Calculates partial eta-squared for linear models or multivariate analogs of eta-squared (or R^2), indicating the partial association for each term in a multivariate linear model. There is a different analog for each of the four standard multivariate test statistics: Pillai's trace, Hotelling-Lawley trace, Wilks' Lambda and Roy's maximum root test.

`etasq(x, ...)`# S3 method for lm
etasq(x, anova = FALSE, partial = TRUE, ...)

# S3 method for mlm
etasq(x, ...)

# S3 method for Anova.mlm
etasq(x, anova = FALSE, ...)

x

A `lm`

, `mlm`

or `Anova.mlm`

object

anova

A logical, indicating whether the result should also contain the
test statistics produced by `Anova()`

.

partial

A logical, indicating whether to calculate partial or classical eta^2.

…

Other arguments passed down to `Anova`

.

When `anova=FALSE`

, a one-column data frame containing the
eta-squared values for each term in the model.

When `anova=TRUE`

, a 5-column (lm) or 7-column (mlm) data frame containing the
eta-squared values and the test statistics produced by `print.Anova()`

for each term in the model.

For univariate linear models, classical \(\eta^2\) = SSH / SST and partial \(\eta^2\) = SSH / (SSH + SSE). These are identical in one-way designs.

Partial eta-squared describes the proportion of total variation attributable to a given factor, partialing out (excluding) other factors from the total nonerror variation. These are commonly used as measures of effect size or measures of (non-linear) strength of association in ANOVA models.

All multivariate tests are based on the \(s=min(p, df_h)\) latent roots of \(H E^{-1}\). The analogous multivariate partial \(\eta^2\) measures are calculated as:

- Pillai's trace (V)
\(\eta^2 = V/s\)

- Hotelling-Lawley trace (T)
\(\eta^2 = T/(T+s)\)

- Wilks' Lambda (L)
\(\eta^2 = L^{1/s}\)

- Roy's maximum root (R)
\(\eta^2 = R/(R+1)\)

Muller, K. E. and Peterson, B. L. (1984).
Practical methods for computing power in testing the Multivariate General Linear Hypothesis
*Computational Statistics and Data Analysis*, 2, 143-158.

Muller, K. E. and LaVange, L. M. and Ramey, S. L. and Ramey, C. T. (1992).
Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications.
*Journal of the American Statistical Association*, 87, 1209-1226.

# NOT RUN { data(Soils) # from car package soils.mod <- lm(cbind(pH,N,Dens,P,Ca,Mg,K,Na,Conduc) ~ Block + Contour*Depth, data=Soils) #Anova(soils.mod) etasq(Anova(soils.mod)) etasq(soils.mod) # same etasq(Anova(soils.mod), anova=TRUE) etasq(soils.mod, test="Wilks") etasq(soils.mod, test="Hotelling") # }