## Single-Species Single-Season Occupancy Models

Here, we’ll run the single-season occupancy models for data on Weta that you analyzed directly in MARK in lab 10. Here, we’re dealing with 2 types of parameters: ‘Psi’ & ‘p’.

### Bring in the data

library(RMark)
## This is RMark 2.2.4
##  Documentation available at http://www.phidot.org/software/mark/rmark/RMarkDocumentation.zip
# you can ignore warning about final line issue that might appear
weta <- convert.inp("http://www.montana.edu/rotella/documents/502/wetaTwoGroups.inp",
group.df = data.frame(Browse = c("Browsed", "Unbrowsed")),
covariates = c(
"obs11", "obs12", "obs13", "obs14", "obs15",
"obs21", "obs22", "obs23", "obs24", "obs25"))
## Warning in readLines(inp.filename): incomplete final line found on 'http://
## www.montana.edu/rotella/documents/502/wetaTwoGroups.inp'
# store the number of sites
n.sites <- length(weta$ch) # store the maximum number of visits n.visits <- max(nchar(weta$ch))

# make a factor that records whether observer 1, 2, or 3 visited a site
# on each visit. A '9' was used to indicate that no observer visited the site.
# So, if there's a 9 for either observer 1 or 2 on a given date, we
# assign a '.' for that day
obs <- matrix(NA, n.sites, n.visits)
for (i in 1:n.sites) {
obs[i, 1] = ifelse(weta$obs11[i] == 1, 1, ifelse(weta$obs21[i] == 1, 2,
ifelse(weta$obs11[i] == 9, ".", 3))) obs[i, 2] = ifelse(weta$obs12[i] == 1, 1,
ifelse(weta$obs22[i] == 1, 2, ifelse(weta$obs12[i] == 9, ".", 3)))
obs[i, 3] = ifelse(weta$obs13[i] == 1, 1, ifelse(weta$obs23[i] == 1, 2,
ifelse(weta$obs13[i] == 9, ".", 3))) obs[i, 4] = ifelse(weta$obs14[i] == 1, 1,
ifelse(weta$obs24[i] == 1, 2, ifelse(weta$obs14[i] == 9, ".", 3)))
obs[i, 5] = ifelse(weta$obs15[i] == 1, 1, ifelse(weta$obs25[i] == 1, 2,
ifelse(weta$obs15[i] == 9, ".", 3))) } head(weta) ## ch freq Browse obs11 obs12 obs13 obs14 obs15 obs21 obs22 obs23 ## 1:1 0000. 1 Browsed 1 0 0 0 9 0 0 1 ## 1:2 0000. 1 Browsed 1 0 0 0 9 0 0 1 ## 1:3 0001. 1 Browsed 1 0 0 0 9 0 0 1 ## 1:5 0000. 1 Browsed 1 0 0 0 9 0 0 1 ## 1:10 1100. 1 Browsed 1 0 0 0 9 0 0 1 ## 1:11 00.10 1 Browsed 1 0 9 0 1 0 0 9 ## obs24 obs25 ## 1:1 0 9 ## 1:2 0 9 ## 1:3 0 9 ## 1:5 0 9 ## 1:10 0 9 ## 1:11 0 0 head(obs) ## [,1] [,2] [,3] [,4] [,5] ## [1,] "1" "3" "2" "3" "." ## [2,] "1" "3" "2" "3" "." ## [3,] "1" "3" "2" "3" "." ## [4,] "1" "3" "2" "3" "." ## [5,] "1" "3" "2" "3" "." ## [6,] "1" "3" "." "3" "1" # can drop obs11, obs12, ..., obs25 from weta since not used weta <- weta[,-c(4:13)] # add 'Obs' values for each day to 'weta' weta$Obs1 = as.factor(obs[, 1])
weta$Obs2 = as.factor(obs[, 2]) weta$Obs3 = as.factor(obs[, 3])
weta$Obs4 = as.factor(obs[, 4]) weta$Obs5 = as.factor(obs[, 5])
head(weta)
##         ch freq  Browse Obs1 Obs2 Obs3 Obs4 Obs5
## 1:1  0000.    1 Browsed    1    3    2    3    .
## 1:2  0000.    1 Browsed    1    3    2    3    .
## 1:3  0001.    1 Browsed    1    3    2    3    .
## 1:5  0000.    1 Browsed    1    3    2    3    .
## 1:10 1100.    1 Browsed    1    3    2    3    .
## 1:11 00.10    1 Browsed    1    3    .    3    1

### Build function to process data & create models

First, the function puts the observer and time covariates into proper form for use in modeling and processes the data. Second, thefunction decleares the structures for ‘p’ and ‘Psi’ that will be used in all-possible combinations of the structures for each parameter type when the function is executed.

