## 547 1
## 548 1
## 549 1
## 550 1
## 551 1
## 552 1
## 553 1
## 554 1
## 555 1
## 556 1
## 557 1
## 558 1
## 559 1
## 560 1
## 561 1
## 562 1
## 563 1
## 564 1
## 565 1
##
## $nocc
## [1] 90
##
## $nocc.secondary
## NULL
##
## $time.intervals
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [71] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##
## $begin.time
## [1] 1
##
## $age.unit
## [1] 1
##
## $initial.ages
## [1] 0
##
## $group.covariates
## NULL
##
## $nstrata
## [1] 1
##
## $strata.labels
## [1] ""
##
## $counts
## NULL
##
## $reverse
## [1] FALSE
##
## $areas
## NULL
##
## $events
## NULL
# 2. Examine and/or modify the ddl. (Not done here)
mall.ddl <- make.design.data(mall.proc)
str(mall.ddl)
## List of 2
## $ S :'data.frame': 89 obs. of 7 variables:
## ..$ par.index : int [1:89] 1 2 3 4 5 6 7 8 9 10 ...
## ..$ model.index: num [1:89] 1 2 3 4 5 6 7 8 9 10 ...
## ..$ group : Factor w/ 1 level "1": 1 1 1 1 1 1 1 1 1 1 ...
## ..$ age : Factor w/ 89 levels "0","1","2","3",..: 1 2 3 4 5 6 7 8 9 10 ...
## ..$ time : Factor w/ 89 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
## ..$ Age : num [1:89] 0 1 2 3 4 5 6 7 8 9 ...
## ..$ Time : num [1:89] 0 1 2 3 4 5 6 7 8 9 ...
## $ pimtypes:List of 1
## ..$ S:List of 1
## .. ..$ pim.type: chr "all"
mall.ddl
## $S
## par.index model.index group age time Age Time
## 1 1 1 1 0 1 0 0
## 2 2 2 1 1 2 1 1
## 3 3 3 1 2 3 2 2
## 4 4 4 1 3 4 3 3
## 5 5 5 1 4 5 4 4
## 6 6 6 1 5 6 5 5
## 7 7 7 1 6 7 6 6
## 8 8 8 1 7 8 7 7
## 9 9 9 1 8 9 8 8
## 10 10 10 1 9 10 9 9
## 11 11 11 1 10 11 10 10
## 12 12 12 1 11 12 11 11
## 13 13 13 1 12 13 12 12
## 14 14 14 1 13 14 13 13
## 15 15 15 1 14 15 14 14
## 16 16 16 1 15 16 15 15
## 17 17 17 1 16 17 16 16
## 18 18 18 1 17 18 17 17
## 19 19 19 1 18 19 18 18
## 20 20 20 1 19 20 19 19
## 21 21 21 1 20 21 20 20
## 22 22 22 1 21 22 21 21
## 23 23 23 1 22 23 22 22
## 24 24 24 1 23 24 23 23
## 25 25 25 1 24 25 24 24
## 26 26 26 1 25 26 25 25
## 27 27 27 1 26 27 26 26
## 28 28 28 1 27 28 27 27
## 29 29 29 1 28 29 28 28
## 30 30 30 1 29 30 29 29
## 31 31 31 1 30 31 30 30
## 32 32 32 1 31 32 31 31
## 33 33 33 1 32 33 32 32
## 34 34 34 1 33 34 33 33
## 35 35 35 1 34 35 34 34
## 36 36 36 1 35 36 35 35
## 37 37 37 1 36 37 36 36
## 38 38 38 1 37 38 37 37
## 39 39 39 1 38 39 38 38
## 40 40 40 1 39 40 39 39
## 41 41 41 1 40 41 40 40
## 42 42 42 1 41 42 41 41
## 43 43 43 1 42 43 42 42
## 44 44 44 1 43 44 43 43
## 45 45 45 1 44 45 44 44
## 46 46 46 1 45 46 45 45
## 47 47 47 1 46 47 46 46
## 48 48 48 1 47 48 47 47
## 49 49 49 1 48 49 48 48
## 50 50 50 1 49 50 49 49
## 51 51 51 1 50 51 50 50
## 52 52 52 1 51 52 51 51
## 53 53 53 1 52 53 52 52
## 54 54 54 1 53 54 53 53
## 55 55 55 1 54 55 54 54
## 56 56 56 1 55 56 55 55
## 57 57 57 1 56 57 56 56
## 58 58 58 1 57 58 57 57
## 59 59 59 1 58 59 58 58
## 60 60 60 1 59 60 59 59
## 61 61 61 1 60 61 60 60
## 62 62 62 1 61 62 61 61
## 63 63 63 1 62 63 62 62
## 64 64 64 1 63 64 63 63
## 65 65 65 1 64 65 64 64
## 66 66 66 1 65 66 65 65
## 67 67 67 1 66 67 66 66
## 68 68 68 1 67 68 67 67
## 69 69 69 1 68 69 68 68
## 70 70 70 1 69 70 69 69
## 71 71 71 1 70 71 70 70
## 72 72 72 1 71 72 71 71
## 73 73 73 1 72 73 72 72
## 74 74 74 1 73 74 73 73
## 75 75 75 1 74 75 74 74
## 76 76 76 1 75 76 75 75
## 77 77 77 1 76 77 76 76
## 78 78 78 1 77 78 77 77
## 79 79 79 1 78 79 78 78
## 80 80 80 1 79 80 79 79
## 81 81 81 1 80 81 80 80
## 82 82 82 1 81 82 81 81
## 83 83 83 1 82 83 82 82
## 84 84 84 1 83 84 83 83
## 85 85 85 1 84 85 84 84
## 86 86 86 1 85 86 85 85
## 87 87 87 1 86 87 86 86
## 88 88 88 1 87 88 87 87
## 89 89 89 1 88 89 88 88
##
## $pimtypes
## $pimtypes$S
## $pimtypes$S$pim.type
## [1] "all"
# 3. Fit a particular model
# This is a model with S varying by robel height
mod.rob <- RMark::mark(mall.proc, ddl=mall.ddl,
model="Nest",
model.parameters=list(
S =list(formula=~Robel)
)
)
##
## Output summary for Nest model
## Name : S(~Robel)
##
## Npar : 2
## -2lnL: 1566.773
## AICc : 1570.775
##
## Beta
## estimate se lcl ucl
## S:(Intercept) 2.9088384 0.1744305 2.5669545 3.2507222
## S:Robel 0.0272703 0.0466152 -0.0640954 0.1186361
##
##
## Real Parameter S
## 1 2 3 4 5 6 7 8
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 9 10 11 12 13 14 15 16
