`afex_plot()`

visualizes results from factorial
experiments and, more generally, data set with interactions of
categorical/factor variables. It does so by combining estimated marginal
means and uncertainties associated with these means in the foreground
with a depiction of the raw data in the background. If models include
continuous covariates, other approaches are recommended (e.g., such as
implemented in package `effects`

or by using the possibility of `afex_plot`

to return the data and
build the plot on ones own).

This document provides an overview of the different models supported
by `afex_plot()`

in addition to the `afex`

objects
(i.e., `afex_aov`

and `mixed`

). In general, these
are models which are supported by the `emmeans`

package as the `afex_plot.default()`

method uses
`emmeans`

to get the estimated marginal means.
`afex_plot.default()`

then guesses whether there are repeated
measures or all samples are independent. Based on this guess (which can
be changed via the `id`

argument) data in the background is
plotted. Calculation of error bars can also be based on this guess (but
the default is to plot the model based error bars obtained from
`emmeans`

).

For a generally introduction to the functionality of
`afex_plot`

see: `afex_plot`

: Publication
Ready Plots for Experimental Designs

Throughout the document, we will need `afex`

as well as
`ggplot2`

. In addition, we load `cowplot`

for function `plot_grid()`

(which allows to easily combine
multiple `ggplot2`

plots). In addition, we will set a
somewhat nicer `ggplot2`

theme.

```
library("afex")
library("ggplot2")
library("cowplot")
theme_set(theme_bw(base_size = 14) +
theme(legend.position="bottom",
panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank()))
```

Importantly, we also set the contrasts for the current `R`

session to sum-to-zero contrasts. For models that include interactions
with categorical variables this generally produces estimates that are
easier to interpret.

Please note, the best way to export a figure is via
`ggsave()`

or a similar function call. For Word and similar
document formats, `png`

is a good file type, for
`LaTeX`

and similar document formats, `pdf`

is a
good file type.

`afex_plot()`

generally supports models implemeneted via
the `stats`

package. Here I show the main model functions
that work with independent samples. These models can be passed to
`afex_plot`

without specifying additional arguments.

Most importantly, `lm`

models work directly. For those we
use the `warpbreaks`

data.

Note that `afex_plot`

produces several messages that are
shown here as comments below the corresponding calls. Important is maybe
that `afex_plot`

assumes all observations (i.e., rows) are
independent. This is of course the case here. In addition, for the first
plot we are informed that the presence of an interaction may lead to a
misleading impression if only a lower-order effect (here a main effect)
is shown. This message is produced by `emmeans`

and passed
through.

```
p1 <- afex_plot(warp.lm, "tension")
## dv column detected: breaks
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
p2 <- afex_plot(warp.lm, "tension", "wool")
## dv column detected: breaks
## No id column passed. Assuming all rows are independent samples.
plot_grid(p1, p2)
```

`glm`

models also work without further setting. Here we
first use a poisson GLM for which we need to generate the data.

```
ins <- data.frame(
n = c(500, 1200, 100, 400, 500, 300),
size = factor(rep(1:3,2), labels = c("S","M","L")),
age = factor(rep(1:2, each = 3)),
claims = c(42, 37, 1, 101, 73, 14))
```

We can then fit the data and pass the model object as is.

```
ins.glm <- glm(claims ~ size + age + offset(log(n)),
data = ins, family = "poisson")
afex_plot(ins.glm, "size", "age")
## dv column detected: claims
## No id column passed. Assuming all rows are independent samples.
```

`afex_plot`

also works with binomial GLMs for which we
also first need to generate some data which we will then fit.

```
## binomial glm adapted from ?predict.glm
ldose <- factor(rep(0:5, 2))
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- numdead/20 ## dv should be a vector, no matrix
budworm.lg <- glm(SF ~ sex*ldose, family = binomial,
weights = rep(20, length(numdead)))
```

For this model, we will produce three plots we can then compare. The
first only shows the main effect of one variable (`ldose`

