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ANOFA-anofa.R
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ANOFA-anofa.R
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####################################################################################
#' @title anofa: analysis of frequency data.
#'
#' @md
#'
#' @description The function `anofa()` performs an anofa of frequencies for designs with up to 4 factors
#' according to the `anofa` framework. See \insertCite{lc23b;textual}{ANOFA} for more.
#'
#'
#' @param data Dataframe in one of wide, long, raw or compiled format;
#'
#' @param formula A formula with the factors on the left-hand side. See below for writing the
#' formula according to the data format.
#'
#' @param factors For raw data formats, provide the factor names.
#'
#' @return a model fit to the given frequencies. The model must always be an omnibus model (for
#' decomposition of the main model, follow the analysis with `emFrequencies()` or `contrastFrequencies()`)
#'
#'
#' @details The data can be given in four formats:
#' * `wide`: In the wide format, there is one line for each participant, and
#' one column for each factor in the design. In the column(s), the level must
#' of the factor is given (as a number, a string, or a factor).
#' * `long`: In the long format, there is an identifier column for each participant,
#' a factor column and a level number for that factor. If there are n participants
#' and m factors, there will be in total n x m lines.
#' * `raw`: In the raw column, there are as many lines as participants, and as many columns as
#' there are levels for each factors. Each cell is a 0|1 entry.
#' * `compiled`: In the compiled format, there are as many lines as there are cells in the
#' design. If there are two factors, with two levels each, there will be 4 lines.
#' See the vignette `DataFormatsForFrequencies` for more on data format and how to write their formula.
#'
#'
#' @references
#' \insertAllCited
#'
#' @examples
#' # Basic example using a single-factor design with the data in compiled format.
#' # Ficticious data present frequency of observation classified according
#' # to Intensity (three levels) and Pitch (two levels) for 6 possible cells.
#' minimalExample
#'
#' formula <- Frequency ~ Intensity * Pitch
#' w <- anofa(formula, minimalExample)
#' summary(w)
#'
#' # To know more about other ways to format the datasets,
#' # see, e.g., `toRaw()`, `toLong()`, `toWide()`
#' w <- anofa(formula, minimalExample)
#' toWide(w)
#' # See the vignette `DataFormatsForFrequencies` for more.
#'
#' # Real-data example using a two-factor design with the data in compiled format:
#' LandisBarrettGalvin2013
#'
#' w <- anofa( obsfreq ~ program * provider, LandisBarrettGalvin2013 )
#' summary(w)
#'
#' # You can ask easier outputs
#' w <- anofa(formula, minimalExample)
#' summarize(w) # or summary(w) for the ANOFA table
#' explain(w) # human-readable ouptut
#'
####################################################################################
#' @importFrom stats aggregate pchisq qchisq qf as.formula
#' @importFrom utils combn
#' @export anofa
#' @importFrom utils capture.output
#
####################################################################################
anofa <- function(
formula = NULL, #mandatory: the design of the data
data = NULL, #mandatory: the data itself
factors = NULL #optional: if the data are in raw format, name the factors
) {
##############################################################################
# STEP 0: preliminary preparations...
##############################################################################
data <- as.data.frame(data) # coerce to data.frame if tibble or compatible
##############################################################################
# STEP 1: Input validation
##############################################################################
# 1.1: is the formula actually a valid formula?
if (!is.formula(formula))
stop("ANOFA::error(11): `formula` argument is not a legitimate formula. Exiting...")
# 1.2: has the formula having 0 or 1 DV?
if (length(formula)==3) {
if (length(all.vars(formula[[2]]))!=1)
stop("ANOFA::error(12): formula argument has more than 0 or 1 DV. Exiting...")
}
# 1.3: are the data actually data?
if( (!is.data.frame(data)) || (dim(data)[2] <= 1))
stop("ANOFA::error(13): `data` argument is not a data.frame or similar data structure. Exiting...")
# 1.4: are the columns named in the formula present in the data?
vars <- all.vars(formula) # extract variables in cbind and with | alike
if (!(all(vars %in% names(data))))
stop("ANOFA::error(14): variables in `formula` are not all in `data`. Exiting...")
