Author: Henrik Singmann
Date: 2025-12-14

# afex_plot: Supported Models

#### Henrik Singmann

#### 2025-12-14

    ## Warning in check_dep_version(dep_pkg = "TMB"): package version mismatch:
    ## glmmTMB was built with TMB package version 1.9.17
    ## Current TMB package version is 1.9.18
    ## Please re-install glmmTMB from source or restore original 'TMB' package (see '?reinstalling' for more information)

# Introduction

`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()
    ## setting contr.sum globally: options(contrasts=c('contr.sum', 'contr.poly'))

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.

# Base R stats models: lm, glm

`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")
    ## dv column detected: breaks
    ## Warning: the 'subbars' function has moved to the reformulas package. Please update your imports, or ask an upstream package maintainter to do so.
    ## This warning is displayed once per session.
    ## No id column passed. Assuming all rows are independent samples.
    ## NOTE: Results may be misleading due to involvement in interactions
     r
    p2 <- afex_plot(warp.lm, "tension", "wool")
    ## dv column detected: breaks
    ## No id column passed. Assuming all rows are independent samples.
     r
    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
     r
    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.
     r
    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.
     r
    plot_grid(a, b, c, labels = "AUTO", nrow = 1)

# nlme mixed model

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

# glmmTMB

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.
     r
    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.
     r
    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")
              )
    ## dv column detected: count

# GLMMadaptive

If we only have a single random-effect grouping factor we can also use `GLMMadaptive`. `GLMMadaptive` provides support for a range of interesting response distributions, such a zero-inflated or hurdle distributions. Importantly, `GLMMadaptive` approximates the integral in the model’s log-likelihood function via the Gold-standard method, adaptive Gaussian quadrature.

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

As before, to crate an `afex_plot()`, we need to pass both the original `data`, and pass the grouping factor (`site`) to the `id`-argument to ensure individual-level data points are aggregated appropriately.

    afex_plot(gm1, "spp", "mined", id = "site",
              data = Salamanders, data_geom = ggplot2::geom_count)
    ## dv column detected: count

# rstanarm

`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.

    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")

# brms

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)