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 17 18 19 20 21 22 23 24
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 25 26 27 28 29 30 31 32
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 33 34 35 36 37 38 39 40
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 41 42 43 44 45 46 47 48
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 49 50 51 52 53 54 55 56
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 57 58 59 60 61 62 63 64
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 65 66 67 68 69 70 71 72
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 73 74 75 76 77 78 79 80
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 81 82 83 84 85 86 87 88
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 89
## 0.952906
summary(mod.rob)
## Output summary for Nest model
## Name : S(~Robel)
##
## Npar : 2
## -2lnL: 1566.773
## AICc : 1570.775
##
## Beta
## estimate se lcl ucl
## S:(Intercept) 2.9088384 0.1744305 2.5669545 3.2507222
## S:Robel 0.0272703 0.0466152 -0.0640954 0.1186361
##
##
## Real Parameter S
## 1 2 3 4 5 6 7 8
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 9 10 11 12 13 14 15 16
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 17 18 19 20 21 22 23 24
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 25 26 27 28 29 30 31 32
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 33 34 35 36 37 38 39 40
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 41 42 43 44 45 46 47 48
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 49 50 51 52 53 54 55 56
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 57 58 59 60 61 62 63 64
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 65 66 67 68 69 70 71 72
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 73 74 75 76 77 78 79 80
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 81 82 83 84 85 86 87 88
## 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906 0.952906
## 89
## 0.952906
# estimates of DSR are for average value of Robel
# Look the objects returned in more details
names(mod.rob)
## [1] "data" "model" "title"
## [4] "model.name" "links" "mixtures"
## [7] "call" "parameters" "time.intervals"
## [10] "number.of.groups" "group.labels" "nocc"
## [13] "begin.time" "covariates" "fixed"
## [16] "design.matrix" "pims" "design.data"
## [19] "strata.labels" "mlogit.list" "profile.int"
## [22] "simplify" "model.parameters" "results"
## [25] "output"
names(mod.rob$results)
## [1] "lnl" "deviance" "deviance.df"
## [4] "npar" "n" "AICc"
## [7] "beta" "real" "beta.vcv"
## [10] "derived" "derived.vcv" "covariate.values"
## [13] "singular" "real.vcv"
# look at estimates on beta and original scale
mod.rob$results$beta # on the logit scale
## estimate se lcl ucl
## S:(Intercept) 2.9088384 0.1744305 2.5669545 3.2507222
## S:Robel 0.0272703 0.0466152 -0.0640954 0.1186361
mod.rob$results$real# on the regular 0-1 scale for each habitat
## estimate se lcl ucl fixed note
## S g1 a0 t1 0.952906 0.0025942 0.9475523 0.9577375
# derived variabldes is the nest survival probability over the (nocc) days
names(mod.rob$results$derived)
## [1] "S Overall Survival"
mod.rob$results$derived$"S Overall Survival"
## estimate se lcl ucl
## 1 0.01366009 0.003309805 0.008484423 0.0219232
# we need to use covariate predictions to get estimated DSR at different Robel heights
head(get.real(mod.rob, "S", se=TRUE))
## all.diff.index par.index estimate se lcl ucl
## S g1 a0 t1 1 1 0.952906 0.0025942 0.9475523 0.9577375
## S g1 a1 t2 2 1 0.952906 0.0025942 0.9475523 0.9577375
## S g1 a2 t3 3 1 0.952906 0.0025942 0.9475523 0.9577375
## S g1 a3 t4 4 1 0.952906 0.0025942 0.9475523 0.9577375
## S g1 a4 t5 5 1 0.952906 0.0025942 0.9475523 0.9577375
## S g1 a5 t6 6 1 0.952906 0.0025942 0.9475523 0.9577375
## fixed note group age time Age Time
## S g1 a0 t1 1 0 1 0 0
## S g1 a1 t2 1 1 2 1 1
## S g1 a2 t3 1 2 3 2 2
## S g1 a3 t4 1 3 4 3 3
## S g1 a4 t5 1 4 5 4 4
## S g1 a5 t6 1 5 6 5 5
# because the DSR depends on the Robel value and NOT the day, we can predict at day =1
# corresonding to index.all.diff=1
range(malldata$Robel)
