#StackBounty: #r #autocorrelation #spatial #generalized-additive-model #mgcv How to interpret large spatial effect in GAM?

Bounty: 50

This question has partly been asked before here:

And does the deviance explained by the term indicate the extent of
spatial autocorrelation?

but didn’t get an explicit answer. Although I’m not interested in spatial autocorrelation per se.

I’m modelling species occurence with a GAM, including a smooth for latitude and longitude to account for spatial autocorrelation. I’ve found that adding extra predictor variables improves the deviance explained by the model only marginally, the biggest change is caused by adding/removing latitude and longitude. Example code below.

Why should the spatial effect be so large? I imagine some of it will be due to things that haven’t been measured in the landscape e.g. if some individuals live somewhere within the study site there will be more observations around that point. I could potentially add this as an independent variable if only I knew where they lived (e.g. by calculating distance to home for all observations).

The implication seems to be that the other varibles don’t describe the drivers of species occurence very well, and wouldn’t be much good for predicting outside of the study area or time period. Are the other variables any use if they only explain a tiny fraction of the data?

# GAM with spatial smooth only
s.gam <- gam(species_obs ~ 
               s(lat, lon, k = 50, m = c(1, 0.5), bs = 'ds')
             + offset(log(duration))
             , data = df, method = 'REML', family = nb)

summary(s.gam)
> ...
> R-sq.(adj) =  0.335   Deviance explained = 53.5%

# spatial GAM with extra predictors
se.gam <- gam(species_obs ~ 
                temp
              + rainfall
              + s(lat, lon, k = 50, m = c(1, 0.5), bs = 'ds')
              + offset(log(duration))
              , data = df, method = 'REML', family = nb)

summary(se.gam)
> ...
> R-sq.(adj) =  0.332   Deviance explained = 57.2%

# non- spatial GAM
ns.gam <- gam(species_obs ~ 
                temp
              + rainfall
              + offset(log(duration))
              , data = df, method = 'REML', family = nb)

summary(ns.gam)
> ...
> R-sq.(adj) =  -0.0045   Deviance explained = 7.21%

Data here:

structure(list(ID = c(398L, 425L, 311L, 66L, 295L, 316L, 2L, 
134L, 67L, 44L, 215L, 359L, 40L, 63L, 161L, 343L, 331L, 346L, 
415L, 326L, 349L, 78L, 228L, 431L, 123L, 406L, 420L, 272L, 419L, 
291L, 113L, 380L, 117L, 26L, 266L, 16L, 324L, 369L, 253L, 333L, 
409L, 265L, 309L, 160L, 109L, 363L, 169L, 105L, 147L, 184L, 204L, 
8L, 286L, 45L, 257L, 111L, 198L, 154L, 58L, 277L, 372L, 362L, 
410L, 385L, 175L, 61L, 304L, 34L, 102L, 149L, 301L, 255L, 407L, 
261L, 17L, 140L, 312L, 345L, 133L, 190L, 354L, 88L, 18L, 285L, 
15L, 314L, 207L, 397L, 336L, 239L, 163L, 315L, 86L, 402L, 387L, 
64L, 90L, 62L, 22L, 247L, 251L, 240L, 292L, 94L, 167L, 80L, 353L, 
394L, 75L, 323L, 427L, 322L, 244L, 356L, 214L, 104L, 373L, 367L, 
408L, 276L, 434L, 55L, 213L, 37L, 379L, 115L, 278L, 317L, 196L, 
5L, 327L, 243L, 318L, 211L, 237L, 186L, 335L, 51L, 32L, 106L, 
70L, 222L, 69L, 125L, 53L, 56L, 191L, 328L, 284L, 126L, 412L, 
1L, 185L, 82L, 194L, 334L, 170L, 360L, 400L, 437L, 224L, 281L, 
413L, 52L, 405L, 101L, 108L, 131L, 201L, 83L, 89L, 159L, 424L, 
216L, 249L, 65L, 283L, 174L, 260L, 57L, 47L, 435L, 297L, 432L, 
337L, 4L, 24L, 152L, 46L, 39L, 289L, 23L, 59L, 98L, 107L, 275L, 
258L, 221L, 296L, 81L, 294L, 195L, 176L, 245L, 230L, 389L, 54L, 
205L, 60L, 377L, 118L, 143L, 3L, 231L, 422L, 332L, 371L, 124L, 
274L, 384L, 130L, 302L, 202L, 13L, 310L, 421L, 110L, 138L, 173L, 
193L, 150L, 352L, 376L, 438L, 429L, 264L, 252L, 73L, 129L, 212L, 
279L, 341L, 430L, 43L, 411L, 181L, 232L, 338L, 114L, 401L), species_obs = c(16, 
5, 33, 3, 61, 7, 2, 4, 12, 72, 21, 25, 3, 31, 34, 59, 28, 381, 
34, 45, 149, 55, 34, 10, 3, 26, 2, 28, 2, 7, 44, 9, 14, 4, 60, 
4, 6, 8, 56, 118, 11, 80, 105, 119, 71, 0, 13, 34, 12, 48, 7, 
3, 133, 34, 8, 69, 127, 125, 7, 9, 50, 5, 9, 80, 11, 11, 51, 
13, 21, 67, 36, 153, 36, 12, 4, 31, 51, 75, 28, 22, 12, 5, 5, 
36, 16, 29, 6, 65, 10, 11, 2, 3, 11, 36, 10, 6, 30, 1, 19, 9, 
55, 9, 18, 16, 19, 18, 31, 388, 54, 5, 65, 39, 54, 5, 7, 14, 
98, 25, 115, 55, 15, 26, 22, 28, 17, 11, 62, 1, 87, 2, 19, 8, 
40, 2, 50, 21, 20, 6, 10, 41, 7, 56, 5, 6, 64, 16, 38, 1, 18, 
5, 8, 4, 48, 7, 66, 19, 7, 12, 21, 263, 22, 16, 14, 37, 39, 14, 
50, 8, 19, 20, 0, 61, 9, 72, 38, 1, 28, 5, 80, 103, 2, 27, 98, 
48, 11, 1, 10, 17, 29, 2, 146, 13, 12, 0, 3, 232, 12, 37, 51, 
29, 25, 38, 4, 42, 27, 18, 13, 7, 16, 15, 12, 35, 5, 14, 33, 
65, 5, 8, 25, 13, 2, 238, 4, 9, 38, 24, 32, 0, 17, 7, 7, 300, 
4, 430, 23, 93, 32, 37, 11, 3, 12, 26, 4, 7, 4, 30, 16, 28, 23, 
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