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R/ANOPA-anopa.R
In ANOPA: Analyses of Proportions using Anscombe Transform
Defines functions
anopa4way
anopa3way
anopa2way
anopa1way
hmean
linesA1notInA2
cleanWSFactors
checkmissingcellsBSFactors
checkforZeros
getAroundNested
getAfterNested
doONEline
addBSfcStructure
getBaseStructure
getCorrStructure
anopa
Documented in
anopa
####################################################################################
#' @name anopafct
#'
#' @title ANOPA: analysis of proportions using Anscombe transform.
#'
#' @md
#'
#' @description The function `anopa()` performs an ANOPA for designs with up to 4 factors
#' according to the ANOPA framework. See \insertCite{lc23;textual}{ANOPA} for more.
#'
#'
#' @param formula A formula with the factors on the left-hand side. See below for writing the
#' formula to match the data format.
#'
#' @param data Dataframe in one of wide, long, or compiled format;
#'
#' @param WSFactors For within-subject designs, provide the factor names and their number of levels.
#' This is expressed as a vector of strings such as "Moment(2)".
#'
#' @return An omnibus analyses of the given proportions. Each factor's significance is
#' assessed, as well as their interactions when there is more than one factor.
#' The results are obtained with `summary()` or `summarize()` as usual. If desired,
#' the corrected-only statistics can be presented \insertCite{w76}{ANOPA} using
#' `corrected()`; the uncorrected statistics only are obtained with `uncorrected()`.
#' For decomposition of the main analyses, follow the main analysis with `emProportions()`,
#' `contrastProportions()`, or `posthocProportions()`)
#'
#' @details Note the following limitations:
#' 1. The main analysis performed by `anopa()` is currently restricted to three
#' factors in total (between and/or within). Contact the author if you plan to analyze
#' more complex designs.
#' 2. If you have repeated-measure design, the data *must* be provided in wide or
#' long format. The correlation between successes cannot be assessed once the data are
#' in a compiled format.
#' 3. The data can be given in three formats:
#' * `wide`: In the wide format, there is one line for each participant, and
#' one column for each between-subject factors in the design. In the column(s), the level
#' of the factor is given (as a number, a string, or a factor). For within-subject
#' factors, the columns contains 0 or 1 based on the status of the measurement.
#' * `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.
#' * `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 \code{vignette("B-DataFormatsForProportions", package = "ANOPA")}
#' for more on data format and how to write their formula.
#'
#'
#' @references
#' \insertAllCited
#'
#' @examples
#' # -- FIRST EXAMPLE --
#' # Basic example using a single between-subject factor design with the data in compiled format.
#' # Ficticious data present success (1) or failure (0) of the observation according
#' # to the state of residency (three levels: Florida, Kentucky or Montana) for
#' # 3 possible cells. There are 175 observations (with unequal n, Montana having only)
#' # 45 observations).
#' minimalBSExample
#' # The data are in compiled format, consequently the data frame has only three lines.
#' # The complete data frame in wide format would be composed of 175 lines, one per participant.
#'
#' # The following formula using curly braces is describing this data format
#' # (note the semicolon to separate the number of successes from the number of observations):
#' formula <- {s; n} ~ state
#'
#' # The analysis is performed using the function `anopa()` with a formula and data:
#' w <- anopa(formula, minimalBSExample)
#' summary(w)
#' # As seen, the proportions of success do not differ across states.
#'
#' # To see the proportions when the data is in compiled format, simply divide the
#' # number of success (s) by the total number of observations (n):
#' minimalBSExample$s / minimalBSExample$n
#'
#' # A plot of the proportions with error bars (default 95% confidence intervals) is
#' # easily obtained with
#' anopaPlot(w)
#'
#' # The data can be re-formated into different formats with,
#' # e.g., `toRaw()`, `toLong()`, `toWide()`
#' head(toWide(w))
#' # In this format, only 1s and 0s are shown, one participant per line.
#' # See the vignette `DataFormatsForFrequencies` for more.
#'
#' # -- SECOND EXAMPLE --
#' # Real-data example using a three-factor design with the data in compiled format:
#' ArringtonEtAl2002
#'
#' # This dataset, shown in compiled format, has three cells missing
#' # (e.g., fishes whose location is African, are Detrivore, feeding Nocturnally)
#' w <- anopa( {s;n} ~ Location * Trophism * Diel, ArringtonEtAl2002 )
#'
#' # The function `anopa()` generates the missing cells with 0 success over 0 observations.
