ANOVA effect sizes for intercepts

[mattansb]

library(easystats)
#> # Attaching packages: easystats 0.4.2
#> v insight     0.14.2.1     v datawizard  0.1.0.9000
#> v bayestestR  0.10.5       v performance 0.7.3.1   
#> v parameters  0.14.0.1     v effectsize  0.4.5.1   
#> v modelbased  0.8.0        v correlation 0.7.0     
#> v see         0.6.4        v report      0.3.5

m <- lm(mpg ~ factor(am) * factor(cyl), mtcars)
a <- car::Anova(m, type = 3)

eta_squared(a)
#> Type 3 ANOVAs only give sensible and informative results when covariates are
#>   mean-centered and factors are coded with orthogonal contrasts (such as those
#>   produced by 'contr.sum', 'contr.poly', or 'contr.helmert', but *not* by the
#>   default 'contr.treatment').
#> # Effect Size for ANOVA (Type III)
#> 
#> Parameter              | Eta2 (partial) |       90% CI
#> ------------------------------------------------------
#> factor(am)             |           0.20 | [0.02, 0.41]
#> factor(cyl)            |           0.41 | [0.15, 0.58]
#> factor(am):factor(cyl) |           0.10 | [0.00, 0.27]

Missing effect size for the intercept

model_parameters(a, eta_squared = TRUE)
#> Type 3 ANOVAs only give sensible and informative results when covariates are
#>   mean-centered and factors are coded with orthogonal contrasts (such as those
#>   produced by 'contr.sum', 'contr.poly', or 'contr.helmert', but *not* by the
#>   default 'contr.treatment').
#> Type 3 ANOVAs only give sensible and informative results when covariates are
#>   mean-centered and factors are coded with orthogonal contrasts (such as those
#>   produced by 'contr.sum', 'contr.poly', or 'contr.helmert', but *not* by the
#>   default 'contr.treatment').
#> Parameter              | Sum_Squares | df | Mean_Square |      F |      p | Eta2 (partial)
#> ------------------------------------------------------------------------------------------
#> (Intercept)            |     1573.23 |  1 |     1573.23 | 171.10 | < .001 |               
#> factor(am)             |       58.43 |  1 |       58.43 |   6.35 | 0.018  |           0.20
#> factor(cyl)            |      167.71 |  2 |       83.85 |   9.12 | < .001 |           0.41
#> factor(am):factor(cyl) |       25.44 |  2 |       12.72 |   1.38 | 0.269  |           0.10
#> Residuals              |      239.06 | 26 |        9.19 |        |        |               
#> 
#> Anova Table (Type 3 tests)

But this can be added with:

eta_squared(a, include_intercept = TRUE)
#> Type 3 ANOVAs only give sensible and informative results when covariates are
#>   mean-centered and factors are coded with orthogonal contrasts (such as those
#>   produced by 'contr.sum', 'contr.poly', or 'contr.helmert', but *not* by the
#>   default 'contr.treatment').
#> # Effect Size for ANOVA (Type III)
#> 
#> Parameter              | Eta2 (partial) |       90% CI
#> ------------------------------------------------------
#> (Intercept)            |           0.87 | [0.78, 0.91]
#> factor(am)             |           0.20 | [0.02, 0.41]
#> factor(cyl)            |           0.41 | [0.15, 0.58]
#> factor(am):factor(cyl) |           0.10 | [0.00, 0.27]

^{Created on 2021-08-05 by the reprex package (v2.0.0)}

[strengejacke]

Why isn't it included in general?

[mattansb]

I don't think an R^2-type effect size make sense for the intercept (which is only available for type-3 ANOVA tables). I'm not sure what the interpretation would even be... It was only added after the {papaja} folk requested it for their compatibility (easystats/effectsize#156 (comment)).

[bwiernik]

Yeah, agreed. Variance accounted for statistics index improvement over the intercept. I don't know exactly what Frederick was thinking about when he asked for that.

[strengejacke]

I don't think an R^2-type effect size make sense for the intercept

Ok, so what should be the solution here? Include it by default, or do nothing?

[mattansb]

I think best to omit for the intercept.

[DominiqueMakowski]

agreed

[strengejacke]

ok, so what is the issue here? I'm not sure if I understand it correctly, but omitting the effect size for the intercept would give you the result you showed in your initial post?

[mattansb]

The issue is that report isn't requesting the intercepts effect size, so it recycles though the effect sizes that are returned, thus (1) giving the intercept an effect size and (2) all other effect sizes are shifted by 1 (and the last one is recycled).

[strengejacke]

Ah, got it. And what can we do in parameters to resolve this issue?

[mattansb]

Nothing needs to be done in parameters - there the effect size is correctly marked as missing:

model_parameters(a, eta_squared = TRUE)
#> Parameter              | Sum_Squares | df | Mean_Square |      F |      p | Eta2 (partial)
#> ------------------------------------------------------------------------------------------
#> (Intercept)            |     1573.23 |  1 |     1573.23 | 171.10 | < .001 |               
#> factor(am)             |       58.43 |  1 |       58.43 |   6.35 | 0.018  |           0.20
#> factor(cyl)            |      167.71 |  2 |       83.85 |   9.12 | < .001 |           0.41
#> factor(am):factor(cyl) |       25.44 |  2 |       12.72 |   1.38 | 0.269  |           0.10
#> Residuals              |      239.06 | 26 |        9.19 |        |        |               
#> 
#> Anova Table (Type 3 tests)

[mattansb]

Why did I open this issue?