How does lattice package in R create gridlines automatically?

Question

In the context of linear mixed effects model, it is extremely useful to plot residuals vs. fitted values to check homoscedasticity (of residuals). When I am using lme4::plot.merMod to plot such a figure, if I understand correctly, lme4 uses lattice to produce the figure. For example, if we regress hp on mpg with carb (from tidyverse::mtcars) as random effects*, we get a following plot:

I don't know, however, how lattice comes up with grey-color horizontal and vertical gridlines and if they represent any statistical aspect about model fit. If lattice just divides the x- and y-axis in four equal parts with these gridlines, how can I achieve such equally-spaced gridlines that consider x- and y-axis range in a base R plot?

Code to reproduce the figure:

library(lme4)
library(tidyverse)
model <- lme4::lmer(data = mtcars, formula = mpg ~ hp + (1 | gear))
plot(model, aspect = 1)

*I am not concerned about correct model specification at the moment.

Answer 1

In base R, this can be done by using graphics::grid (as suggested by Prof. Bolker):

library(lme4)
library(tidyverse)
library(broom.mixed)

model <- lme4::lmer(data = mtcars, formula = mpg ~ hp + (1 | gear))
data <- broom.mixed::augment(model)

par(pty='s')    # to keep aspect ratio 1
plot(data$.fixed, data$.resid)
graphics::grid(nx = 4, lty = 1)

Or by directly using:

plot(data$.fixed, data$.resid, panel.first = grid(4, lty = 1))

Answer 2

The gridlines are produced by the call to grid::grid.segments inside lattice::panel.grid (see lattice::panel.grid).

When lme4::plot.merMod is called, it calls lattice::panel.grid, which in turn calls grid::grid.segments(h = 3, v = 3, ...). This results in partitioning the viewport in four equal parts - horizontally as well as vertically - by three horizontal and three vertical lines.

I provide a figure below, drawn using grid, that might confirm this:

library(lme4)
library(tidyverse)
library(broom.mixed)

model <- lme4::lmer(data = mtcars, formula = mpg ~ hp + (1 | gear))
data <- broom.mixed::augment(model)

v <- 3    # to reproduce default call to panel.grid
grid.newpage()
vp <- viewport(width=unit(3, "inches"), height=unit(3, "inches"))
pushViewport(vp)
pushViewport(dataViewport(data$.fitted, data$.resid))
grid.rect()
grid.xaxis()
grid.yaxis()
grid.text("LU", x=unit(0, "npc"), y=unit(1, "npc"), gp=gpar(col="red"))
grid.text("LB", x=unit(0,"npc"), y=unit(0, "npc"), gp=gpar(col="red"))
grid.text("1", x=unit(0.25,"npc"), y=unit(0, "npc"), gp=gpar(col="blue"))
grid.text("2", x=unit(0.5,"npc"), y=unit(0, "npc"), gp=gpar(col="darkgreen"))
grid.text("3", x=unit(0.75,"npc"), y=unit(0, "npc"), gp=gpar(col="darkred"))
grid.points(x=data$.fitted, y=data$.resid)
grid.segments(x0 = 1:v / (v+1),
              x1 = 1:v / (v+1),
              gp = gpar(col = "pink", lty = 2, lwd = 2),
              default.units = "npc")
grid.segments(y0 = 1:v / (v+1),
              y1 = 1:v / (v+1),
              gp = gpar(col = "orange", lty = 3, lwd = 2),
              default.units = "npc")
pushViewport(vp)

The red colored texts LB and LU show left-bottom and left-upper corners of the viewport. The colored numbers 1, 2, and 3 overlapping on x-axis are placed at 0.25 npc, 0.5 npc and 0.75 npc away from LB i.e. the origin of the viewport, respectively. This is because npc* means:

Normalised Parent Coordinates. Treats the bottom-left corner of the current viewport as the location (0, 0) and the top-right corner as (1, 1).

We see that the call (in the above code) to grid.segments plots lines that overlap with these colored numbers.

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*See Table 1 in grid Graphics.