# Create function to fit the 18 models in the book
fit.weta.models <- function() {
#  use 'make.time.factor' to create time-varying dummy variables Obs1 and Obs2
#  observer 3 is used as the intercept to match what we did in MARK
weta = make.time.factor(weta, "Obs", 1:5, intercept = 3)

# Process data
weta.process = process.data(weta, model = "Occupancy", groups = "Browse")
weta.ddl = make.design.data(weta.process)

#  time factor variable copied to 'Day' to match name used in the lab
weta.ddl$p$Day = weta.ddl$p$time

# Define p models
p.dot = list(formula =  ~ 1)
p.browse = list(formula =  ~ Browse)
p.day = list(formula =  ~ Day)
p.obs = list(formula =  ~ Obs1 + Obs2)
p.day.obs = list(formula =  ~ Day + Obs1 + Obs2)
p.day.browse = list(formula =  ~ Day + Browse)
p.obs.browse = list(formula =  ~ Obs1 + Obs2 + Browse)
p.day.obs.browse = list(formula =  ~ Day + Obs1 + Obs2 + Browse)
# Define Psi models
Psi.dot = list(formula =  ~ 1)
Psi.browse = list(formula =  ~ Browse)

# Create model list
cml = create.model.list("Occupancy")

# Run and return marklist of models
return(mark.wrapper(cml, data = weta.process, ddl = weta.ddl))
}

### Run the models and examine the output

It’s very simple to then run the function and each of the models. As implemented here, the output from each of the models appears in the console where it can be reviewed when the function written above is called. If you don’t want the output from every model to appear automatically, see the note above the “mark.wrapper” command for how to set the option of suppressing the output. One can also examine model-specific output in other ways as shown below.