## [1] 0.625 9.250
pred.data <- data.frame(Robel=seq(min(malldata$Robel), max(malldata$Robel), length.out=50),
index=1)
head(pred.data)
## Robel index
## 1 0.6250000 1
## 2 0.8010204 1
## 3 0.9770408 1
## 4 1.1530612 1
## 5 1.3290816 1
## 6 1.5051020 1
# we plot the results
# because the DSR is the same for all days, we use the time=1 values
plotdata <- covariate.predictions(mod.rob, data=pred.data)$estimates
head(plotdata)
## vcv.index model.index par.index Robel index estimate se
## 1 1 1 1 0.6250000 1 0.9491111 0.007112088
## 2 1 1 1 0.8010204 1 0.9493425 0.006720197
## 3 1 1 1 0.9770408 1 0.9495729 0.006335469
## 4 1 1 1 1.1530612 1 0.9498022 0.005958547
## 5 1 1 1 1.3290816 1 0.9500306 0.005590208
## 6 1 1 1 1.5051020 1 0.9502580 0.005231429
## lcl ucl fixed
## 1 0.9332221 0.9613761
## 2 0.9344286 0.9610059
## 3 0.9356051 0.9606383
## 4 0.9367506 0.9602748
## 5 0.9378640 0.9599167
## 6 0.9389436 0.9595660
dsr.rob.plot <- ggplot(data=plotdata, aes(x=Robel, y=estimate))+
ggtitle("DSR by Robel height for mallards")+
geom_line()+
geom_ribbon(aes(ymin=lcl, ymax=ucl),alpha=0.1)+
ylab("DSR (95% ci)")
dsr.rob.plot
ggsave(dsr.rob.plot,
file=file.path("..","..","..","..","MyStuff","Images","mallard-dsr-robel.png"), h=4, w=6, units="in", dpi=300)
# fit a null models
# 3. Fit a particular model
# This is a model with S varying by habitat type
mod.null <- RMark::mark(mall.proc, ddl=mall.ddl,
model="Nest",
model.parameters=list(
S =list(formula=~1)
)
)
##
## Output summary for Nest model
## Name : S(~1)
##
## Npar : 1
## -2lnL: 1567.116
## AICc : 1569.117
##
## Beta
## estimate se lcl ucl
## S:(Intercept) 3.005653 0.0576808 2.892598 3.118707
##
##
## Real Parameter S
## 1 2 3 4 5 6 7
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 8 9 10 11 12 13 14
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 15 16 17 18 19 20 21
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 22 23 24 25 26 27 28
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 29 30 31 32 33 34 35
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 36 37 38 39 40 41 42
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 43 44 45 46 47 48 49
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 50 51 52 53 54 55 56
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 57 58 59 60 61 62 63
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 64 65 66 67 68 69 70
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 71 72 73 74 75 76 77
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 78 79 80 81 82 83 84
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 85 86 87 88 89
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
summary(mod.null)
## Output summary for Nest model
## Name : S(~1)
##
## Npar : 1
## -2lnL: 1567.116
## AICc : 1569.117
##
## Beta
## estimate se lcl ucl
## S:(Intercept) 3.005653 0.0576808 2.892598 3.118707
##
##
## Real Parameter S
## 1 2 3 4 5 6 7
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 8 9 10 11 12 13 14
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 15 16 17 18 19 20 21
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 22 23 24 25 26 27 28
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 29 30 31 32 33 34 35
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 36 37 38 39 40 41 42
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 43 44 45 46 47 48 49
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 50 51 52 53 54 55 56
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 57 58 59 60 61 62 63
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 64 65 66 67 68 69 70
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 71 72 73 74 75 76 77
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 78 79 80 81 82 83 84
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
## 85 86 87 88 89
## 0.9528288 0.9528288 0.9528288 0.9528288 0.9528288
collect.models(type="Nest")
## model npar AICc DeltaAICc weight Deviance
## 1 S(~1) 1 1569.117 0.000000 0.6961759 1567.116
## 2 S(~Robel) 2 1570.775 1.658307 0.3038241 1566.773
cleanup(ask=FALSE)