
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 mlm
etasq(x, ...)
# S3 method for Anova.mlm
etasq(x, anova = FALSE, ...)
# S3 method for lm
etasq(x, anova = FALSE, partial = TRUE, ...)
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.
A lm
, mlm
or Anova.mlm
object
Other arguments passed down to Anova
.
A logical, indicating whether the result should also contain
the test statistics produced by Anova()
.
A logical, indicating whether to calculate partial or classical eta^2.
Michael Friendly
For univariate linear models, classical
Partial eta-squared describes the proportion of total variation attributable to a given factor, partialling 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
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.
library(car)
data(Soils, package="carData")
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")
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