Predicting with time as covariate

Question

I have an indicator (intervention coverage in %) where data stop in 2015 and I would like to extrapolate/project data till 2018.

I have used the following code that basically predicts data using glm with time as covariate in the logit space.

My colleagues think a GAM model would be better but I don't see what would be the added value. Could you explain what would be the difference and which model would be best to use?

df_na <- df3 %>%
  filter(!is.na(y))

func <- function(data,country){
  data = subset(data,iso3==country)
  data[match(2010:2015,data$year),]$y
}

proj <- function(y, year=2010:2015, target=2018){
  period <- year[1]:target
  yhat <- predict(glm(y ~ year, family=quasibinomial), newdata=data.frame(year=period),type="response") 
  return(data.frame(year=period, y=yhat))
}

res <-   lapply(unique(df_na$iso3),function(i){
  data.frame(country=i,proj(func(df_na,country=i)))
})

res <- do.call(rbind,res)

Answer 1

In your logistic model with year, time is assumed to act linearly on the logodds. With an additive model estimated with gam, a smooth action replaces the linear action, represented with a spline function. That gives a nice test on the assumption of linearity.

But, you want to use the model for extrapolation? A spline model will not help much with that ... you would first have to extrapolate the spline, how? On the other hand, if the gam model shows that linearity does not hold, using the linear model for extrapolation would be foolhardy. So that's your answer: The gam model mostly is a useful test (informal) on your first model.