req_suggested_packages <- c("emmeans", "ggplot2", "cowplot", "ggbeeswarm", "ggpol", "nlme", "glmmTMB", "rstanarm", "brms", "MEMSS") pcheck <- lapply(req_suggested_packages, requireNamespace, quietly = TRUE) if (any(!unlist(pcheck))) { message("Required package(s) for this vignette are not available/installed and code will not be executed.") knitr::opts_chunk$set(eval = FALSE) }

options(width = 90) knitr::opts_chunk$set(dpi=72) knitr::knit_hooks$set(document = function(x){ gsub("```\n*```r*\n*", "", x) })

`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.

```
set_sum_contrasts()
```

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.

warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)

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") p2 <- afex_plot(warp.lm, "tension", "wool") 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")

`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") b <- afex_plot(budworm.lg, "ldose", "sex") ## data point is hidden behind mean! c <- afex_plot(budworm.lg, "ldose", "sex", data_arg = list(size = 4, color = "red")) 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" )

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)

library("glmmTMB") set_sum_contrasts() tmb <- glmmTMB(count~spp * mined + (1|site), ziformula = ~spp * mined, family=nbinom2, Salamanders) save(tmb, file = "inst/extdata/tmb_example_fit.rda", compress = "xz")

library("glmmTMB") data(Salamanders, package = "glmmTMB") load(system.file("extdata/", "tmb_example_fit.rda", package = "afex"))

`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 )

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") 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")) 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(tmb, "spp", "mined", id = "site", data = Salamanders, data_geom = ggbeeswarm::geom_beeswarm, data_arg = list(dodge.width = 0.5, cex = 0.4, color = "darkgrey") )

`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")

load(system.file("extdata/", "plots_rstanarm.rda", package = "afex")) grid::grid.newpage(); grid::grid.draw(b12)

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")

grid::grid.newpage(); grid::grid.draw(b34)

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.

b5 <- afex_plot(mm, "Machine") ## dv column detected: score ## No id column passed. Assuming all rows are independent samples. b6 <- afex_plot(mm, "Machine", id = "Worker") ## dv column detected: score plot_grid(b5, b6, labels = "AUTO")

grid::grid.newpage(); grid::grid.draw(b56)

library("rstanarm") ## requires resetting the ggplot2 theme library("ggplot2") theme_set(theme_bw(base_size = 14) + theme(legend.position="bottom", panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())) set_sum_contrasts() cbpp <- lme4::cbpp cbpp$prob <- with(cbpp, incidence / size) example_model <- stan_glmer(prob ~ period + (1|herd), data = cbpp, family = binomial, weight = size, chains = 2, cores = 1, seed = 12345, iter = 500) b1 <- afex_plot(example_model, "period") b2 <- afex_plot(example_model, "period", data_geom = geom_violin) b12 <- ggplotGrob(plot_grid(b1, b2)) cbpp_l <- vector("list", nrow(cbpp)) for (i in seq_along(cbpp_l)) { cbpp_l[[i]] <- data.frame( herd = cbpp$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) b3 <- afex_plot(example_model2, "period") b4 <- afex_plot(example_model2, "period", id = "herd") b34 <- plot_grid(b3, b4) data("Machines", package = "MEMSS") mm <- stan_lmer(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) b5 <- afex_plot(mm, "Machine") b6 <- afex_plot(mm, "Machine", id = "Worker", data = Machines) b56 <- ggplotGrob(plot_grid(b5, b6)) save(b12, b34, b56, file = "../inst/extdata/plots_rstanarm.rda", compress = "xz", version = 2)

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`

.

bb1 <- afex_plot(mm2, "Machine", data = Machines, dv = "score") ## No id column passed. Assuming all rows are independent samples. bb2 <- afex_plot(mm2, "Machine", id = "Worker", data = Machines, dv = "score") plot_grid(bb1, bb2)

load(system.file("extdata/", "plots_brms.rda", package = "afex")) grid::grid.newpage(); grid::grid.draw(bbout)

library("brms") data("Machines", package = "MEMSS") mm2 <- brm(score ~ Machine + (Machine|Worker), data=Machines, chains = 2, cores = 1, seed = 12345, iter = 500) bb1 <- afex_plot(mm2, "Machine", data = Machines, dv = "score") bb2 <- afex_plot(mm2, "Machine", id = "Worker", data = Machines, dv = "score") bbout <- ggplotGrob(plot_grid(bb1, bb2)) save(bbout, file = "../inst/extdata/plots_brms.rda", version = 2)

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.

library("GLMMadaptive") data(Salamanders, package = "glmmTMB") gm1 <- mixed_model(count~spp * mined, random = ~ 1 | site, data = Salamanders, family = zi.poisson(), zi_fixed = ~ mined) afex_plot(gm1, "spp", data = Salamanders)

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