##############################################################################
# STEP 2: Harmonize the data format
##############################################################################
# 2.1: Keep only the columns named
data <- data[, names(data) %in% vars]
# 2.2: Convert data to compiled format based on the formula
if (is.one.sided( formula ) ) {
# if no left-side terms: must be wide or raw formats
if (has.cbind.terms( formula )) { # | : list all the variables
# if there are cbind in rhs, must be raw format
freq <- "Frequency"
internalData <- rtoc(data, freq, formula, factors )
} else {
# otherwise, must be wide format
freq <- "Frequency"
internalData <- wtoc(data, freq )
}
} else {
# if left-side term: must be compiled or long formats
if (has.nested.terms( formula )) {
# if | in lhs: must be long format
freq <- "Frequency"
internalData <- ltoc(data, freq, formula)
} else {
# if no | in lhs: must be compiled format: NOTHING TO DO!
freq <- formula[[2]]
internalData <- data
}
}
# 2.3: Keep the factor names
fact <- names(internalData)[ ! names(internalData) == freq]
if( (length(fact)>4) || (length(fact) < 1))
stop("ANOFA::error(15): Too many factors. Exiting...")
##############################################################################
# STEP 3: run the analysis, depending on the number of factors
##############################################################################
# 3.1: to avoid integer overflow, convert frequencies to num
internalData[[freq]] = as.numeric( internalData[[freq]])
# 3.2: perform the analysis based on the number of factors
analysis <- switch( length(fact),
anofa1way(internalData, freq, fact),
anofa2way(internalData, freq, fact),
anofa3way(internalData, freq, fact),
anofa4way(internalData, freq, fact),
)
##############################################################################
# STEP 4: return the object
##############################################################################
# 4.1: preserve everything in an object of class ANOFAobject
res <- list(
type = "ANOFAomnibus",
formula = as.formula(formula),
compiledData = internalData,
freqColumn = freq,
factColumns = fact,
nlevels = unlist(analysis[[1]]),
clevels = analysis[[2]],
results = analysis[[3]]
)
class(res) <- c("ANOFAobject", class(res) )
return( res )
}
##############################################################################
# Subfunctions
##############################################################################
anofa1way <- function(dataC, freq, factor) {
# First, we determine the number of levels for the factor
A <- length(unique(dataC[[factor]]))
clevels <- list(as.character(unique(dataC[[factor]])))
# Second, we compute the cell frequencies ni
nd <- sum(dataC[[freq]])
ni <- unlist(dataC[[freq]])
# Third, we computed the expected frequencies e
ei <- nd * rep(1/A, A)
# Fourth, get the G statistics
Gtotal <- 2 * sum(sum(ni * (log(ni)- log(ei))))
# Fifth, the correction factor (Williams, 1976)
ctotal <- 1+ (A^2-1)/ ( 6 * (A-1) * nd)
# Finally, getting the p-values for each corrected effect
ptotal = 1- pchisq(Gtotal/ ctotal, df = A-1)
results <- data.frame(
G = Gtotal,
df = A-1,
Gcorrected = Gtotal/ ctotal,
pvalue = ptotal,
etasq = anofaES(ni / nd)
)
rownames(results) <- factor
return( list( list(A), clevels, results ))
}
anofa2way <- function(dataC, freq, factors ) {
# First, we determine the number of levels for each factors
A <- length(unique(dataC[[factors[1]]]))
B <- length(unique(dataC[[factors[2]]]))
# Second, we compute the marginal frequencies n
ndd <- sum(dataC[[freq]])
nid <- aggregate(as.formula(paste(freq, factors[1], sep="~")),
data = dataC, sum)[[freq]]
