Modified Compact Letter Display to Irregular Designs

This functions get the compact letter display for objects of class "glht". Modification was done to get the letters to design with missing cells, non completelly crossed factorial designs and nested factorial designs. These models are usually declared by a model matrix to have all effects estimated. It is assumed that Tukey contrasts was used.

cld2(object, level = 0.05)

Arguments

object	an object returned by glht(). It is assumed that the matrix used as the linfct argument in glht corresponds to a matrix to get Tukey contrasts of least squares means.
level	the nominal significance level.

Value

an object of class "cld" with letters to resume mean comparisons.

See also

apc(), LE_matrix(), glht().

Examples

# Toy data 1: experiment with cultivars in several locations.
td1 <- expand.grid(loc = gl(5, 1),
                   block = gl(3, 1),
                   cult = LETTERS[1:6])
td1 <- subset(td1, !(loc == 1 & cult == "A"))
td1 <- subset(td1, !(loc == 2 & cult == "B"))
xtabs(~loc + cult, td1)
#>    cult
#> loc A B C D E F
#>   1 0 3 3 3 3 3
#>   2 3 0 3 3 3 3
#>   3 3 3 3 3 3 3
#>   4 3 3 3 3 3 3
#>   5 3 3 3 3 3 3
td1$y <- seq_len(nrow(td1))

library(lme4)
#> Loading required package: Matrix

# Fit the mixed model.
m0 <- lmer(y ~ loc * cult + (1 | loc:block), data = td1)
#> fixed-effect model matrix is rank deficient so dropping 2 columns / coefficients
logLik(m0)
#> 'log Lik.' -86.46157 (df=30)

# The same model but without rank deficience.
td1$loccult <- with(td1, interaction(loc, cult, drop = TRUE))
m1 <- lmer(y ~ loccult + (1 | loc:block), data = td1)
logLik(m1)
#> 'log Lik.' -86.46157 (df=30)

library(doBy)

X <- LE_matrix(lm(nobars(formula(m1)), data = td1), effect = "loccult")
rownames(X) <- levels(td1$loccult)
dim(X)
#> [1] 28 28

Xs <- X[grepl(x = rownames(X), "^1\\."),]
Xc <- apc(Xs)

library(multcomp)

g <- summary(glht(m1, linfct = Xc), test = adjusted(type = "fdr"))

cld2(g)
#> 1.B 1.C 1.D 1.E 1.F 
#> "e" "d" "c" "b" "a" 

confint(glht(m1, linfct = Xs), calpha = univariate_calpha())
#> 
#> 	 Simultaneous Confidence Intervals
#> 
#> Fit: lmer(formula = y ~ loccult + (1 | loc:block), data = td1)
#> 
#> Quantile = 1.96
#> 95% confidence level
#>  
#> 
#> Linear Hypotheses:
#>          Estimate lwr     upr    
#> 1.B == 0 17.0000  11.6346 22.3654
#> 1.C == 0 30.0000  24.6346 35.3654
#> 1.D == 0 45.0000  39.6346 50.3654
#> 1.E == 0 60.0000  54.6346 65.3654
#> 1.F == 0 75.0000  69.6346 80.3654
#>