comp.var: Components of variation

In GAD: Analysis of Variance from General Principles

Components of variation

Description

This function calculates components of variation for fixed and random factors.

Usage

comp.var(object, anova.tab = NULL)

Arguments

object	an object of class "lm", containing the specified design with random and/or fixed factors.
anova.tab	an object containing the results returned by gad or pooling functions. See examples below.

Details

This function calculates components of variation for any combination of orthogonal/nested and fixed/random factors. For pooled terms, comp.var function seeks for the denominator of the removed term and keep its type (fixed or random).

Note that there are differences on the interpretation of the results between fixed and random factors. For fixed factors, the components of variation calculated are just the sum of squares divided by the degrees of freedom and the hypothesis only concern those levels that were included in the model. On the other hand, for random factors the components of variation calculated are truly variance components and are interpretable as measures of variability of a population of levels, which are randomly sampled. However, for most of studies that aims to compare the amount of variation attributed to each term, the estimates of components of variation for both fixed and random factors are important and directly comparable (Anderson et al., 2008).

Eventually, the estimates of components of variation for some terms in the model can be negative. The term in question generally has a large p-value and its estimative is usually set to zero, since a negative estimate is illogical. An alternative to this problem is remove the term using pooling function and re-analyse the model (Fletcher and Underwood, 2002).

Value

A list of length 2, containing the mean squares estimates ($mse) and the table of components of variation ($comp.var) for the model.

The $comp.var table contains four columns: “Type” shows whether terms are fixed or random; “Estimate” shows the estimate of component of variation (in squared units); “Square root” shows the square root of the “Estimate” column (original unit); and “Percentage” shows the percentage of variability attributable to each term (both fixed and random factors).

Author(s)

Eliandro Gilbert ([e-mail])

References

Anderson, M.J., Gorley, R.N., Clarke, K.R. 2008. PERMANOVA+ for PRIMER: Guide to Software and Statistical Methods. PRIMER-E: Plymouth, UK.

Fletcher, D.J., Underwood, A.J. 2002. How to cope with negative estimates of components of variance in ecological field studies. Journal of Experimental Marine Biology and Ecology 273, 89-95.

See Also

gad, pooling, estimates

Examples

library(GAD)
data(crabs)
head(crabs)

Re <- as.random(crabs$Region)   # random factor
Lo <- as.random(crabs$Location) # random factor nested in Region
Si <- as.random(crabs$Site)     # random factor nested in Location

model <- lm(Density ~ Re + Lo%in%Re + Si%in%Lo%in%Re, data = crabs)

C.test(model)                     # Checking homogeneity of variances
estimates(model)                  # Checking model structure
model.tab <- gad(model)           # Storing the result of ANOVA on a new object
model.tab                         # Checking ANOVA results
comp.var(model, anova.tab = model.tab) # Calculating the components of variations

GAD documentation built on May 29, 2024, 5:58 a.m.