ndj <- aggregate(as.formula(paste(freq, factors[2], sep="~")),
data = dataC, sum)[[freq]]
# ... and the observed frequencies in a matrix
# nij <- matrix(rep(0, A*B), ncol = B)
# for (i in 1:A) {
# for (j in 1:B) {
# nij[i,j] = dataC[dataC[[factors[1]]]==unique(dataC[[factors[1]]])[i] & dataC[[factors[2]]]==unique(dataC[[factors[2]]])[j],][[freq]]
# }
# }
#print(nij)
#print("Ss")
#print(paste(freq, paste(factors, collapse="+"),sep="~"))
temp <- aggregate(as.formula(paste(freq, paste(factors, collapse="+"),sep="~")), data = dataC, sum)
#print(temp)
nij <- matrix(temp[[freq]], A)
#print(nij)
clevels <- list(as.character(unique(temp[[factors[[1]]]])),
as.character(unique(temp[[factors[[2]]]])))
#print(clevels)
# Third, we computed the expected frequencies e
edd <- ndd / (A * B)
eid <- ndd / A
edj <- ndd / B
eij <- outer(nid, ndj)/ndd
#print(dim(nij))
#print(dim(eij))
# Fourth, get the G statistics
Gtotal <- 2 * sum(sum(nij * (log(nij)- log(edd))))
Grow <- 2 * sum(sum(nid * (log(nid)- log(eid))))
Gcol <- 2 * sum(sum(ndj * (log(ndj)- log(edj))))
Grxc <- 2 * sum(sum(nij * (log(nij)- log(eij))))
# Fifth, the correction factor (Williams, 1976) for each factor
crow <- 1+ (A^2-1)/ ( 6 * (A-1) * ndd)
ccol <- 1+ (B^2-1)/ ( 6 * (B-1) * ndd)
crxc <- 1+ ((A*B)^2-1)/ ( 6 * (A-1) * (B-1) * ndd)
# Finally, getting the p-values for each corrected effect
prow = 1- pchisq(Grow/ crow, df = A-1)
pcol = 1- pchisq(Gcol/ ccol, df = B-1)
prxc = 1- pchisq(Grxc/ crxc, df = (A-1)*(B-1))
# assembling the results in a table
results <- data.frame(
G = c(Gtotal, Grow, Gcol, Grxc),
df = c(A*B-1, A-1, B-1, (A-1)*(B-1)),
Gcorrected = c(NA, Grow/ crow, Gcol/ ccol, Grxc/ crxc),
pvalue = c(NA, prow, pcol, prxc),
etasq = c(NA, anofaES(nid/ndd), anofaES(ndj/ndd), anofaES(nij/ndd) )
)
rownames(results) <-c("Total", factors, paste(factors, collapse=":"))
return( list( list(A, B), clevels, results ))
}
anofa3way <- function(dataC, freq, factors ) {
# First, we determine the number of levels for each factors
A <- length(unique(dataC[[factors[1]]]))
B <- length(unique(dataC[[factors[2]]]))
C <- length(unique(dataC[[factors[3]]]))
# Second, we compute the grand total and the marginal frequencies in n variables
# The factors are noted with the letters i, j, k and l
# In this notation, "d" denotes the dot.
nddd <- sum(dataC[[freq]])
# first-order marginals
nidd <- aggregate(as.formula(paste(freq, factors[1], sep="~")),
data = dataC, sum)[[freq]]
ndjd <- aggregate(as.formula(paste(freq, factors[2], sep="~")),
data = dataC, sum)[[freq]]
nddk <- aggregate(as.formula(paste(freq, factors[3], sep="~")),
data = dataC, sum)[[freq]]
# second-order marginals
by2 <-lapply(combn(factors,2,simplify=FALSE), function(x) paste(x, collapse=" + "))
nijd <- matrix(aggregate(as.formula(paste(freq, by2[[1]],sep="~")),
data = dataC, sum)[[freq]], A)
nidk <- matrix(aggregate(as.formula(paste(freq, by2[[2]],sep="~")),
data = dataC, sum)[[freq]], A)
ndjk <- matrix(aggregate(as.formula(paste(freq, by2[[3]],sep="~")),
data = dataC, sum)[[freq]], B)
# and finally the observed frequencies in a matrix
nijk <- array( (temp <- aggregate(as.formula(paste(freq, paste(factors, collapse="*"),sep="~")),
data = dataC, sum))[[freq]],c(A,B,C))
# we preserve the label names in the order of the aggregate (which tend to change ordering...)
clevels <- list(as.character(unique(temp[[factors[[1]]]])),
as.character(unique(temp[[factors[[2]]]])),
as.character(unique(temp[[factors[[3]]]])))
# Third, we computed the expected frequencies e
eddd <- nddd / (A * B * C)
# first-order expectation
eidd <- rep(nddd / A, A)
edjd <- rep(nddd / B, B)
eddk <- rep(nddd / C, C)