weta.models <- fit.weta.models()
##
## p.browse.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Browse)Psi(~Browse)
##
## Npar :  4
## -2lnL:  258.2606
## AICc :  266.8576
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.6107331 0.3022127 -1.2030700 -0.0183963
## p:BrowseUnbrowsed   -0.0296221 0.4859581 -0.9821000  0.9228558
## Psi:(Intercept)      1.1336537 0.6935108 -0.2256276  2.4929350
## Psi:BrowseUnbrowsed -1.1980364 0.8416136 -2.8475991  0.4515262
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3518920 0.3518920 0.3518920 0.3518920 0.3518920
## Group:BrowseUnbrowsed 0.3451663 0.3451663 0.3451663 0.3451663 0.3451663
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7565125
## Group:BrowseUnbrowsed 0.4839099
##
## p.day.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Day)Psi(~Browse)
##
## Npar :  7
## -2lnL:  245.4368
## AICc :  261.1868
##
## Beta
##                       estimate        se        lcl       ucl
## p:(Intercept)       -0.6100131 0.4312907 -1.4553430 0.2353168
## p:Day2              -0.1551354 0.5283107 -1.1906245 0.8803536
## p:Day3              -0.9792832 0.5881659 -2.1320883 0.1735219
## p:Day4              -0.1827222 0.5424144 -1.2458546 0.8804101
## p:Day5               0.9811154 0.5456452 -0.0883492 2.0505800
## Psi:(Intercept)      1.2078314 0.6959862 -0.1563015 2.5719643
## Psi:BrowseUnbrowsed -1.2351491 0.7508901 -2.7068938 0.2365956
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3520562 0.3175295 0.1694829 0.3115816 0.5917253
## Group:BrowseUnbrowsed 0.3520562 0.3175295 0.1694829 0.3115816 0.5917253
##
##
## Real Parameter Psi
##                              1
## Group:BrowseBrowsed   0.769915
## Group:BrowseUnbrowsed 0.493171
##
## p.day.browse.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Day + Browse)Psi(~Browse)
##
## Npar :  8
## -2lnL:  245.408
## AICc :  263.6937
##
## Beta
##                       estimate        se        lcl       ucl
## p:(Intercept)       -0.5832511 0.4579072 -1.4807492 0.3142470
## p:Day2              -0.1542413 0.5281840 -1.1894819 0.8809993
## p:Day3              -0.9689625 0.5909318 -2.1271889 0.1892639
## p:Day4              -0.1738073 0.5446955 -1.2414105 0.8937958
## p:Day5               0.9942177 0.5513073 -0.0863446 2.0747801
## p:BrowseUnbrowsed   -0.0882306 0.5206885 -1.1087802 0.9323189
## Psi:(Intercept)      1.1623669 0.7146130 -0.2382746 2.5630083
## Psi:BrowseUnbrowsed -1.1516424 0.8802055 -2.8768452 0.5735604
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3581849 0.3235527 0.1747668 0.3192853 0.6013196
## Group:BrowseUnbrowsed 0.3381651 0.3045502 0.1624046 0.3004220 0.5799909
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7617625
## Group:BrowseUnbrowsed 0.5026811
##
## p.day.obs.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Day + Obs1 + Obs2)Psi(~Browse)
##
## Npar :  9
## -2lnL:  239.5994
## AICc :  260.5027
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.2297010 0.4732890 -1.1573474  0.6979454
## p:Day2              -0.1548925 0.5504441 -1.2337630  0.9239780
## p:Day3              -0.9431918 0.5997284 -2.1186595  0.2322759
## p:Day4              -0.0706551 0.5629219 -1.1739820  1.0326718
## p:Day5               1.0354542 0.5639409 -0.0698700  2.1407784
## p:Obs1              -1.0700177 0.4601063 -1.9718261 -0.1682093
## p:Obs2              -0.3435561 0.4357548 -1.1976355  0.5105234
## Psi:(Intercept)      1.1933135 0.6757956 -0.1312459  2.5178729
## Psi:BrowseUnbrowsed -1.1693203 0.7412937 -2.6222560  0.2836154
##
##
## Real Parameter p
##                               1         2         3         4        5
## Group:BrowseBrowsed   0.3545613 0.3246093 0.1728514 0.3453743 0.626219
## Group:BrowseUnbrowsed 0.3545613 0.3246093 0.1728514 0.3453743 0.626219
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7673332
## Group:BrowseUnbrowsed 0.5059980
##
## p.day.obs.browse.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Day + Obs1 + Obs2 + Browse)Psi(~Browse)
##
## Npar :  10
## -2lnL:  239.5993
## AICc :  263.2059
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.2312156 0.4977480 -1.2068017  0.7443704
## p:Day2              -0.1547383 0.5506911 -1.2340928  0.9246162
## p:Day3              -0.9437800 0.6027615 -2.1251925  0.2376325
## p:Day4              -0.0708173 0.5631909 -1.1746714  1.0330367
## p:Day5               1.0348547 0.5672487 -0.0769527  2.1466621
## p:Obs1              -1.0703414 0.4612909 -1.9744716 -0.1662111
## p:Obs2              -0.3437551 0.4362502 -1.1988055  0.5112954
## p:BrowseUnbrowsed    0.0052088 0.5293598 -1.0323365  1.0427541
## Psi:(Intercept)      1.1957593 0.7216656 -0.2187053  2.6102240
## Psi:BrowseUnbrowsed -1.1740827 0.8861536 -2.9109438  0.5627783
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3541856 0.3242823 0.1725302 0.3449677 0.6256992
