etasq: Measures of Partial Association (Eta-squared) for Linear...
In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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 class 'lm'
etasq(x, anova = FALSE, partial = TRUE,  ...)

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

## S3 method for class '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`.

For univariate linear models, classical η^2 = SSH / SST and partial η^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, 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 s=min(p, df_h) latent roots of H E^{-1}. The analogous multivariate partial η^2 measures are calculated as:

Pillai's trace (V): η^2 = V/s
Hotelling-Lawley trace (T): η^2 = T/(T+s)
Wilks' Lambda (L): η^2 = L^{1/s}
Roy's maximum root (R): η^2 = R/(R+1)

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.

Michael Friendly

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 Claculations for General Linear Multivariate Models Including Repeated Measures Applications. Journal of the American Statistical Association, 87, 1209-1226.

Anova

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")

Loading required package: car
                  eta^2
Block         0.5585973
Contour       0.6692989
Depth         0.5983772
Contour:Depth 0.2058495
                  eta^2
Block         0.5585973
Contour       0.6692989
Depth         0.5983772
Contour:Depth 0.2058495

Type II MANOVA Tests: Pillai test statistic
                eta^2 Df test stat approx F num Df den Df    Pr(>F)    
Block         0.55860  3    1.6758   3.7965     27     81 1.777e-06 ***
Contour       0.66930  2    1.3386   5.8468     18     52 2.730e-07 ***
Depth         0.59838  3    1.7951   4.4697     27     81 8.777e-08 ***
Contour:Depth 0.20585  6    1.2351   0.8640     54    180    0.7311    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
                  eta^2
Block         0.5701385
Contour       0.7434504
Depth         0.8294239
Contour:Depth 0.2250388
                  eta^2
Block         0.5823516
Contour       0.8009753
Depth         0.9421533
Contour:Depth 0.2456774