# second-order expectation
eijd <- outer(nidd, ndjd)/nddd
eidk <- outer(nidd, nddk)/nddd
edjk <- outer(ndjd, nddk)/nddd
# third-order expectation (there might be a matrix operation for that?)
eijk <- array(NA, c(A,B,C))
for(i in 1:A) for(j in 1:B) for(k in 1:C) {
eijk[i,j,k] <- nddd * ( nijd[i,j] * nidk[i,k] * ndjk[j,k]
) / (
nidd[i] * ndjd[j] * nddk[k]
)
}
# Fourth, get the G statistics
Gtotal <- 2 * sum(sum(sum(sum(nijk * (log(nijk)- log(eddd))))))
# for the main effects
Gidd <- 2 * sum(nidd * (log(nidd)- log(eidd)))
Gdjd <- 2 * sum(ndjd * (log(ndjd)- log(edjd)))
Gddk <- 2 * sum(nddk * (log(nddk)- log(eddk)))
# for the 2-way interactions
Gijd <- 2 * sum(nijd * (log(nijd)- log(eijd)))
Gidk <- 2 * sum(nidk * (log(nidk)- log(eidk)))
Gdjk <- 2 * sum(ndjk * (log(ndjk)- log(edjk)))
# for the 3-way interactions
Gijk <- 2 * sum(nijk * (log(nijk)- log(eijk)))
# Fifth, the correction factor (Williams, 1976) for each factor
c1 <- 1+ ((A)^2-1)/ ( 6 * (A-1) * nddd)
c2 <- 1+ ((B)^2-1)/ ( 6 * (B-1) * nddd)
c3 <- 1+ ((C)^2-1)/ ( 6 * (C-1) * nddd)
c12 <- 1+ ((A*B)^2-1)/ ( 6 * (A-1) * (B-1) * nddd)
c13 <- 1+ ((A*C)^2-1)/ ( 6 * (A-1) * (C-1) * nddd)
c23 <- 1+ ((B*C)^2-1)/ ( 6 * (B-1) * (C-1) * nddd)
c123 <- 1+ ((A*B*C)^2-1)/ ( 6 * (A-1) * (B-1) * (C-1) * nddd)
# Finally, getting the p-values for each corrected effect
pidd = 1- pchisq(Gidd/ c1, df = A-1)
pdjd = 1- pchisq(Gdjd/ c2, df = B-1)
pddk = 1- pchisq(Gddk/ c3, df = C-1)
pijd = 1- pchisq(Gijd/ c12, df = (A-1)*(B-1) )
pidk = 1- pchisq(Gidk/ c13, df = (A-1)*(C-1) )
pdjk = 1- pchisq(Gdjk/ c23, df = (B-1)*(C-1) )
pijk = 1- pchisq(Gijk/ c123, df = (A-1)*(B-1)*(C-1))
# assembling the results in a table
results <- data.frame(
G = c(Gtotal,
Gidd, Gdjd, Gddk,
Gijd, Gidk, Gdjk,
Gijk),
df = c(A*B*C-1,
A-1, B-1, C-1,
(A-1)*(B-1), (A-1)*(C-1), (B-1)*(C-1),
(A-1)*(B-1)*(C-1) ),
Gcorrected = c(NA,
Gidd/c1, Gdjd/c2, Gddk/c3,
Gijd/c12, Gidk/c13, Gdjk/c23,
Gijk/c123 ),
pvalue = c( NA,
pidd, pdjd, pddk,
pijd, pidk, pdjk,
pijk),
etasq = c( NA,
anofaES(nidd/nddd), anofaES(ndjd/nddd), anofaES(nddk/nddd),
anofaES(nijd/nddd), anofaES(nidk/nddd), anofaES(ndjk/nddd),
anofaES(nijk/nddd)
)
)
by2 <-lapply(combn(factors,2,simplify=FALSE), function(x) paste(x, collapse=":"))
rownames(results) <-c("Total", factors,
by2, paste(factors, collapse=":"))
return( list( list(A, B, C), clevels, results ))
}
anofa4way <- function(dataC, freq, factors ) {
# First, we determine the number of levels for each factors
A <- length(unique(dataC[[factors[1]]]))
B <- length(unique(dataC[[factors[2]]]))
C <- length(unique(dataC[[factors[3]]]))
D <- length(unique(dataC[[factors[4]]]))