## Group:BrowseUnbrowsed 0.3553780 0.3254247 0.1732751 0.3461456 0.6269183
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7677695
## Group:BrowseUnbrowsed 0.5054189
##
## p.dot.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~1)Psi(~Browse)
##
## Npar :  3
## -2lnL:  258.2643
## AICc :  264.6172
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.6222546 0.2366510 -1.0860906 -0.1584187
## Psi:(Intercept)      1.1492336 0.6557678 -0.1360713  2.4345384
## Psi:BrowseUnbrowsed -1.2252779 0.7205607 -2.6375769  0.1870211
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3492688 0.3492688 0.3492688 0.3492688 0.3492688
## Group:BrowseUnbrowsed 0.3492688 0.3492688 0.3492688 0.3492688 0.3492688
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7593709
## Group:BrowseUnbrowsed 0.4809981
##
## p.obs.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Obs1 + Obs2)Psi(~Browse)
##
## Npar :  5
## -2lnL:  252.0421
## AICc :  262.9512
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.2158421 0.3270212 -0.8568038  0.4251195
## p:Obs1              -1.0294215 0.4324360 -1.8769960 -0.1818469
## p:Obs2              -0.2796125 0.4033747 -1.0702269  0.5110020
## Psi:(Intercept)      1.1178711 0.6269315 -0.1109148  2.3466569
## Psi:BrowseUnbrowsed -1.1792046 0.7017341 -2.5546035  0.1961943
##
##
## Real Parameter p
##                               1         2         3         4        5
## Group:BrowseBrowsed   0.3629248 0.3689858 0.3590562 0.3701787 0.381149
## Group:BrowseUnbrowsed 0.3629248 0.3689858 0.3590562 0.3701787 0.381149
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7535936
## Group:BrowseUnbrowsed 0.4846714
##
## p.obs.browse.Psi.browse
##
## Output summary for Occupancy model
## Name : p(~Obs1 + Obs2 + Browse)Psi(~Browse)
##
## Npar :  6
## -2lnL:  252.0156
## AICc :  265.308
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.2435662 0.3699471 -0.9686625  0.4815301
## p:Obs1              -1.0359711 0.4345995 -1.8877862 -0.1841560
## p:Obs2              -0.2822415 0.4036974 -1.0734883  0.5090054
## p:BrowseUnbrowsed    0.0801247 0.4916892 -0.8835862  1.0438356
## Psi:(Intercept)      1.1560851 0.6937771 -0.2037180  2.5158883
## Psi:BrowseUnbrowsed -1.2478563 0.8329962 -2.8805288  0.3848162
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3560008 0.3620285 0.3521193 0.3632330 0.3741922
## Group:BrowseUnbrowsed 0.3745749 0.3807311 0.3706075 0.3819606 0.3931360
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7606206
## Group:BrowseUnbrowsed 0.4770733
##
## p.browse.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Browse)Psi(~1)
##
## Npar :  3
## -2lnL:  260.4498
## AICc :  266.8027
##
## Beta
##                     estimate        se        lcl       ucl
## p:(Intercept)     -0.4905233 0.2676562 -1.0151295 0.0340828
## p:BrowseUnbrowsed -0.4891207 0.4133656 -1.2993172 0.3210758
## Psi:(Intercept)    0.6363421 0.4480518 -0.2418394 1.5145237
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3797703 0.3797703 0.3797703 0.3797703 0.3797703
## Group:BrowseUnbrowsed 0.2729624 0.2729624 0.2729624 0.2729624 0.2729624
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6539261
## Group:BrowseUnbrowsed 0.6539261
##
## p.day.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Day)Psi(~1)
##
## Npar :  6
## -2lnL:  248.7948
## AICc :  262.0871
##
## Beta
##                   estimate        se        lcl       ucl
## p:(Intercept)   -0.6211679 0.4312580 -1.4664335 0.2240977
## p:Day2          -0.1466836 0.5280647 -1.1816906 0.8883233
## p:Day3          -0.9798368 0.5873288 -2.1310013 0.1713276
## p:Day4          -0.1642081 0.5426922 -1.2278849 0.8994686
## p:Day5           0.9972785 0.5470389 -0.0749178 2.0694748
## Psi:(Intercept)  0.5311520 0.3961420 -0.2452864 1.3075904
##
##
## Real Parameter p
##                               1        2         3         4         5
## Group:BrowseBrowsed   0.3495159 0.316944 0.1678412 0.3131624 0.5929347
## Group:BrowseUnbrowsed 0.3495159 0.316944 0.1678412 0.3131624 0.5929347
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6297518
## Group:BrowseUnbrowsed 0.6297518
##
## p.day.browse.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Day + Browse)Psi(~1)
##
## Npar :  7
## -2lnL:  247.1824
## AICc :  262.9324
##
## Beta
##                     estimate        se        lcl       ucl
## p:(Intercept)     -0.5072781 0.4370940 -1.3639824 0.3494261
## p:Day2            -0.1403519 0.5220271 -1.1635251 0.8828212
## p:Day3            -0.9099775 0.5840456 -2.0547069 0.2347520
## p:Day4            -0.1068076 0.5373022 -1.1599200 0.9463048
## p:Day5             1.0599832 0.5383203  0.0048753 2.1150911
## p:BrowseUnbrowsed -0.5489152 0.4206973 -1.3734820 0.2756516
## Psi:(Intercept)    0.7125470 0.4723259 -0.2132118 1.6383058
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3758318 0.3435238 0.1950922 0.3511278 0.6347630
