Plotting Estimates (Fixed Effects) of Regression Models

## Install package "strengejacke" from GitHub (`devtools::install_github("strengejacke/strengejacke")`) to load all sj-packages at once!

This document describes how to plot estimates as forest plots (or dot whisker plots) of various regression models, using the plot_model() function. plot_model() is a generic plot-function, which accepts many model-objects, like lm, glm, lme, lmerMod etc.

plot_model() allows to create various plot tyes, which can be defined via the type-argument. The default is type = "fe", which means that fixed effects (model coefficients) are plotted. For mixed effects models, only fixed effects are plotted by default as well.

library(sjPlot)
library(sjlabelled)
library(sjmisc)
library(ggplot2)

data(efc)
theme_set(theme_sjplot())

Fitting a logistic regression model

First, we fit a model that will be used in the following examples. The examples work in the same way for any other model as well.

# create binary response
y <- ifelse(efc$neg_c_7 < median(na.omit(efc$neg_c_7)), 0, 1)

# create data frame for fitting model
df <- data.frame(
  y = to_factor(y),
  sex = to_factor(efc$c161sex),
  dep = to_factor(efc$e42dep),
  barthel = efc$barthtot,
  education = to_factor(efc$c172code)
)

# set variable label for response
set_label(df$y) <- "High Negative Impact"

# fit model
m1 <- glm(y ~., data = df, family = binomial(link = "logit"))

Plotting estimates of generalized linear models

The simplest function call is just passing the model object as argument. By default, estimates are sorted in descending order, with the highest effect at the top.

plot_model(m1)

The “neutral” line, i.e. the vertical intercept that indicates no effect (x-axis position 1 for most glm’s and position 0 for most linear models), is drawn slightly thicker than the other grid lines. You can change the line color with the vline.color-argument.

plot_model(m1, vline.color = "red")

Sorting estimates

By default, the estimates are sorted in the same order as they were introduced into the model. Use sort.est = TRUE to sort estimates in descending order, from highest to lowest value.

plot_model(m1, sort.est = TRUE)

Another way to sort estimates is to use the order.terms-argument. This is a numeric vector, indicating the order of estimates in the plot. In the summary, we see that “sex2” is the first term, followed by the three dependency-categories (position 2-4), the Barthel-Index (5) and two levels for intermediate and high level of education (6 and 7).

summary(m1)
#> 
#> Call:
#> glm(formula = y ~ ., family = binomial(link = "logit"), data = df)
#> 
#> Coefficients:
#>              Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)  0.700232   0.576715   1.214 0.224682    
#> sex2         0.649136   0.186186   3.486 0.000489 ***
#> dep2         0.485259   0.361498   1.342 0.179480    
#> dep3         1.125130   0.361977   3.108 0.001882 ** 
#> dep4         0.910194   0.441774   2.060 0.039368 *  
#> barthel     -0.029802   0.004732  -6.298 3.02e-10 ***
#> education2   0.226525   0.200298   1.131 0.258081    
#> education3   0.283600   0.249327   1.137 0.255346    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for binomial family taken to be 1)
#> 
#>     Null deviance: 1122.16  on 814  degrees of freedom
#> Residual deviance:  939.77  on 807  degrees of freedom
#>   (93 observations deleted due to missingness)
#> AIC: 955.77
#> 
#> Number of Fisher Scoring iterations: 4

Now we want the educational levels (6 and 7) first, than gender (1), followed by dependency (2-4)and finally the Barthel-Index (5). Use this order as numeric vector for the order.terms-argument.

plot_model(m1, order.terms = c(6, 7, 1, 2, 3, 4, 5))

Estimates on the untransformed scale

By default, plot_model() automatically exponentiates coefficients, if appropriate (e.g. for models with log or logit link). You can explicitley prevent transformation by setting the transform-argument to NULL, or apply any transformation by using a character vector with the function name.

plot_model(m1, transform = NULL)

plot_model(m1, transform = "plogis")