# Second, we compute the grand total and the marginal frequencies in n variables
# The factors are noted with the letters i, j, k and l
# In this notation, "d" denotes the dot.
ndddd <- sum(dataC[[freq]])
# first-order marginals
niddd <- aggregate(as.formula(paste(freq, factors[1], sep="~")),
data = dataC, sum)[[freq]]
ndjdd <- aggregate(as.formula(paste(freq, factors[2], sep="~")),
data = dataC, sum)[[freq]]
nddkd <- aggregate(as.formula(paste(freq, factors[3], sep="~")),
data = dataC, sum)[[freq]]
ndddl <- aggregate(as.formula(paste(freq, factors[4], sep="~")),
data = dataC, sum)[[freq]]
# second-order marginals
by2 <-lapply(combn(factors,2,simplify=FALSE), function(x) paste(x, collapse=" + "))
nijdd <- matrix(aggregate(as.formula(paste(freq, by2[[1]],sep="~")),
data = dataC, sum)[[freq]], A)
nidkd <- matrix(aggregate(as.formula(paste(freq, by2[[2]],sep="~")),
data = dataC, sum)[[freq]], A)
niddl <- matrix(aggregate(as.formula(paste(freq, by2[[3]],sep="~")),
data = dataC, sum)[[freq]], A)
ndjkd <- matrix(aggregate(as.formula(paste(freq, by2[[4]],sep="~")),
data = dataC, sum)[[freq]], B)
ndjdl <- matrix(aggregate(as.formula(paste(freq, by2[[5]],sep="~")),
data = dataC, sum)[[freq]], B)
nddkl <- matrix(aggregate(as.formula(paste(freq, by2[[6]],sep="~")),
data = dataC, sum)[[freq]], C)
# third-order marginals
by3 <-lapply(combn(factors,3,simplify=FALSE), function(x) paste(x, collapse=" + "))
nijkd <- array(aggregate(as.formula(paste(freq, by3[[1]],sep="~")),
data = dataC, sum)[[freq]], c(A,B,C))
nijdl <- array(aggregate(as.formula(paste(freq, by3[[2]],sep="~")),
data = dataC, sum)[[freq]], c(A,B,D))
nidkl <- array(aggregate(as.formula(paste(freq, by3[[3]],sep="~")),
data = dataC, sum)[[freq]], c(A,C,D))
ndjkl <- array(aggregate(as.formula(paste(freq, by3[[4]],sep="~")),
data = dataC, sum)[[freq]], c(B,C,D))
# and finally the observed frequencies in a matrix
nijkl <- array((temp<-aggregate(as.formula(paste(freq, paste(factors, collapse="*"),sep="~")),
data = dataC, sum))[[freq]],c(A,B,C,D))
clevels <- list(as.character(unique(temp[[factors[[1]]]])),
as.character(unique(temp[[factors[[2]]]])),
as.character(unique(temp[[factors[[3]]]])),
as.character(unique(temp[[factors[[4]]]])) )
# Third, we computed the expected frequencies e
edddd <- ndddd / (A * B * C * D)
# first-order expectation
eiddd <- rep(ndddd / A, A)
edjdd <- rep(ndddd / B, B)
eddkd <- rep(ndddd / C, C)
edddl <- rep(ndddd / D, D)
# second-order expectation
eijdd <- outer(niddd, ndjdd)/ndddd
eidkd <- outer(niddd, nddkd)/ndddd
eiddl <- outer(niddd, ndddl)/ndddd
edjkd <- outer(ndjdd, nddkd)/ndddd
edjdl <- outer(ndjdd, ndddl)/ndddd
eddkl <- outer(nddkd, ndddl)/ndddd
# third-order expectation (there might be a matrix operation for that?)
eijkd <- array(NA, c(A,B,C))
for(i in 1:A) for(j in 1:B) for(k in 1:C) {
eijkd[i,j,k] <- ndddd * nijdd[i,j] * nidkd[i,k] * ndjkd[j,k] /(niddd[i] * ndjdd[j] * nddkd[k] )
}
eijdl <- array(NA, c(A,B,D))
for(i in 1:A) for(j in 1:B) for(l in 1:D) {
eijdl[i,j,l] <- ndddd * nijdd[i,j] * niddl[i,l] * ndjdl[j,l] /(niddd[i] * ndjdd[j] * ndddl[l] )
}
eidkl <- array(NA, c(A,C,D))
for(i in 1:A) for(k in 1:C) for(l in 1:D) {
eidkl[i,k,l] <- ndddd * nidkd[i,k] * niddl[i,l] * nddkl[k,l] /(niddd[i] * nddkd[k] * ndddl[l] )
}
edjkl <- array(NA, c(B,C,D))
for(j in 1:B) for(k in 1:C) for(l in 1:D) {
edjkl[j,k,l] <- ndddd * ndjkd[j,k] * ndjdl[j,l] * nddkl[k,l] /(ndjdd[j] * nddkd[k] * ndddl[l] )
