Summarise evidence

Evidence summary by unmarked

Earlier we used modSel() to summarise the evidence for our models, so we could decide which is best supported by our field data

Let’s refresh our memory of the information modSel() provides:

ModSelect

             nPars    AIC delta   AICwt cumltvWt
hnLC_.           3 271.39  0.00 6.1e-01     0.61
hnLC_DTC         4 272.40  1.01 3.7e-01     0.98
hazLC_.          4 279.16  7.77 1.3e-02     0.99
hazLC_DTC        5 280.55  9.15 6.3e-03     1.00
haz._DTC         4 330.69 59.30 8.1e-14     1.00
modelhn._DTC     3 339.81 68.42 8.5e-16     1.00
haz._.           3 352.00 80.61 1.9e-18     1.00
hn._.            2 361.13 89.74 2.0e-20     1.00

Model name
Number of parameters
AIC
Delta AIC
Model weight
Cumulative model weight

Evidence summary by AICcmodavg

In R, code libraries evolve as people contribute new packages, which means there are often multiple ways to achieve roughly the same end

We want to summarise evidence from Information Theory, and packages like AICcmodavg can help with that! 💪

Install and load AICcmodavg:

install.packages("AICcmodavg") # Install package
library(AICcmodavg) # Load package

AICcmodavg is useful beyond distance sampling

The AICcmodavg package helps with any analyses involving model comparison with Information Theory: linear models, occupancy modelling, capture-recapture etc

Compare AIC tables

Let’s tabulate AIC-based information with AICcmodavg’s aictab() function, and compare the output with modSel() 👀

Output from modSel():

             nPars    AIC delta   AICwt cumltvWt
hnLC_.           3 271.39  0.00 6.1e-01     0.61
hnLC_DTC         4 272.40  1.01 3.7e-01     0.98
hazLC_.          4 279.16  7.77 1.3e-02     0.99
hazLC_DTC        5 280.55  9.15 6.3e-03     1.00
haz._DTC         4 330.69 59.30 8.1e-14     1.00
modelhn._DTC     3 339.81 68.42 8.5e-16     1.00
haz._.           3 352.00 80.61 1.9e-18     1.00
hn._.            2 361.13 89.74 2.0e-20     1.00

Output from aictab():


Model selection based on AIC:

          K    AIC Delta_AIC AICWt Cum.Wt      LL
hnLC_.    3 271.39      0.00  0.64   0.64 -132.70
hnLC_DTC  4 272.69      1.29  0.34   0.98 -132.34
hazLC_.   4 279.16      7.77  0.01   0.99 -135.58
hazLC_DTC 5 281.05      9.66  0.01   1.00 -135.53
haz._DTC  4 330.78     59.38  0.00   1.00 -161.39
hn._DTC   3 340.06     68.67  0.00   1.00 -167.03
haz._.    3 352.00     80.61  0.00   1.00 -173.00
hn._.     2 361.13     89.74  0.00   1.00 -178.56

The two functions provide almost the same information:

Column names differ slightly e.g. K instead of nPars for number of parameters
aictab() adds LogLikelihood values (LL)

Small sample correction with AICc

The real power of aictab() lies in its ability to summarise evidence adjusted by the small sample correction factor AICc, which is its default setting:

❌ Without correction factor:

AICtable <- aictab(models, second.ord = FALSE)
AICtable


Model selection based on AIC:

          K    AIC Delta_AIC AICWt Cum.Wt      LL
hnLC_.    3 271.39      0.00  0.64   0.64 -132.70
hnLC_DTC  4 272.69      1.29  0.34   0.98 -132.34
hazLC_.   4 279.16      7.77  0.01   0.99 -135.58
hazLC_DTC 5 281.05      9.66  0.01   1.00 -135.53
haz._DTC  4 330.78     59.38  0.00   1.00 -161.39
hn._DTC   3 340.06     68.67  0.00   1.00 -167.03
haz._.    3 352.00     80.61  0.00   1.00 -173.00
hn._.     2 361.13     89.74  0.00   1.00 -178.56

✅ With correction factor:

AICctable <- aictab(models) # Use AICc
AICctable


Model selection based on AICc:

          K   AICc Delta_AICc AICcWt Cum.Wt      LL
hnLC_.    3 274.39       0.00   0.88   0.88 -132.70
hnLC_DTC  4 278.40       4.01   0.12   1.00 -132.34
hazLC_.   4 284.88      10.49   0.00   1.00 -135.58
hazLC_DTC 5 291.05      16.66   0.00   1.00 -135.53
haz._DTC  4 336.49      62.10   0.00   1.00 -161.39
hn._DTC   3 343.06      68.67   0.00   1.00 -167.03
haz._.    3 355.00      80.61   0.00   1.00 -173.00
hn._.     2 362.46      88.07   0.00   1.00 -178.56

❓ What differences do you see?

Do these differences change the conclusions you draw from your analysis?

Use AICc

The weight of evidence shifted further in favour of our top model hnLC_., which allows detectability to vary by landcover class but keeps density constant between transects

This is because we have a relatively small sample size of 12 transects

Always use AICc

Even if you have a larger sample size from your own fieldwork, we recommend you follow Anderson’s advice and base all your analyses on AICc