).
The other show the interaction of the two variables. Because for
binomial GLMs we then only have one data point (with several
observations), the individual data points and mean cannot be
distinguished. This is made clear in the ther two (panels B and C).

```
a <- afex_plot(budworm.lg, "ldose")
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean!
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
c <- afex_plot(budworm.lg, "ldose", "sex",
data_arg = list(size = 4, color = "red"))
## dv column detected: SF
## No id column passed. Assuming all rows are independent samples.
plot_grid(a, b, c, labels = "AUTO", nrow = 1)
```

Hot to use `afex_plot`

for mixed models fitted with
`afex::mixed`

(or `lme4`

directly) is shown in the other
vignette. However, we can also use `afex_plot`

for mixed
models fitted with the older `nlme`

package. For this,
however we need to pass the data used for fitting via the
`data`

argument.

We can change on which of the two nested factors the individual data
points in the background are based via the `id`

argument.
This is shown below.

```
## nlme mixed model
data(Oats, package = "nlme")
Oats$nitro <- factor(Oats$nitro)
oats.1 <- nlme::lme(yield ~ nitro * Variety,
random = ~ 1 | Block / Variety,
data = Oats)
plot_grid(
afex_plot(oats.1, "nitro", "Variety", data = Oats), # A
afex_plot(oats.1, "nitro", "Variety", data = Oats), # B
afex_plot(oats.1, "nitro", "Variety", data = Oats, id = "Block"), # C
afex_plot(oats.1, "nitro", data = Oats), # D
afex_plot(oats.1, "nitro", data = Oats, id = c("Block", "Variety")), # E
afex_plot(oats.1, "nitro", data = Oats, id = "Block"), # F
labels = "AUTO"
)
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## dv column detected: yield
## dv column detected: yield
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: yield
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: yield
## NOTE: Results may be misleading due to involvement in interactions
```

Support for `glmmTMB`

is also provided. Here we use an example data set for which we model
zero-inflation as well as overdispersion. The latter is achieved with a
variant of the negative binomial distribution.

```
library("glmmTMB")
tmb <- glmmTMB(count~spp * mined + (1|site),
ziformula = ~spp * mined,
family=nbinom2, Salamanders)
```

`afex_plot`

does not automatically detect the
random-effect for `site`

. This means that per default all 644
data points are shown. When plotting only one variable, in which the
default `data_geom`

is
`ggbeeswarm::geom_beeswarm`

, this can lead to rather ugly
plots due to the zero inflation. This is shon in panel A below. In panel
B, we address this by changing the geom to a violin plot. In panel C, we
address this by aggregating the data within site, but still use the
beeswarm plot. Note that for panel C it is necessary to pass the data
via the `data`

argument as otherwise `site`

cannot
be found for aggregation.

```
plot_grid(
afex_plot(tmb, "spp"),
afex_plot(tmb, "spp", data_geom = geom_violin),
afex_plot(tmb, "spp", id = "site", data = Salamanders),
labels = "AUTO", nrow = 1
)
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
## NOTE: Results may be misleading due to involvement in interactions
## dv column detected: count
## NOTE: Results may be misleading due to involvement in interactions
```

When plotting both variables, the problem is somewhat hidden, because
instead of beeswarm plots, semi-transparency (i.e., `alpha`

< 1) is used to show overlapping points. In panel B we again make
this clearer but this time by adding jitter (on both the y- and x-axis)
and increasing the degree of semi-transparancy (i.e., decreasing
alpha).

```
a <- afex_plot(tmb, "spp", "mined")
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
b <- afex_plot(tmb, "spp", "mined", data_alpha = 0.3,
data_arg = list(
position =
ggplot2::position_jitterdodge(
jitter.width = 0.2,
jitter.height = 0.5,
dodge.width = 0.5 ## needs to be same as dodge
),
color = "darkgrey"))
## dv column detected: count
## No id column passed. Assuming all rows are independent samples.
plot_grid(a, b, labels = "AUTO")
```

For the final plot we also plot the interaction, but this time aggregate the individual-data within site. This allows us again to use a beeswarm plot (after decreasing the width of the “bees”) and produces a relatively clear result.

