# Exploratory Modelling

    library(brolgar)

It can be useful to fit a model to explore your data. One technique is to fit a linear model for each group in a dataset. For example, you could fit a linear model for each key in the data.

`brolgar` provides a helper function to help with this, called `key_slope()`.

`key_slope()` returns the intercept and slope estimate for each key, given a linear model formula. We can get the number of observations, and slope information for each individual to identify those that are decreasing over time.

    key_slope(wages,ln_wages ~ xp)
    #> # A tibble: 888 × 3
    #>       id .intercept .slope_xp
    #>    <int>      <dbl>     <dbl>
    #>  1    31       1.41    0.101
    #>  2    36       2.04    0.0588
    #>  3    53       2.29   -0.358
    #>  4   122       1.93    0.0374
    #>  5   134       2.03    0.0831
    #>  6   145       1.59    0.0469
    #>  7   155       1.66    0.0867
    #>  8   173       1.61    0.100
    #>  9   206       1.73    0.180
    #> 10   207       1.62    0.0884
    #> # ℹ 878 more rows

We can then join these summaries back to the data:

    library(dplyr)
    wages_slope <- key_slope(wages,ln_wages ~ xp) %>%
      left_join(wages, by = "id")

    wages_slope
    #> # A tibble: 6,402 × 11
    #>       id .intercept .slope_xp ln_wages    xp   ged xp_since_ged black hispanic
    #>    <int>      <dbl>     <dbl>    <dbl> <dbl> <int>        <dbl> <int>    <int>
    #>  1    31       1.41    0.101      1.49 0.015     1        0.015     0        1
    #>  2    31       1.41    0.101      1.43 0.715     1        0.715     0        1
    #>  3    31       1.41    0.101      1.47 1.73      1        1.73      0        1
    #>  4    31       1.41    0.101      1.75 2.77      1        2.77      0        1
    #>  5    31       1.41    0.101      1.93 3.93      1        3.93      0        1
    #>  6    31       1.41    0.101      1.71 4.95      1        4.95      0        1
    #>  7    31       1.41    0.101      2.09 5.96      1        5.96      0        1
    #>  8    31       1.41    0.101      2.13 6.98      1        6.98      0        1
    #>  9    36       2.04    0.0588     1.98 0.315     1        0.315     0        0
    #> 10    36       2.04    0.0588     1.80 0.983     1        0.983     0        0
    #> # ℹ 6,392 more rows
    #> # ℹ 2 more variables: high_grade <int>, unemploy_rate <dbl>

And highlight those individuals with a negative slope using `gghighlight`:

    library(gghighlight)

    wages_slope %>%
      as_tibble() %>% # workaround for gghighlight + tsibble
      ggplot(aes(x = xp,
                 y = ln_wages,
                 group = id)) +
      geom_line() +
      gghighlight(.slope_xp < 0)

# Find keys near other summaries with `keys_near()`

We might want to further summarise our exploratory modelling by finding those slopes that are near a five number summary values:

    summary(wages_slope$.slope_xp)
    #>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's
    #> -4.57692 -0.00189  0.04519  0.04490  0.08458 13.21569       38

Finding those groups that are near these values can be surprisingly challenging!

`brolgar` makes it easier by providing the `keys_near()` function. You tell it what the key is, what variable you want to summarise by, and then by default it returns those keys near the five number summary. Let’s return the keys near the `.slope_xp`:

    wages_slope %>%
      keys_near(key = id,
                var = .slope_xp)
    #> # A tibble: 31 × 5
    #>       id .slope_xp stat  stat_value stat_diff
    #>    <int>     <dbl> <fct>      <dbl>     <dbl>
    #>  1  2092  -0.00189 q_25    -0.00189         0
    #>  2  2092  -0.00189 q_25    -0.00189         0
    #>  3  2092  -0.00189 q_25    -0.00189         0
    #>  4  2092  -0.00189 q_25    -0.00189         0
    #>  5  2092  -0.00189 q_25    -0.00189         0
    #>  6  2092  -0.00189 q_25    -0.00189         0
    #>  7  6770   0.0846  q_75     0.0846          0
    #>  8  6770   0.0846  q_75     0.0846          0
    #>  9  6770   0.0846  q_75     0.0846          0
    #> 10  6770   0.0846  q_75     0.0846          0
    #> # ℹ 21 more rows

Here it returns the `id`, the `.slope_xp`, and the statistic that it was closest to, and what the difference between the slope_xp and the statistic.

You can visualise these summary keys by joining them back to the data:

    wages_slope %>%
      keys_near(key = id,
                var = .slope_xp) %>%
      left_join(wages, by = "id") %>%
      ggplot(aes(x = xp,
                 y = ln_wages,
                 group = id,
                 colour = stat)) +
      geom_line()

You can read more about `keys_near()` in the Identifying interesting observations vignette.