## Group:BrowseUnbrowsed 0.2580376 0.2320904 0.1228008 0.2381224 0.5009475
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6709637
## Group:BrowseUnbrowsed 0.6709637
##
## p.day.obs.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Day + Obs1 + Obs2)Psi(~1)
##
## Npar :  8
## -2lnL:  242.5466
## AICc :  260.8323
##
## Beta
##                   estimate        se        lcl        ucl
## p:(Intercept)   -0.2384162 0.4726739 -1.1648570  0.6880246
## p:Day2          -0.1376623 0.5473984 -1.2105633  0.9352387
## p:Day3          -0.9640981 0.5967627 -2.1337530  0.2055568
## p:Day4          -0.0470487 0.5606895 -1.1460001  1.0519027
## p:Day5           1.0484584 0.5618024 -0.0526744  2.1495912
## p:Obs1          -1.1043723 0.4588470 -2.0037124 -0.2050322
## p:Obs2          -0.3562762 0.4349636 -1.2088049  0.4962525
## Psi:(Intercept)  0.5804494 0.4093417 -0.2218603  1.3827591
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3498032 0.3239235 0.1668317 0.3462006 0.6249679
## Group:BrowseUnbrowsed 0.3498032 0.3239235 0.1668317 0.3462006 0.6249679
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6411708
## Group:BrowseUnbrowsed 0.6411708
##
## p.day.obs.browse.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Day + Obs1 + Obs2 + Browse)Psi(~1)
##
## Npar :  9
## -2lnL:  241.4147
## AICc :  262.318
##
## Beta
##                     estimate        se        lcl        ucl
## p:(Intercept)     -0.1481327 0.4801259 -1.0891794  0.7929140
## p:Day2            -0.1651114 0.5413288 -1.2261158  0.8958931
## p:Day3            -0.9041529 0.5926704 -2.0657869  0.2574810
## p:Day4            -0.0471992 0.5539722 -1.1329848  1.0385864
## p:Day5             1.0834174 0.5521178  0.0012665  2.1655682
## p:Obs1            -1.0500604 0.4556463 -1.9431271 -0.1569937
## p:Obs2            -0.3159094 0.4276196 -1.1540439  0.5222250
## p:BrowseUnbrowsed -0.4698723 0.4303053 -1.3132708  0.3735261
## Psi:(Intercept)    0.7375144 0.4801905 -0.2036591  1.6786878
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3758849 0.3432312 0.1928306 0.3719965 0.6581578
## Group:BrowseUnbrowsed 0.2735025 0.2462340 0.1299282 0.2702147 0.5461738
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6764521
## Group:BrowseUnbrowsed 0.6764521
##
## p.dot.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~1)Psi(~1)
##
## Npar :  2
## -2lnL:  261.7871
## AICc :  265.9611
##
## Beta
##                   estimate        se        lcl        ucl
## p:(Intercept)   -0.6218311 0.2363737 -1.0851235 -0.1585387
## Psi:(Intercept)  0.4751239 0.3745432 -0.2589808  1.2092287
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3493651 0.3493651 0.3493651 0.3493651 0.3493651
## Group:BrowseUnbrowsed 0.3493651 0.3493651 0.3493651 0.3493651 0.3493651
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6165958
## Group:BrowseUnbrowsed 0.6165958
##
## p.obs.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Obs1 + Obs2)Psi(~1)
##
## Npar :  4
## -2lnL:  255.3578
## AICc :  263.9548
##
## Beta
##                   estimate        se        lcl        ucl
## p:(Intercept)   -0.2216020 0.3270493 -0.8626185  0.4194146
## p:Obs1          -1.0413814 0.4314191 -1.8869627 -0.1958000
## p:Obs2          -0.2729065 0.4037457 -1.0642481  0.5184351
## Psi:(Intercept)  0.4862374 0.3740421 -0.2468851  1.2193600
##
##
## Real Parameter p
##                              1         2         3         4         5
## Group:BrowseBrowsed   0.361047 0.3674223 0.3573965 0.3684661 0.3795116
## Group:BrowseUnbrowsed 0.361047 0.3674223 0.3573965 0.3684661 0.3795116
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6192197
## Group:BrowseUnbrowsed 0.6192197
##
## p.obs.browse.Psi.dot
##
## Output summary for Occupancy model
## Name : p(~Obs1 + Obs2 + Browse)Psi(~1)
##
## Npar :  5
## -2lnL:  254.5045
## AICc :  265.4136
##
## Beta
##                     estimate        se        lcl        ucl
## p:(Intercept)     -0.1342856 0.3424409 -0.8054698  0.5368985
## p:Obs1            -0.9958830 0.4292169 -1.8371482 -0.1546178
## p:Obs2            -0.2570374 0.3990736 -1.0392217  0.5251469
## p:BrowseUnbrowsed -0.4044099 0.4288018 -1.2448614  0.4360416
## Psi:(Intercept)    0.6197218 0.4419715 -0.2465424  1.4859860
##
##
## Real Parameter p
##                               1         2         3         4         5
## Group:BrowseBrowsed   0.3851866 0.3915447 0.3817047 0.3925023 0.4032983
## Group:BrowseUnbrowsed 0.2948381 0.3004336 0.2917853 0.3012788 0.3108495
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.6501553
## Group:BrowseUnbrowsed 0.6501553

