# Support Functions for Model Extensions

library(effectsize)

## Supporting ANOVA Effect Sizes

To add support for you model, create a new .anova_es() method function. This functions should generally do 3 things:

1. Build a data frame with all the required information.
2. Pass the data frame to one of the 3 functions.
3. Set some attributes to the output.

### Simple ANOVA tables

The input data frame must have these columns: - Parameter (char) - The name of the parameter or, more often, the term. - Sum_Squares (num) - The sum of squares. - df (num) - The degrees of freedom associated with the Sum_Squares. - Mean_Square_residuals (num; optional) - if not present, is calculated as Sum_Squares / df. (Any other column is ignored.)

And exactly 1 row Where Parameter is Residual.

Optionally, one of the rows can have a (Intercept) value for Parameter.

An example of a minimally valid data frame:

min_aov <- data.frame(
Parameter = c("(Intercept)", "A", "B", "Residuals"),
Sum_Squares = c(30, 40, 10, 100),
df = c(1, 1, 2, 50)
)

Pass the data frame to .es_aov_simple():

.es_aov_simple(
min_aov,
type = "eta", partial = TRUE, generalized = FALSE,
include_intercept = FALSE,
ci = 0.95, alternative = "greater",
verbose = TRUE
)
>   Parameter Eta2_partial   CI CI_low CI_high
> 1         A        0.286 0.95   0.12       1
> 2         B        0.091 0.95   0.00       1

The output is a data frame with the columns: Parameter, the effect size, and (optionally) CI + CI_low + CI_high,

And with the following attributes: generalized, ci, alternative, anova_type (NA or NULL), approximate.

You can then set the anova_type attribute to {1, 2, 3, or NA} and return the output.

### ANOVA Tables with Multiple Error Strata

(e.g., aovlist models.)

The input data frame must have these columns:

• Group (char) - The strata
• Parameter (char)
• Sum_Squares (num)
• df (num)
• Mean_Square_residuals (num; optional)

And exactly 1 row per Group Where Parameter is Residual.

Optionally, one of the rows can have a (Intercept) value for Parameter.

An example of a minimally valid data frame:

min_aovlist <- data.frame(
Group = c("S", "S", "S:A", "S:A"),
Parameter = c("(Intercept)", "Residuals", "A", "Residuals"),
Sum_Squares = c(34, 21, 34, 400),
df = c(1, 12, 4, 30)
)

Pass the data frame to .es_aov_strata(), along with a list of predictors (including the stratifying variables) to the DV_names argument:

.es_aov_strata(
min_aovlist,
DV_names = c("S", "A"),
type = "omega", partial = TRUE, generalized = FALSE,
ci = 0.95, alternative = "greater",
verbose = TRUE,
include_intercept = TRUE
)
>   Group   Parameter Omega2_partial   CI CI_low CI_high
> 1     S (Intercept)           0.57 0.95   0.21       1
> 2   S:A           A           0.00 0.95   0.00       1

The output is a data frame with the columns: Group, Parameter, the effect size, and (optionally) CI + CI_low + CI_high,

And with the following attributes: generalized, ci, alternative, approximate.

You can then set the anova_type attribute to {1, 2, 3, or NA} and return the output.

### Approximate Effect sizes

When sums of squares cannot be extracted, we can still get approximate effect sizes based on the F_to_eta2() family of functions.

The input data frame must have these columns:

• Parameter (char)
• F (num) - The F test statistic.
• df (num) - effect degrees of freedom.
• (Can also have a t col instead, in which case df is set to 1, and F is t^2).
• df_error (num) - error degrees of freedom.

Optionally, one of the rows can have (Intercept) as the Parameter.

An example of a minimally valid data frame:

min_anova <- data.frame(
Parameter = c("(Intercept)", "A", "B"),
F = c(4, 7, 0.7),
df = c(1, 1, 2),
df_error = 34
)

Pass the table to .es_aov_table():

.es_aov_table(
min_anova,
type = "eta", partial = TRUE, generalized = FALSE,
include_intercept = FALSE,
ci = 0.95, alternative = "greater",
verbose = TRUE
)
>   Parameter Eta2_partial   CI CI_low CI_high
> 1         A         0.17 0.95  0.023       1
> 2         B         0.04 0.95  0.000       1

The output is a data frame with the columns: Parameter, the effect size, and (optionally) CI + CI_low + CI_high,

And with the following attributes: generalized, ci, alternative, approximate.

You can then set the anova_type attribute to {1, 2, 3, or NA} and return the output, and optionally the approximate attribute, and return the output.

### Example

Let’s fit a simple linear model and change its class:

mod <- lm(mpg ~ factor(cyl) + am, mtcars)

class(mod) <- "superMODEL"

We now need a new .anova_es.superMODEL function:

.anova_es.superMODEL <- function(model, ...) {
# Get ANOVA table
anov <- suppressWarnings(stats:::anova.lm(model))
anov <- as.data.frame(anov)

# Clean up
anov[["Parameter"]] <- rownames(anov)
colnames(anov)[2:1] <- c("Sum_Squares", "df")

# Pass
out <- .es_aov_simple(anov, ...)

# Set attribute
attr(out, "anova_type") <- 1

out
}

And… that’s it! Our new superMODEL class of models is fully supported!

eta_squared(mod)
> # Effect Size for ANOVA (Type I)
>
> Parameter   | η² (partial) |       95% CI
> -----------------------------------------
> factor(cyl) |         0.76 | [0.61, 1.00]
> am          |         0.12 | [0.00, 1.00]
>
> - One-sided CIs: upper bound fixed at [1.00].
eta_squared(mod, partial = FALSE)
> # Effect Size for ANOVA (Type I)
>
> Parameter   |   η² |       95% CI
> ---------------------------------
> factor(cyl) | 0.73 | [0.57, 1.00]
> am          | 0.03 | [0.00, 1.00]
>
> - One-sided CIs: upper bound fixed at [1.00].
omega_squared(mod)
> # Effect Size for ANOVA (Type I)
>
> Parameter   | ω² (partial) |       95% CI
> -----------------------------------------
> factor(cyl) |         0.73 | [0.56, 1.00]
> am          |         0.08 | [0.00, 1.00]
>
> - One-sided CIs: upper bound fixed at [1.00].
# Etc...