How to interpret the partial effect plots for parametric terms while using gratia::draw() and gratia::parametric_effects()?

Question

I am asking a question akin to this one: https://stackoverflow.com/questions/71884457/what-does-the-y-axis-effect-mean-after-using-gratiadraw-for-a-gam but am wondering the same question for parametric terms not smooths.

My data looks like this:

    df<-structure(list(spreg = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L), levels = c("n", "y"), class = c("ordered", 
"factor")), Landings = c(48974, 16933, 18389, 16433, 5720, 3775, 
1388, 97109, 148609, 104267, 77454, 128938, 108096, 126957, 102396, 
16165, 59423, 2892, 4728, 3783, 4785, 11359, 5323, 6106, 167, 
568, 480, 2208, 4378, 1908), year = c(2007, 2009, 2011, 2013, 
2015, 2018, 2007, 2007, 2007, 2012, 2015, 2018, 2007, 2007, 2012, 
2015, 2018, 2008, 2010, 2006, 2008, 2011, 2008, 2011, 2007, 2010, 
2007, 2014, 2015, 2014)), row.names = c(1L, 2L, 3L, 4L, 5L, 6L, 
7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 
20L, 21L, 22L, 23L, 24L, 25L, 26L, 28L, 29L, 30L, 31L), class = "data.frame")

My code looks like this:

library(mgcv)
library(gratia)
gam<-gam(Landings~s(year)+spreg,data=df)
draw(parametric_effects(gam))

Partial effect plot looks like this:

This is what summary(gam) looks like:

Family: gaussian 
Link function: identity 

Formula:
Landings ~ s(year) + spreg

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)    30460      11178   2.725   0.0112 *
spreg.L       -16964      15961  -1.063   0.2974  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
          edf Ref.df     F p-value
s(year) 1.374  1.652 0.229   0.798

R-sq.(adj) =  -0.00914   Deviance explained = 7.35%
GCV = 2.6732e+09  Scale est. = 2.3726e+09  n = 30

I want to report these partial effect plots for parametric terms but I am having trouble finding a good description of the partial effect plots for fixed effects. Is this the estimate and 95% credible interval like the smooth partial effect plots?

Answer 1

With ordered factors, the intercept represents the expected value of the response at the mean of the factor's levels; in the snippet of data, this is 1.5, and the remaining coefficients represent polynomials of the factor levels. In the model shown, there is only a linear polynomial term because there are two levels.

With this kind of factor, the output from parametric_effect() is the model estimate (partial effect) for each factor level:

r$> ds <- data_slice(m, spreg = evenly(spreg))
r$> fitted_values(m, data = ds, exclude = c("(Intercept)", "s(year)"))          
# A tibble: 2 × 6
  spreg  year  fitted     se   lower  upper
  <ord> <dbl>   <dbl>  <dbl>   <dbl>  <dbl>
1 n      2010  11996. 11286. -10124. 34115.
2 y      2010 -11996. 11286. -34115. 10124.

which, because there is only a linear polynomial contrast, the two estimates equally deviate from the intercept (the mean of the levels) in opposite directions (hence the sign on the fitted value).