Showing value labels

By default, just the dots and error bars are plotted. Use show.values = TRUE to show the value labels with the estimates values, and use show.p = FALSE to suppress the asterisks that indicate the significance level of the p-values. Use value.offset to adjust the relative positioning of value labels to the dots and lines.

plot_model(m1, show.values = TRUE, value.offset = .3)

Labelling the plot

As seen in the above examples, by default, the plotting-functions of sjPlot retrieve value and variable labels if the data is labelled, using the sjlabelled-package. If the data is not labelled, the variable names are used. In such cases, use the arguments title, axis.labels and axis.title to annotate the plot title and axes. If you want variable names instead of labels, even for labelled data, use "" as argument-value, e.g. axis.labels = "", or set auto.label to FALSE.

Furthermore, plot_model() applies case-conversion to all labels by default, using the snakecase-package. This converts labels into human-readable versions. Use case = NULL to turn case-conversion off, or refer to the package-vignette of the snakecase-package for further options.

data(iris)
m2 <- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Species, data = iris)

# variable names as labels, but made "human readable"
# separating dots are removed
plot_model(m2)

# to use variable names even for labelled data
plot_model(m1, axis.labels = "", title = "my own title")

Pick or remove specific terms from plot

Use terms resp. rm.terms to select specific terms that should (not) be plotted.

# keep only coefficients sex2, dep2 and dep3
plot_model(m1, terms = c("sex2", "dep2", "dep3"))

# remove coefficients sex2, dep2 and dep3
plot_model(m1, rm.terms = c("sex2", "dep2", "dep3"))

Standardized estimates

For linear models, you can also plot standardized beta coefficients, using type = "std" or type = "std2". These two options differ in the way how coefficients are standardized. type = "std2" plots standardized beta values, however, standardization follows Gelman’s (2008) suggestion, rescaling the estimates by dividing them by two standard deviations instead of just one.

plot_model(m2, type = "std")

Bayesian models (fitted with Stan)

plot_model() also supports stan-models fitted with the rstanarm or brms packages. However, there are a few differences compared to the previous plot examples.

First, of course, there are no confidence intervals, but uncertainty intervals - high density intervals, to be precise.

Second, there’s not just one interval range, but an inner and outer probability. By default, the inner probability is fixed to .5 (50%), while the outer probability is specified via ci.lvl (which defaults to .89 (89%) for Bayesian models). However, you can also use the arguments prob.inner and prob.outer to define the intervals boundaries.

Third, the point estimate is by default the median, but can also be another value, like mean. This can be specified with the bpe-argument.

if (require("rstanarm", quietly = TRUE)) {
  # make sure we apply a nice theme
  library(ggplot2)
  theme_set(theme_sjplot())
  
  data(mtcars)
  m <- stan_glm(mpg ~ wt + am + cyl + gear, data = mtcars, chains = 1)
  
  # default model
  plot_model(m)
  # same model, with mean point estimate, dot-style for point estimate
  # and different inner/outer probabilities of the HDI
  plot_model(
    m, 
    bpe = "mean",
    bpe.style = "dot",
    prob.inner = .4,
    prob.outer = .8
  )
}

Tweaking plot appearance

There are several options to customize the plot appearance:

The colors-argument either takes the name of a valid colorbrewer palette (see also the related vignette), "bw" or "gs" for black/white or greyscaled colors, or a string with a color name.
value.offset and value.size adjust the positioning and size of value labels, if shown.
dot.size and line.size change the size of dots and error bars.
vline.color changes the neutral “intercept” line.
width, alpha and scale are passed down to certain ggplot-geoms, like geom_errorbar() or geom_density_ridges().

plot_model(
  m1, 
  colors = "Accent", 
  show.values = TRUE,
  value.offset = .4,
  value.size = 4,
  dot.size = 3,
  line.size = 1.5,
  vline.color = "blue",
  width = 1.5
)

References

Gelman A (2008) Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine 27: 2865–2873.

Daniel Lüdecke

2024-11-29