}
# forth-order expectation (there might be a matrix operation for that?)
eijkl <- array(NA, c(A,B,C,D))
for(i in 1:A) for(j in 1:B) for(k in 1:C) for(l in 1:D) {
eijkl[i,j,k,l] <- 1/ndddd * ( niddd[i] * ndjdd[j] * nddkd[k] * ndddl[l] *
nijkd[i,j,k] * nijdl[i,j,l] * nidkl[i,k,l] * ndjkl[j,k,l]
) / (
nijdd[i,j] * nidkd[i,k] * niddl[i,l] * ndjkd[j,k] * ndjdl[j,l] * nddkl[k,l]
)
}
# Fourth, get the G statistics
Gtotal <- 2 * sum(sum(sum(sum(nijkl * (log(nijkl)- log(edddd))))))
# for the main effects
Giddd <- 2 * sum(niddd * (log(niddd)- log(eiddd)))
Gdjdd <- 2 * sum(ndjdd * (log(ndjdd)- log(edjdd)))
Gddkd <- 2 * sum(nddkd * (log(nddkd)- log(eddkd)))
Gdddl <- 2 * sum(ndddl * (log(ndddl)- log(edddl)))
# for the 2-way interactions
Gijdd <- 2 * sum(nijdd * (log(nijdd)- log(eijdd)))
Gidkd <- 2 * sum(nidkd * (log(nidkd)- log(eidkd)))
Giddl <- 2 * sum(niddl * (log(niddl)- log(eiddl)))
Gdjkd <- 2 * sum(ndjkd * (log(ndjkd)- log(edjkd)))
Gdjdl <- 2 * sum(ndjdl * (log(ndjdl)- log(edjdl)))
Gddkl <- 2 * sum(nddkl * (log(nddkl)- log(eddkl)))
# for the 3-way interactions
Gijkd <- 2 * sum(nijkd * (log(nijkd)- log(eijkd)))
Gijdl <- 2 * sum(nijdl * (log(nijdl)- log(eijdl)))
Gidkl <- 2 * sum(nidkl * (log(nidkl)- log(eidkl)))
Gdjkl <- 2 * sum(ndjkl * (log(ndjkl)- log(edjkl)))
# and the 4-way interaction
Gijkl <- 2 * sum(nijkl * (log(nijkl)- log(eijkl)))
# Fifth, the correction factor (Williams, 1976) for each factor
c1 <- 1+ ((A)^2-1)/ ( 6 * (A-1) * ndddd)
c2 <- 1+ ((B)^2-1)/ ( 6 * (B-1) * ndddd)
c3 <- 1+ ((C)^2-1)/ ( 6 * (C-1) * ndddd)
c4 <- 1+ ((D)^2-1)/ ( 6 * (D-1) * ndddd)
c12 <- 1+ ((A*B)^2-1)/ ( 6 * (A-1) * (B-1) * ndddd)
c13 <- 1+ ((A*C)^2-1)/ ( 6 * (A-1) * (C-1) * ndddd)
c14 <- 1+ ((A*D)^2-1)/ ( 6 * (A-1) * (D-1) * ndddd)
c23 <- 1+ ((B*C)^2-1)/ ( 6 * (B-1) * (C-1) * ndddd)
c24 <- 1+ ((B*D)^2-1)/ ( 6 * (B-1) * (D-1) * ndddd)
c34 <- 1+ ((C*D)^2-1)/ ( 6 * (C-1) * (D-1) * ndddd)
c123 <- 1+ ((A*B*C)^2-1)/ ( 6 * (A-1) * (B-1) * (C-1) * ndddd)
c124 <- 1+ ((A*B*D)^2-1)/ ( 6 * (A-1) * (B-1) * (D-1) * ndddd)
c134 <- 1+ ((A*C*D)^2-1)/ ( 6 * (A-1) * (C-1) * (D-1) * ndddd)
c234 <- 1+ ((B*C*D)^2-1)/ ( 6 * (B-1) * (C-1) * (D-1) * ndddd)
