使用 GAM 分析时空模式

Question

I am trying to analyse the spatio-temporal risk from disease using the following model;

mod2 = gam(TB ~ offset(log(Population)) + 
       s(Indigenous, k = 10, bs = "cr") + 
       s(Urbanisation, k = 10, bs = "cr") +
       s(Density, k = 10, bs = "cr") + Poverty + 
       s(Poor_Sanitation, k = 10, bs = "cr") + 
       Unemployment + Timeliness + Year + 
              Region + s(lon, lat), 
              data = TBdata, 
              family = nb(link = 'log'))

My issue is that I also want to analyze the difference is years (2012-2014) which i am not confident that my model does at the moment. How would I be able to do this? I've tried using 'Years' in an interaction with 'Population' as it makes some sort of sense but wasn't able to do this successfully.

Data if needed;

TBdata
# A tibble: 1,671 × 14
Indigenous Illiteracy Urbanisation Density Poverty Poor_Sanitation Unemployment Timeliness  Year    TB Population Region   lon    lat
<dbl>      <dbl>        <dbl>   <dbl>   <dbl>           <dbl>        <dbl>      <dbl> <int> <int>      <int>  <int> <dbl>  <dbl>
 1      0.335       6.35         84.1   0.714    31.3            15.3         5.41       59.2  2012   323     559543  11001 -60.7 -12.1 
 2      6.45        8.49         71.4   0.743    48.6            29.4         5.92       58.1  2012    15      73193  11002 -64.0  -9.43

Added information;

After editing my model i am now trying to plot my predictions.

I have used the current code which produces the following plot, although I think i might be missing my predictions so im just currently plotting the smooth function;

mod2 = gam(TB ~ offset(log(Population)) + s(Indigenous, k = 10, bs = "cr") + s(Urbanisation, k = 10, bs = "cr") +
              s(Density, k = 10, bs = "cr") + Poverty + s(Poor_Sanitation, k = 10, bs = "cr") + Unemployment + Timeliness +
              as.factor(Year) + Region + s(lon, lat), 
              data = TBdata, 
              family = nb(link = 'log'))

model summary

#plot
plot(mod2, contour.col = 'white', too.far = 0.10, scheme = 2, rug = T)

Although i think this shows the spatial trends I now need this for the different years, so i think what i want is a plot showing my predictions for each of the years (2012, 2013 and 2014)

Answer 1

When you plot() your model, you are just visualising the estimated smooth functions. As you only have a single spatial smooth, you get a single plot. There's no interaction between factor(Year) and s(lon,lat) .

Do yourself a favour and either convert Year to a factor in the data or create a new variable fYear that is factor(Year) . I'm going to assume you did the former in the below

If you want an interaction you need to use something like this Year + s(lon, lat, by = Year) in your model.

Then you'll get nlevels(factor(Year)) spatial smooths when you plot() your GAM.

But even then those aren't predictions ; you'll notice that the scale is centred about 0 (the grand mean of the data in the reference year in this case). To get plots of predictions you either need to use predict() with newdata set to a data frame containing all the combinations of the predictors you want to predict for/at, or use vis.gam() . For the latter you'll want:

layout(matrix(c(1:3), nrow = 1))
vis.gam(mod2, view = c("lon", "lat"), cond = list(Year = "2012"),
        plot.type = "contour")
vis.gam(mod2, view = c("lon", "lat"), cond = list(Year = "2013"), 
        plot.type = "contour")
vis.gam(mod2, view = c("lon", "lat"), cond = list(Year = "2014"), 
        plot.type = "contour")
layout(1)

anything that you don't include in the list passed to cond will use a value that is either the observation closest to the median of the each respective continuous covariate or the modal level for factor variables.