#' # Afterwards, cells with missing values are imputed based on the option:
#' getOption("ANOPA.zeros")
#' # where 0.05 is 1/20 of a success over one observations (arcsine transforms allows
#' # fractions of success; it remains to be studied what imputation strategy is best...)
#'
#' # The analysis suggests a main effect of Trophism (type of food ingested)
#' # but the interaction Trophism by Diel (moment of feeding) is not to be neglected...
#' summary(w) # or summarize(w)
#'
#' # The above presents both the uncorrected statistics as well as the corrected
#' # ones for small samples (Williams, 1976). You can obtain only the uncorrected...
#' uncorrected(w)
#'
#' #... or the corrected ones
#' corrected(w)
#'
#' # Finally, the data may have repeated measures and still be accessible in a compiled
#' # format, as is the case of this short example:
#' minimalMxExampleCompiled
#'
#' # As seen, it has one "group" factor (between) and two repeated measures (under the
#' # "foraging" or "frg" within factor). The groups are unequal, ranging form 16 to 81.
#' # Finally, as this is repeated measures, there are correlations in each group
#' # (generally weak except possibly for the "treatment3" group).
#'
#' # Such a compiled structure can be provided to anopa() by specifying the
#' # repeated measures first (within cbind()), next the number of observation column,
#' # and finally, the column containing the measure of correlation (any names can be used):
#' v <- anopa( {cbind(frg.before,frg.after); Count; uAlpha} ~ group,
#' minimalMxExampleCompiled,
#' WSFactors = "foraging(2)")
#' anopaPlot(v)
#' summary(v)
#'
#'
#' # You can also ask easier outputs with:
#' explain(w) # human-readable ouptut NOT YET DONE
#'
####################################################################################
#'
#' @importFrom stats pchisq as.formula
#' @importFrom utils combn
#' @importFrom utils capture.output
#' @export anopa
#' @importFrom Rdpack reprompt
#' @importFrom utils compareVersion packageVersion
#'
####################################################################################
anopa <- function(
formula = NULL, #mandatory: the design of the data
data = NULL, #mandatory: the data itself
WSFactors = NULL #optional: if the data are in raw format, name the factors
) {
##############################################################################
## NB. Herein, the following abbreviations are used
## WS: Within-subject design
## BS: Between-subject design
## MX: Mixed, within+between, design
##############################################################################
##############################################################################
# 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("ANOPA::error(11): Argument `formula` is not a legitimate formula. Exiting...")
# 1.1b: if the formula has crange, replace with cbind
if (has.crange.terms(formula)) {
#print("testing crange")
range <- sub.formulas(formula, "crange")[[1]]
beg <- match(paste(range[[2]]), names(data))
end <- match(paste(range[[3]]), names(data))
tmp <- paste("cbind(", paste(names(data)[beg:end],collapse=","),")", sep="")
#print(tmp)
pos <- sub.formula.locations(formula,"crange")
if (length(pos)>1)
stop("ANOPA::error(11.1): crange is found in more than one location. Existing...")
formula[[pos[[1]]]] <- as.formula(paste(tmp,"~whatever"))[[2]]
ANOPAmessage(paste("ANOPA::fyi: Here is how the crange is unpacked: ", tmp))
}
# 1.2: has the formula 1 or more DV?
if (is.one.sided( formula )) {
stop("ANOPA::error(12): Argument `formula` has no DV. Exiting...")
}
# 1.3: are the data actually data?
if( (!is.data.frame(data)) || (dim(data)[2] <= 1))
stop("ANOPA::error(13): Argument `data` 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, cbind and nested alike
vars <- vars[!(vars == ".")] # remove .
if (!(all(vars %in% names(data))))
stop("ANOPA::error(14): Variables in `formula` are not all in `data`. Exiting...")
# 1.5: If wide format with repeated-measures, are the WSFactors given?
if ((has.cbind.terms(formula)) && is.null(WSFactors))
stop("ANOPA::error(15): Argument `WSFactors` must be defined in wide format with repeated measures. Exiting...")
# 1.6: correct version of superb?
version_above <- function(pkg, than) {
as.logical(compareVersion(as.character(packageVersion(pkg)), than))
}
if (!version_above("superb","0.95.22"))
stop("ANOPA::error(16): superb version installed is prior to 0.95.23. Update package superb. Exiting...")