`afex_plot()`

also supports Bayesian models that are also
supported via `emmeans`

. For example, we can easily fit a
binomial model with `rstanarm`

.

```
library("rstanarm") ## requires resetting the ggplot2 theme
theme_set(theme_bw(base_size = 14) +
theme(legend.position="bottom",
panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank()))
cbpp <- lme4::cbpp
cbpp$prob <- with(cbpp, incidence / size)
example_model <- stan_glmer(prob ~ period + (1|herd),
data = cbpp, family = binomial, weight = size,
chains = 2, cores = 1, seed = 12345, iter = 500)
```

We can directly pass this model to `afex_plot`

. However,
we also see quite some zeros leading to a not super nice plot. It looks
a bit better using a violin plot for the raw data.

```
b1 <- afex_plot(example_model, "period")
## dv column detected: prob
## No id column passed. Assuming all rows are independent samples.
b2 <- afex_plot(example_model, "period", data_geom = geom_violin)
## dv column detected: prob
## No id column passed. Assuming all rows are independent samples.
plot_grid(b1, b2, labels = "AUTO")
```

We can also produce a plot based on the individual Bernoulli observations in the data. For this, we first need to expand the data such that we have one row per observation. With this, we can then fit the essentially same model as above.

```
cbpp_l <- vector("list", nrow(cbpp))
for (i in seq_along(cbpp_l)) {
cbpp_l[[i]] <- data.frame(
herd = cbpp$herd[i],
period = cbpp$period[i],
incidence = rep(0, cbpp$size[i])
)
cbpp_l[[i]]$incidence[seq_len(cbpp$incidence[i])] <- 1
}
cbpp_l <- do.call("rbind", cbpp_l)
cbpp_l$herd <- factor(cbpp_l$herd, levels = levels(cbpp$herd))
cbpp_l$period <- factor(cbpp_l$period, levels = levels(cbpp$period))
example_model2 <- stan_glmer(incidence ~ period + (1|herd),
data = cbpp_l, family = binomial,
chains = 2, cores = 1, seed = 12345, iter = 500)
```

Again, this model can be directly passed to `afex_plot`

.
However, here we see even more 0 as the data is not yet aggregated.
Consequently, we need to pass `id = "herd"`

to aggregate the
individual observations within each herd.

```
b3 <- afex_plot(example_model2, "period")
## dv column detected: incidence
## No id column passed. Assuming all rows are independent samples.
b4 <- afex_plot(example_model2, "period", id = "herd")
## dv column detected: incidence
plot_grid(b3, b4, labels = "AUTO")
```

We can of course also fit a model assuming a normal distribution
using `rstanarm`

. For example using the `Machines`

data.

```
data("Machines", package = "MEMSS")
mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines,
chains = 2, cores = 1, seed = 12345, iter = 500)
```

As before, we can pass this model directly to `afex_plot`

(see panel A). However, the data is again not aggregated within the
grouping variable `Worker`

. If we want to aggregate the
individual data points for the grouping factor, we need to pass both the
name of the grouping variable (`Worker`

) and the data used
for fitting.

We can also fit the `Machines`

data using `brms`

.

```
library("brms")
data("Machines", package = "MEMSS")
mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines,
chains = 2, cores = 1, seed = 12345, iter = 500)
```

However, to pass a `brms`

object to `afex_plot`

we need to pass both, the `data`

used for fitting as well as
the name of the dependent variable (here `score`

) via the
`dv`

argument. We again build the plot such that the left
panel shows the raw data without aggregation and the right panel shows
the data aggregated within the grouping factor `Worker`

.

Some models are unfortunately not yet supported. For example, models
fit with the new and pretty cool looking `GLMMadaptive`

package using some of the special families do not seem to produce
reasonable results. The following unfortunately does not produce a
reasonable plot.