c1234 <- 1+ ((A*B*C*D)^2-1)/ ( 6 * (A-1) * (B-1) * (C-1) * (D-1) * ndddd)
# Finally, getting the p-values for each corrected effect
piddd = 1- pchisq(Giddd/ c1, df = A-1)
pdjdd = 1- pchisq(Gdjdd/ c2, df = B-1)
pddkd = 1- pchisq(Gddkd/ c3, df = C-1)
pdddl = 1- pchisq(Gdddl/ c4, df = D-1)
pijdd = 1- pchisq(Gijdd/ c12, df = (A-1)*(B-1) )
pidkd = 1- pchisq(Gidkd/ c13, df = (A-1)*(C-1) )
piddl = 1- pchisq(Giddl/ c14, df = (A-1)*(D-1) )
pdjkd = 1- pchisq(Gdjkd/ c23, df = (B-1)*(C-1) )
pdjdl = 1- pchisq(Gdjdl/ c24, df = (B-1)*(D-1) )
pddkl = 1- pchisq(Gddkl/ c34, df = (C-1)*(D-1) )
pijkd = 1- pchisq(Gijkd/ c123, df = (A-1)*(B-1)*(C-1))
pijdl = 1- pchisq(Gijdl/ c124, df = (A-1)*(B-1)*(D-1))
pidkl = 1- pchisq(Gidkl/ c134, df = (A-1)*(C-1)*(D-1))
pdjkl = 1- pchisq(Gdjkl/ c234, df = (B-1)*(C-1)*(D-1))
pijkl = 1- pchisq(Gijkl/ c1234, df = (A-1)*(B-1)*(C-1)*(D-1) )
# assembling the results in a table
results <- data.frame(
G = c(Gtotal,
Giddd, Gdjdd, Gddkd, Gdddl,
Gijdd, Gidkd, Giddl, Gdjkd, Gdjdl, Gddkl,
Gijkd, Gijdl, Gidkl, Gdjkl,
Gijkl),
df = c(A*B*C*D-1,
A-1, B-1, C-1, D-1,
(A-1)*(B-1), (A-1)*(C-1), (A-1)*(D-1),(B-1)*(C-1),(B-1)*(D-1),(C-1)*(D-1),
(A-1)*(B-1)*(C-1), (A-1)*(B-1)*(D-1), (A-1)*(C-1)*(D-1),(B-1)*(C-1)*(D-1),
(A-1)*(B-1)*(C-1)*(D-1) ),
Gcorrected = c(NA,
Giddd/c1, Gdjdd/c2, Gddkd/c3, Gdddl/c4,
Gijdd/c12, Gidkd/c13, Giddl/c14, Gdjkd/c23, Gdjdl/c24, Gddkl/c34,
Gijkd/c123, Gijdl/c124, Gidkl/c124, Gdjkl/c234,
Gijkl/c1234),
pvalue = c(NA,
piddd, pdjdd, pddkd, pdddl,
pijdd, pidkd, piddl, pdjkd, pdjdl, pddkl,
pijkd, pijdl, pidkl, pdjkl,
pijkl),
etasq = c(NA,
anofaES(niddd/ndddd), anofaES(ndjdd/ndddd), anofaES(nddkd/ndddd), anofaES(ndddl/ndddd),
anofaES(nijdd/ndddd), anofaES(nidkd/ndddd), anofaES(niddl/ndddd),
anofaES(ndjkd/ndddd), anofaES(ndjdl/ndddd), anofaES(nddkl/ndddd),
anofaES(nijkd/ndddd), anofaES(nijdl/ndddd), anofaES(nidkl/ndddd), anofaES(ndjkl/ndddd),
anofaES(nijkl/ndddd)
)
)
by2 <-lapply(combn(factors,2,simplify=FALSE), function(x) paste(x, collapse=":"))
by3 <-lapply(combn(factors,3,simplify=FALSE), function(x) paste(x, collapse=":"))
rownames(results) <-c("Total", factors,
by2, by3, paste(factors, collapse=":"))
return( list( list(A, B, C, D), clevels, results ))
}