##############################################################################
# STEP 2: Manage WS factors
##############################################################################
# 2.0: Keep only the columns named
data <- data[, names(data) %in% vars]
# 2.1: get cbind/crange variables if Wide (WS or MX) formats
if (!in.formula(formula, "{") && has.cbind.terms(formula)) {
# extract vars from cbind
bvars <- c()
for (i in 2:length(formula[[2]]))
bvars <- c(bvars, paste(formula[[2]][[i]]))
cleanedWSF <- cleanWSFactors(WSFactors, bvars)
}
# 2.2: get cbind variables if Compiled (WS or MX)
if (in.formula(formula, "{") && has.cbind.terms(formula)) {
# extract vars from cbind
bvars <- c()
for (i in 2:length(formula[[2]][[2]]))
bvars <- c(bvars, paste(formula[[2]][[2]][[i]]))
cleanedWSF <- cleanWSFactors(WSFactors, bvars)
}
# 2.3: get WSfactors in Long format before they are erased
if (has.nested.terms(formula)) {
tmp <- getAroundNested(formula)
wsvars <- unique(data[[paste(tmp[[2]])]])
cleanedWSF <- cleanWSFactors(WSFactors, wsvars)
}
##############################################################################
# STEP 3: Harmonize the data format to wide
##############################################################################
# 3.1: Set defaults
uAlpha <- -99.9 # no correlation
BSFactors <- WSFactors <- c()
WSLevels <- BSLevels <- 1
WSDesign <- data.frame()
compData <- NULL
countCol <- "n"
alphaCol <- "uAlpha"
# 3.2: Convert data to wide format based on the format as infered from the formula
if (in.formula(formula, "{") && has.cbind.terms(formula)) {
# Case 1: Compiled (WS or MX) template: {cbind(b1,..,bm);n;r} ~ Factors
bracedvars <- c(paste(bvars), paste(formula[[2]][[3]]), paste(formula[[2]][[4]]))
BSFactors <- complement(vars, bracedvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(data[,x])) ))
DVvars <- bvars # ??
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
countCol <- paste(formula[[2]][[3]])
alphaCol <- paste(formula[[2]][[4]])
compData <- data # data are in compiled format
wideData <- lapply(1:(dim(data)[1]), doONEline,
DF = data,
BSfacts = BSFactors,
WSfacts = bvars,
CountCol = paste(formula[[2]][[3]]),
AlphaCol = paste(formula[[2]][[4]])
)
wideData <- do.call(rbind, wideData)
} else if (in.formula(formula, "{")) {
#case 1: Compiled (BS only) template: {s;n} ~ Factors
bracedvars <- c(paste(formula[[2]][[2]]), paste(formula[[2]][[3]]))
wideData <- ctow(data, bracedvars[1], bracedvars[2] )
BSFactors <- complement(vars, bracedvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ))
DVvars <- paste(formula[[2]][[2]])
} else if (has.cbind.terms(formula)) {
#case 2: Wide (WS or MX)
# 2.1: Wide (WS) template: cbind(b1,...,bm) ~ .
# 2.2: Wide (MX) template: cbind(b1,...,bm) ~ Factors
BSFactors <- complement(vars, bvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(data[,x])) ))
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
WSDesign <- cleanedWSF[[3]]
DVvars <- bvars
wideData <- data # nothing to do, already correct format
# computes correlation with unitaryAlpha
factors <- names(data)[!(names(data) %in% bvars )]
if (length(factors) == 0) {
# adds a dummy BS factor
data[["dummyBSfactor"]] <- 1; factors <- "dummyBSfactor"
}
uAlpha <- plyr::ddply(data, factors, function(x) {unitaryAlpha(as.matrix(x[bvars]))} )$V1
} else if (has.nested.terms(formula)) {
#case 3: long (BS or WS or MX)
# 3.1: long (BS) template: b ~ BSFactors | Id
# 3.2: long (WS) template: b ~ WSConditions | Id
# 3.3: long (MX) template: b ~ BSFactors * WSConditions | Id
idvar <- getAfterNested( formula )
DVvars <- paste(formula[[2]])
# get vars that are changing for a given Id
Factors <- names(data)[ !(names(data) %in% c(idvar, DVvars))]
BSFactors <- c()
WSFactors <- c()
for (i in Factors) {
if (dim(unique(data[data[[idvar]] == 1,][c(idvar, i)]))[1] > 1) {
WSFactors <- c(WSFactors, i)
} else {
BSFactors <- c(BSFactors, i)
}
}
wideData <- ltow(data, idvar, tmp[[2]], DVvars )
# take the success name under Variable
DVvars <- names(wideData)[!(names(wideData) %in% c( all.vars(formula[[3]]), "n"))]
BSFactors <- complement(names(wideData), DVvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ) )
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
WSDesign <- cleanedWSF[[3]]
# computes correlation with unitaryAlpha
if (!is.null(WSFactors)) {
factors <- names(wideData)[!(names(wideData) %in% wsvars )]
if (length(factors) == 0) {
# adds a dummy BS factor
wideData[["dummyBSfactor"]] <- 1; factors <- "dummyBSfactor"
}
uAlpha <- plyr::ddply(wideData, factors,
function(x) {unitaryAlpha(as.matrix(x[wsvars]))}
)$V1
wideData[["dummyBSfactor"]] <- NULL
}
} else if (length(formula[[1]]) == 1) {
#case 2.3: Wide (BS) template: b ~ Factors
wideData <- data # nothing to do, already correct format
# extract vars from rhs formula
BSFactors <- all.vars(formula[[3]])
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ) )
WSLevels <-1
DVvars <- paste(formula[[2]])
