estimates: Estimates of an ANOVA design

In GAD: GAD: Analysis of variance from general principles

Description

This function is used to construct the mean squares estimates of an ANOVA design, considering the complications imposed by nested/orthogonal and fixed/random factors.

Usage

estimates(object)

Arguments

object

an object of class lm, containing the specified design with random and/or fixed factors

Details

Determines what each mean square estimates in an ANOVA design by a set of procedures originally described by Cornfield and Tukey (1956). This version is a modification proposed by Underwood (1997), which does not allow for the use of fixed nested factors. The steps involve the construction of a table of multipliers with a row for each source of variation and a column for each term in the model that is not an interaction. The mean square estimates for each source of variation is obtained by determining which components belong to each mean square and what is their magnitude. This enables the recognition of appropriate F-ratios.

Value

A list of length 3, containing the table of multipliers ($tm), the mean squares estimates ($mse) and the F-ratio versus ($f.versus) for the model.

Author(s)

Leonardo Sandrini-Neto ([e-mail])

References

Cornfield, J., Tukey, J.W. 1956. Average values of mean squares in factorials. Annals of Mathematical Statistics, 27, 907-949.

Underwood, A.J. 1997. Experiments in Ecology: Their Logical Design and Interpretation Using Analysis of Variance. Cambridge University Press, Cambridge.

See Also

gad, estimates

Examples

#Example 1
library(GAD)
data(rohlf95)
CG <- as.fixed(rohlf95$cages)
MQ <- as.random(rohlf95$mosquito) 
model_R <- lm(wing ~ CG + CG%in%MQ, data = rohlf95)
estimates(model_R)
##
##
#Example 2
data(snails)
O <- as.random(snails$origin)
S <- as.random(snails$shore)
B <- as.random(snails$boulder)
C <- as.random(snails$cage)
model_C <- lm(growth ~ O + S + O*S + B%in%S + O*(B%in%S) + C%in%(O*(B%in%S)),
              data = snails)
estimates(model_C)

Example output

Loading required package: matrixStats
Loading required package: R.methodsS3
R.methodsS3 v1.8.1 (2020-08-26 16:20:06 UTC) successfully loaded. See ?R.methodsS3 for help.
$tm
      CG MQ n
CG     0  4 2
CG:MQ  1  1 2
Res    1  1 1

$mse
         Mean square estimates
CG       "Res + CG:MQ + CG"   
CG:MQ    "Res + CG:MQ"        
Residual "Res"                

$f.versus
      F-ratio versus
CG    "CG:MQ"       
CG:MQ "Residual"    

$tm
        O S B C n
O       1 4 3 2 5
S       2 1 3 2 5
O:S     1 1 3 2 5
S:B     2 1 1 2 5
O:S:B   1 1 1 2 5
O:S:B:C 1 1 1 1 5
Res     1 1 1 1 1

$mse
         Mean square estimates                  
O        "Res + O:S:B:C + O:S:B + O:S + O"      
S        "Res + O:S:B:C + O:S:B + S:B + O:S + S"
O:S      "Res + O:S:B:C + O:S:B + O:S"          
S:B      "Res + O:S:B:C + O:S:B + S:B"          
O:S:B    "Res + O:S:B:C + O:S:B"                
O:S:B:C  "Res + O:S:B:C"                        
Residual "Res"                                  

$f.versus
        F-ratio versus
O       "O:S"         
S       "No test"     
O:S     "O:S:B"       
S:B     "O:S:B"       
O:S:B   "O:S:B:C"     
O:S:B:C "Residual"    

GAD documentation built on May 2, 2019, 3:01 a.m.