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I am confused about if you can, and how to, make population average predictions from a fitted GAM? Any advice or directions to good worked examples would be much appreciated?

I am using GAMs to model growth through time across 200 animals, example data are here.

I read in my example data

test <- read.csv("test.csv", header = T)

test$tagged <- factor(test$tagged)
test$sex_t0 <- factor(test$sex_t0)
test$scale_id <- factor(test$scale_id)

and run my model

gam1 <- gam(weight_t ~ 
                 tagged + 
                 sex_t0 +
                 s(age.x, k = 6) + 
                 s(scale_id, bs = "re") + 
                 s(age.x, scale_id, bs = "re"), 
             data = long, 
             method = "REML", 
             family = Gamma(link = "log"))

I then create a new data frame to predict from

pred.dat <- data.frame(tagged = c(rep(0, 752), rep(1, 752)), 
                        sex_t0 = c(rep("f", 376), rep("m", 376), rep("f", 376), rep("m", 376)),
                        age.x = c(rep(seq(9, 384, 1), 4)),
                        scale_id = rep(1, 1504))

pred.dat$tagged <- factor(pred.dat$tagged)
pred.dat$sex_t0 <- factor(pred.dat$sex_t0)
pred.dat$scale_id <- factor(pred.dat$scale_id)

When predicting from my fitted GAM I can use the exclude = option, which I understand sets my random effects to 0 and essentially does not account for them when making predictions, see here. This is also suggested by the plots that I produce which shows confidence intervals increasing greatly through time, suggesting that the random intercept and slope that I have included in my model has not been accounted for when predicting (some increase in variation with age would be expected, but not as much as is shown if this was a population averaged prediction).

preds <- predict(gam1, 
                  newdata = pred.dat, 
                  exclude = c("s(scale_id)", 
                              "s(age.x, scale_id)"), 
                  se = T, type = 'response')

enter image description here

I interpret the help page for predict.gam (perhaps incorrectly) that type="iterms" can be used to produce population averaged predictions from a fitted gam. However, if I use this I no longer get a single estimated value for the predictions and their standard errors.

preds <- predict(gam1, 
                  newdata = pred.dat, 
                  se = T, type = "iterms")

Any advice on how to produce population averaged predictions from a fitted gam would be appreciated? I have read a number of pages but remain confused (here, here, here, here, and others).

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    $\begingroup$ Shouldn't the second smooth to exclude be: "s(age.x,scale_id)"? Simon usually doesn't put spaces in the labels for smooths. Double check this; run summary(gam1) & check the label there. What you are doing should be working (if you have the right smooth labels), but you shouldn't be forming a confidence band on the expectation from the model using the standard error on the response scale. Instead predict on the link scale, add plus/minus 2*se to the predicted value to get the CI on the link scale then use the inverse of the link to put the predicted value and the CI onto the response scale. $\endgroup$ Commented Nov 10, 2020 at 2:02
  • $\begingroup$ Thanks Gavin! You were correct, removing the space from the smooth fixed it...so simple! I have been trying to work that one out for about 24 hours now.... $\endgroup$ Commented Nov 10, 2020 at 2:40

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