# Estimate Marginal Means (Model-based average at each factor level)

Source:`R/estimate_means.R`

`estimate_means.Rd`

Estimate average value of response variable at each factor levels. For
plotting, check the examples in `visualisation_recipe()`

. See also
other related functions such as `estimate_contrasts()`

and
`estimate_slopes()`

.

## Usage

```
estimate_means(
model,
at = "auto",
fixed = NULL,
transform = "response",
ci = 0.95,
backend = "emmeans",
...
)
```

## Arguments

- model
A statistical model.

- at
The predictor variable(s)

*at*which to evaluate the desired effect / mean / contrasts. Other predictors of the model that are not included here will be collapsed and "averaged" over (the effect will be estimated across them).- fixed
A character vector indicating the names of the predictors to be "fixed" (i.e., maintained), so that the estimation is made at these values.

- transform
Is passed to the

`type`

argument in`emmeans::emmeans()`

. See this vignette. Can be`"none"`

(default for contrasts),`"response"`

(default for means),`"mu"`

,`"unlink"`

,`"log"`

.`"none"`

will leave the values on scale of the linear predictors.`"response"`

will transform them on scale of the response variable. Thus for a logistic model,`"none"`

will give estimations expressed in log-odds (probabilities on logit scale) and`"response"`

in terms of probabilities.- ci
Confidence Interval (CI) level. Default to

`0.95`

(`95%`

).- backend
Whether to use 'emmeans' or 'marginaleffects' as a backend. The latter is experimental and some features might not work.

- ...
Other arguments passed for instance to

`insight::get_datagrid()`

.

## Details

See the **Details** section below, and don't forget to also check out the
Vignettes
and README examples for
various examples, tutorials and use cases.

The `estimate_slopes()`

, `estimate_means()`

and `estimate_contrasts()`

functions are forming a group, as they are all based on *marginal*
estimations (estimations based on a model). All three are also built on the
emmeans package, so reading its documentation (for instance for
`emmeans::emmeans()`

and `emmeans::emtrends()`

) is recommended to understand
the idea behind these types of procedures.

Model-based

**predictions**is the basis for all that follows. Indeed, the first thing to understand is how models can be used to make predictions (see`estimate_link()`

). This corresponds to the predicted response (or "outcome variable") given specific predictor values of the predictors (i.e., given a specific data configuration). This is why the concept of`reference grid()`

is so important for direct predictions.**Marginal "means"**, obtained via`estimate_means()`

, are an extension of such predictions, allowing to "average" (collapse) some of the predictors, to obtain the average response value at a specific predictors configuration. This is typically used when some of the predictors of interest are factors. Indeed, the parameters of the model will usually give you the intercept value and then the "effect" of each factor level (how different it is from the intercept). Marginal means can be used to directly give you the mean value of the response variable at all the levels of a factor. Moreover, it can also be used to control, or average over predictors, which is useful in the case of multiple predictors with or without interactions.**Marginal contrasts**, obtained via`estimate_contrasts()`

, are themselves at extension of marginal means, in that they allow to investigate the difference (i.e., the contrast) between the marginal means. This is, again, often used to get all pairwise differences between all levels of a factor. It works also for continuous predictors, for instance one could also be interested in whether the difference at two extremes of a continuous predictor is significant.Finally,

**marginal effects**, obtained via`estimate_slopes()`

, are different in that their focus is not values on the response variable, but the model's parameters. The idea is to assess the effect of a predictor at a specific configuration of the other predictors. This is relevant in the case of interactions or non-linear relationships, when the effect of a predictor variable changes depending on the other predictors. Moreover, these effects can also be "averaged" over other predictors, to get for instance the "general trend" of a predictor over different factor levels.

**Example:** Let's imagine the following model `lm(y ~ condition * x)`

where
`condition`

is a factor with 3 levels A, B and C and `x`

a continuous
variable (like age for example). One idea is to see how this model performs,
and compare the actual response y to the one predicted by the model (using
`estimate_response()`

). Another idea is evaluate the average mean at each of
the condition's levels (using `estimate_means()`

), which can be useful to
visualize them. Another possibility is to evaluate the difference between
these levels (using `estimate_contrasts()`

). Finally, one could also estimate
the effect of x averaged over all conditions, or instead within each
condition (`using [estimate_slopes]`

).