### Examine model-selection table

Once the models are run, we can examine the model-selection table. We can also examine model-specific output.

options(width = 160)
weta.models
##                                         model npar     AICc DeltaAICc      weight  Deviance
## 7           p(~Day + Obs1 + Obs2)Psi(~Browse)    9 260.5027 0.0000000 0.196120806  239.5994
## 8                p(~Day + Obs1 + Obs2)Psi(~1)    8 260.8323 0.3296085 0.166322153  242.5466
## 9                         p(~Day)Psi(~Browse)    7 261.1868 0.6841742 0.139301929 -162.9434
## 10                             p(~Day)Psi(~1)    6 262.0871 1.5844719 0.088809612 -159.5854
## 6       p(~Day + Obs1 + Obs2 + Browse)Psi(~1)    9 262.3180 1.8152900 0.079129506  241.4147
## 4                     p(~Day + Browse)Psi(~1)    7 262.9324 2.4297042 0.058199614 -161.1979
## 15                p(~Obs1 + Obs2)Psi(~Browse)    5 262.9512 2.4485251 0.057654499  252.0421
## 5  p(~Day + Obs1 + Obs2 + Browse)Psi(~Browse)   10 263.2059 2.7032416 0.050760071  239.5993
## 3                p(~Day + Browse)Psi(~Browse)    8 263.6937 3.1910585 0.039773529 -162.9723
## 16                     p(~Obs1 + Obs2)Psi(~1)    4 263.9548 3.4521591 0.034905739  255.3578
## 11                          p(~1)Psi(~Browse)    3 264.6172 4.1145554 0.025064516 -150.1160
## 13       p(~Obs1 + Obs2 + Browse)Psi(~Browse)    6 265.3080 4.8052919 0.017744665  252.0156
## 14            p(~Obs1 + Obs2 + Browse)Psi(~1)    5 265.4136 4.9109451 0.016831603  254.5045
## 12                               p(~1)Psi(~1)    2 265.9611 5.4583972 0.012801114 -146.5931
## 2                           p(~Browse)Psi(~1)    3 266.8027 6.3000354 0.008404045 -147.9305
## 1                      p(~Browse)Psi(~Browse)    4 266.8576 6.3549091 0.008176599 -150.1197

### Use AIC instead of AICc for model selection

Here, we use AIC so that we can compare direclty with results presented in the Occupancy book. You can see that things match (as they should) for most models but that something appears amiss in the book with the Psi(.)p(Obs+Browse) model as it should have 5 parameters but is only listed as having 4 in the book (it is assigned k=5 here).

