PRDV420: Introduction to R Programming

Let's take a look at the equivalent model for two continuous variables. Initially things proceed almost identically to the previous example:

mod1 <- lm(y ~ x1 + x2, data = sim4)
mod2 <- lm(y ~ x1 * x2, data = sim4)

grid <- sim4 %>% 
data_grid(
  x1 = seq_range(x1, 5), 
  x2 = seq_range(x2, 5) 
) %>% 
gather_predictions(mod1, mod2)
grid
#> # A tibble: 50 x 4
#>   model    x1    x2   pred
#>   <chr> <dbl> <dbl>  <dbl>
#> 1 mod1   -1    -1    0.996
#> 2 mod1   -1    -0.5 -0.395
#> 3 mod1   -1     0   -1.79 
#> 4 mod1   -1     0.5 -3.18 
#> 5 mod1   -1     1   -4.57 
#> 6 mod1   -0.5  -1    1.91 
#> # … with 44 more rows

Note my use of seq_range() inside data_grid(). Instead of using every unique value of x, I'm going to use a regularly spaced grid of five values between the minimum and maximum numbers. It's probably not super important here, but it's a useful technique in general. There are two other useful arguments to seq_range():

• pretty = TRUE will generate a "pretty" sequence, i.e. something that looks nice to the human eye. This is useful if you want to produce tables of output:

  seq_range(c(0.0123, 0.923423), n = 5)
  #> [1] 0.0123000 0.2400808 0.4678615 0.6956423 0.9234230
  seq_range(c(0.0123, 0.923423), n = 5, pretty = TRUE)
  #> [1] 0.0 0.2 0.4 0.6 0.8 1.0

• trim = 0.1 will trim off 10% of the tail values. This is useful if the variables have a long tailed distribution and you want to focus on generating values near the center:

  x1 <- rcauchy(100)
  seq_range(x1, n = 5)
  #> [1] -115.86934  -83.52130  -51.17325  -18.82520   13.52284
  seq_range(x1, n = 5, trim = 0.10)
  #> [1] -13.841101  -8.709812  -3.578522   1.552767   6.684057
  seq_range(x1, n = 5, trim = 0.25)
  #> [1] -2.17345439 -1.05938856  0.05467728  1.16874312  2.28280896
  seq_range(x1, n = 5, trim = 0.50)
  #> [1] -0.7249565 -0.2677888  0.1893788  0.6465465  1.1037141

• expand = 0.1 is in some sense the opposite of trim() it expands the range by 10%.

  x2 <- c(0, 1)
  seq_range(x2, n = 5)
  #> [1] 0.00 0.25 0.50 0.75 1.00
  seq_range(x2, n = 5, expand = 0.10)
  #> [1] -0.050  0.225  0.500  0.775  1.050
  seq_range(x2, n = 5, expand = 0.25)
  #> [1] -0.1250  0.1875  0.5000  0.8125  1.1250
  seq_range(x2, n = 5, expand = 0.50)
  #> [1] -0.250  0.125  0.500  0.875  1.250

Next let's try and visualise that model. We have two continuous predictors, so you can imagine the model like a 3d surface. We could display that using geom_tile():

ggplot(grid, aes(x1, x2)) + 
geom_tile(aes(fill = pred)) + 
facet_wrap(~ model)

That doesn't suggest that the models are very different! But that's partly an illusion: our eyes and brains are not very good at accurately comparing shades of colour. Instead of looking at the surface from the top, we could look at it from either side, showing multiple slices:

ggplot(grid, aes(x1, pred, colour = x2, group = x2)) + 
geom_line() +
facet_wrap(~ model)
ggplot(grid, aes(x2, pred, colour = x1, group = x1)) + 
geom_line() +
facet_wrap(~ model)