Interpret output of lm with ordinal factor

Question

I have something similar to the following example:

library(tidyverse)
library(yardstick)
#> For binary classification, the first factor level is assumed to be the event.
#> Use the argument `event_level = "second"` to alter this as needed.
#> 
#> Attaching package: 'yardstick'
#> The following object is masked from 'package:readr':
#> 
#>     spec
data <- tibble(y = c(rnorm(30), rnorm(30,0.5), rnorm(30,1)),
           x = c(rep("a", 30), rep("b", 30), rep("c", 30)),
           covar = rnorm(90,0.1)) %>%
    mutate(x = factor(x, levels = c("a", "b", "c"), ordered = TRUE))
lm(y ~ x + covar, data = data) %>%
    tidy()
#> # A tibble: 4 × 5
#>   term        estimate std.error statistic     p.value
#>   <chr>          <dbl>     <dbl>     <dbl>       <dbl>
#> 1 (Intercept)   0.584      0.101     5.79  0.000000114
#> 2 x.L           0.522      0.175     2.99  0.00369    
#> 3 x.Q          -0.108      0.176    -0.615 0.540      
#> 4 covar        -0.0128     0.102    -0.125 0.901

^{Created on 2022-03-09 by the reprex package (v2.0.1)}

Where I'd like to know if y depends on x, but I also like to consider a covariate covar.

How do I interpret the output of the lm model? What are x.L and x.Q? I couldn't find this in the documentation for the function.

Answer 1

You have defined x as and ordered factor. Evidently this is more than a categorical variable, it is a variable of ordinal level. This means that there is information in the order of the levels.

In this ordinal case, lm defaults to polynomial contrasts: it will check for a linear (L), quadratic (Q), cubic (C), and so on ... effects. lm will fit "number of levels minus 1" polynomial contrasts. In your case, x has 3 levels, hence x.L and x.Q were present in the output.