options(width = 160)
# Store and view a model table that uses AIC rather than AICc
AIC.table = weta.models
AIC.table$model.table = model.table(weta.models, use.AIC = TRUE) AIC.table ## model npar AIC DeltaAIC weight Deviance ## 7 p(~Day + Obs1 + Obs2)Psi(~Browse) 9 257.5994 0.00000 0.275827626 239.5994 ## 8 p(~Day + Obs1 + Obs2)Psi(~1) 8 258.5466 0.94712 0.171780264 242.5466 ## 6 p(~Day + Obs1 + Obs2 + Browse)Psi(~1) 9 259.4147 1.81529 0.111289078 241.4147 ## 9 p(~Day)Psi(~Browse) 7 259.4368 1.83740 0.110065553 -162.9434 ## 5 p(~Day + Obs1 + Obs2 + Browse)Psi(~Browse) 10 259.5993 1.99991 0.101475879 239.5993 ## 10 p(~Day)Psi(~1) 6 260.7948 3.19539 0.055817148 -159.5854 ## 4 p(~Day + Browse)Psi(~1) 7 261.1824 3.58293 0.045984810 -161.1979 ## 3 p(~Day + Browse)Psi(~Browse) 8 261.4080 3.80857 0.041078757 -162.9723 ## 15 p(~Obs1 + Obs2)Psi(~Browse) 5 262.0421 4.44266 0.029917576 252.0421 ## 16 p(~Obs1 + Obs2)Psi(~1) 4 263.3578 5.75837 0.015496143 255.3578 ## 13 p(~Obs1 + Obs2 + Browse)Psi(~Browse) 6 264.0156 6.41621 0.011152583 252.0156 ## 11 p(~1)Psi(~Browse) 3 264.2643 6.66484 0.009848864 -150.1160 ## 14 p(~Obs1 + Obs2 + Browse)Psi(~1) 5 264.5045 6.90508 0.008734111 254.5045 ## 12 p(~1)Psi(~1) 2 265.7871 8.18771 0.004599378 -146.5931 ## 1 p(~Browse)Psi(~Browse) 4 266.2606 8.66112 0.003629940 -150.1197 ## 2 p(~Browse)Psi(~1) 3 266.4498 8.85032 0.003302290 -147.9305 ### Look at output from top model # View the model names names(weta.models) ## [1] "p.browse.Psi.browse" "p.browse.Psi.dot" "p.day.browse.Psi.browse" "p.day.browse.Psi.dot" "p.day.obs.browse.Psi.browse" ## [6] "p.day.obs.browse.Psi.dot" "p.day.obs.Psi.browse" "p.day.obs.Psi.dot" "p.day.Psi.browse" "p.day.Psi.dot" ## [11] "p.dot.Psi.browse" "p.dot.Psi.dot" "p.obs.browse.Psi.browse" "p.obs.browse.Psi.dot" "p.obs.Psi.browse" ## [16] "p.obs.Psi.dot" "model.table" # examine the output from top-ranked model (#7) and # store top model in object with short name top <- weta.models$p.day.obs.Psi.browse

# look at summary of top model's output
summary(top, showall = FALSE)
## Output summary for Occupancy model
## Name : p(~Day + Obs1 + Obs2)Psi(~Browse)
##
## Npar :  9
## -2lnL:  239.5994
## AICc :  260.5027
##
## Beta
##                       estimate        se        lcl        ucl
## p:(Intercept)       -0.2297010 0.4732890 -1.1573474  0.6979454
## p:Day2              -0.1548925 0.5504441 -1.2337630  0.9239780
## p:Day3              -0.9431918 0.5997284 -2.1186595  0.2322759
## p:Day4              -0.0706551 0.5629219 -1.1739820  1.0326718
## p:Day5               1.0354542 0.5639409 -0.0698700  2.1407784
## p:Obs1              -1.0700177 0.4601063 -1.9718261 -0.1682093
## p:Obs2              -0.3435561 0.4357548 -1.1976355  0.5105234
## Psi:(Intercept)      1.1933135 0.6757956 -0.1312459  2.5178729
## Psi:BrowseUnbrowsed -1.1693203 0.7412937 -2.6222560  0.2836154
##
##
## Real Parameter p
##                               1         2         3         4        5
## Group:BrowseBrowsed   0.3545613 0.3246093 0.1728514 0.3453743 0.626219
## Group:BrowseUnbrowsed 0.3545613 0.3246093 0.1728514 0.3453743 0.626219
##
##
## Real Parameter Psi
##                               1
## Group:BrowseBrowsed   0.7673332
## Group:BrowseUnbrowsed 0.5059980

### Model Average Psi

Here, model-averaging is done for Psi in each habitat setting.

Mod.Avg.Psi <- model.average(weta.models, "Psi")
Mod.Avg.Psi
##                      par.index  estimate        se fixed    note     group age time Age Time    Browse
## Psi gBrowsed a0 t1          11 0.7102669 0.1268297                 Browsed   0    1   0    0   Browsed
## Psi gUnbrowsed a0 t1        12 0.5670989 0.1314801               Unbrowsed   0    1   0    0 Unbrowsed