## Examples

```
library(modelbased)
# Frequentist models
# -------------------
model <- lm(Petal.Length ~ Sepal.Width * Species, data = iris)
estimate_means(model)
#> We selected `at = c("Species")`.
#> NOTE: Results may be misleading due to involvement in interactions
#> Estimated Marginal Means
#>
#> Species | Mean | SE | 95% CI
#> ---------------------------------------
#> setosa | 1.43 | 0.08 | [1.28, 1.58]
#> versicolor | 4.50 | 0.07 | [4.35, 4.65]
#> virginica | 5.61 | 0.06 | [5.50, 5.72]
#>
#> Marginal means estimated at Species
estimate_means(model, fixed = "Sepal.Width")
#> We selected `at = c("Species")`.
#> Estimated Marginal Means
#>
#> Species | Sepal.Width | Mean | SE | 95% CI
#> -----------------------------------------------------
#> setosa | 3.06 | 1.43 | 0.08 | [1.28, 1.58]
#> versicolor | 3.06 | 4.50 | 0.07 | [4.35, 4.65]
#> virginica | 3.06 | 5.61 | 0.06 | [5.50, 5.72]
#>
#> Marginal means estimated at Species
estimate_means(model, at = c("Species", "Sepal.Width"), length = 2)
#> Estimated Marginal Means
#>
#> Species | Sepal.Width | Mean | SE | 95% CI
#> -----------------------------------------------------
#> setosa | 2.00 | 1.35 | 0.21 | [0.92, 1.77]
#> versicolor | 2.00 | 3.61 | 0.15 | [3.33, 3.90]
#> virginica | 2.00 | 4.88 | 0.17 | [4.54, 5.23]
#> setosa | 4.40 | 1.54 | 0.15 | [1.24, 1.84]
#> versicolor | 4.40 | 5.63 | 0.29 | [5.05, 6.20]
#> virginica | 4.40 | 6.53 | 0.25 | [6.04, 7.02]
#>
#> Marginal means estimated at Species, Sepal.Width
estimate_means(model, at = "Species=c('versicolor', 'setosa')")
#> NOTE: Results may be misleading due to involvement in interactions
#> Estimated Marginal Means
#>
#> Species | Mean | SE | 95% CI
#> ---------------------------------------
#> versicolor | 4.50 | 0.07 | [4.35, 4.65]
#> setosa | 1.43 | 0.08 | [1.28, 1.58]
#>
#> Marginal means estimated at Species
estimate_means(model, at = "Sepal.Width=c(2, 4)")
#> NOTE: Results may be misleading due to involvement in interactions
#> Estimated Marginal Means
#>
#> Sepal.Width | Mean | SE | 95% CI
#> ----------------------------------------
#> 2.00 | 3.28 | 0.10 | [3.07, 3.49]
#> 4.00 | 4.35 | 0.10 | [4.15, 4.55]
#>
#> Marginal means estimated at Sepal.Width
estimate_means(model, at = c("Species", "Sepal.Width=0"))
#> Estimated Marginal Means
#>
#> Species | Sepal.Width | Mean | SE | 95% CI
#> -----------------------------------------------------
#> setosa | 0.00 | 1.18 | 0.50 | [0.19, 2.17]
#> versicolor | 0.00 | 1.93 | 0.49 | [0.97, 2.90]
#> virginica | 0.00 | 3.51 | 0.51 | [2.50, 4.52]
#>
#> Marginal means estimated at Species, Sepal.Width
estimate_means(model, at = "Sepal.Width", length = 5)
#> NOTE: Results may be misleading due to involvement in interactions
#> Estimated Marginal Means
#>
#> Sepal.Width | Mean | SE | 95% CI
#> ----------------------------------------
#> 2.00 | 3.28 | 0.10 | [3.07, 3.49]
#> 2.60 | 3.60 | 0.06 | [3.49, 3.71]
#> 3.20 | 3.92 | 0.04 | [3.84, 4.01]
#> 3.80 | 4.25 | 0.08 | [4.08, 4.41]
#> 4.40 | 4.57 | 0.14 | [4.30, 4.84]
#>
#> Marginal means estimated at Sepal.Width
estimate_means(model, at = "Sepal.Width=c(2, 4)")
#> NOTE: Results may be misleading due to involvement in interactions
#> Estimated Marginal Means
#>
#> Sepal.Width | Mean | SE | 95% CI
#> ----------------------------------------
#> 2.00 | 3.28 | 0.10 | [3.07, 3.49]
#> 4.00 | 4.35 | 0.10 | [4.15, 4.55]
#>
#> Marginal means estimated at Sepal.Width
# Methods that can be applied to it:
means <- estimate_means(model, fixed = "Sepal.Width")
#> We selected `at = c("Species")`.
plot(means) # which runs visualisation_recipe()
standardize(means)
#> Estimated Marginal Means (standardized)
#>
#> Species | Sepal.Width | Mean | SE | 95% CI
#> --------------------------------------------------------
#> setosa | 0.00 | -1.32 | 0.04 | [-1.40, -1.23]
#> versicolor | 0.00 | 0.42 | 0.04 | [ 0.34, 0.50]
#> virginica | 0.00 | 1.05 | 0.03 | [ 0.99, 1.11]
#>
#> Marginal means estimated at Species
# \donttest{
data <- iris
data$Petal.Length_factor <- ifelse(data$Petal.Length < 4.2, "A", "B")
model <- lmer(Petal.Length ~ Sepal.Width + Species + (1 | Petal.Length_factor), data = data)
estimate_means(model)
#> We selected `at = c("Species")`.
#> Estimated Marginal Means
#>
#> Species | Mean | SE | 95% CI
#> ----------------------------------------
#> setosa | 1.67 | 0.34 | [-1.97, 5.32]
#> versicolor | 4.27 | 0.34 | [ 0.10, 8.44]
#> virginica | 5.25 | 0.34 | [ 1.37, 9.13]
#>
#> Marginal means estimated at Species
estimate_means(model, at = "Sepal.Width", length = 3)
#> Estimated Marginal Means
#>
#> Sepal.Width | Mean | SE | 95% CI
#> -----------------------------------------
#> 2.00 | 3.40 | 0.35 | [ 0.01, 6.79]
#> 3.20 | 3.78 | 0.33 | [-0.82, 8.37]
#> 4.40 | 4.15 | 0.35 | [ 1.28, 7.02]
#>
#> Marginal means estimated at Sepal.Width
# }
```