} else {
# error...
stop("ANOPA::error(17): Unrecognized data format. Exiting...")
}
# 3.3: Keep the factor names
allFactors <- c(WSFactors, BSFactors)
# 3.4: Acknolwedge limitations of the present package
if( (length(allFactors) < 1) )
stop("ANOPA::error(18a): No factor provided. Exiting...")
if( (length(allFactors)>4) || (length(allFactors) < 1) )
stop("ANOPA::error(18b): Too many factors. Exiting...")
if( length(allFactors)==4 )
stop("ANOPA::error(18c): Four factors; contact the author. Exiting...")
##############################################################################
# STEP 4: run the analysis, depending on the number of factors
##############################################################################
# 4.0: additional checks on within...
if (prod(WSLevels) != length(DVvars))
stop("ANOPA::error(19): There are missing within-subject level columns. Exiting...")
# 4.1: to avoid integer overflow, convert integers to num
for (i in DVvars)
wideData[[i]] <- as.numeric( wideData[[i]] )
# 4.2: compile the data if was not given compiled
if (is.null(compData))
compData <- wtoc(wideData, DVvars, "n")
# 4.3: check for all sorts of missing (not there or there with zeros...)
compData <- checkmissingcellsBSFactors(compData, BSFactors, DVvars)
compData <- checkforZeros(compData, DVvars)
# 4.4: sort the data
if (length(BSFactors) > 0)
compData <- compData[ do.call(order, data.frame(compData[,BSFactors]) ), ]
# 4.4: perform the analysis based on the number of factors
analysis <- switch( length(allFactors),
anopa1way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa2way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa3way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa4way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels)
)
##############################################################################
# STEP 5: return the object
##############################################################################
# 5.1: preserve everything in an object of class ANOPAobject
res <- list(
type = "ANOPAomnibus",
formula = as.formula(formula),
BSfactColumns = BSFactors,
BSfactNlevels = BSLevels,
WSfactColumns = WSFactors,
WSfactDesign = WSDesign,
WSfactNlevels = WSLevels,
DVvariables = DVvars,
AlphaVariable = alphaCol,
NVariable = countCol,
wideData = wideData, # raw data are absolutely needed for plot only
compData = compData, # compiled data are used for analyzes
omnibus = analysis # results of the omnibus analysis
)
class(res) <- c("ANOPAobject", class(res) )
return( res )
}
##############################################################################
# Subfunctions to generate long from compiled
##############################################################################
getCorrStructure <- function(mat, targetUA) {
# This function is used when the design has repeated measures
# and the data are provided as compiled. In that case,
# the exact dispositions of 1s and 0s cannot be determined and
# so random rearrangments are tested to get uAlpha as close as possible.
bestDiff = 999
ncol = dim(mat)[2]
for (seed in 1:2000) {
set.seed(seed)
for (col in 2:ncol) {
mat[,col] = sample(mat[,col])
}
currentUA = unitaryAlpha(mat)
if (abs(currentUA - targetUA) < .0001) {
# close enough!
bestmat = mat
break
}
if (abs(currentUA - targetUA) < bestDiff) {
bestDiff = abs(currentUA - targetUA)
bestmat = mat
}
}
# check that correlation are not too far from target
if (abs(targetUA-unitaryAlpha(bestmat)) > 0.25) {
ANOPAwarning("ANOPA::warning(111): Cannot reconstitute the correlation structure. Consider using raw (wide or long) data...")
}
return(bestmat)
}
getBaseStructure <- function(line, cnt) {
# expand a line of the compiled data into a matrix
mat <- data.frame( toDelete123 = 1:cnt )
for (i in names(line)) {
mat[[i]] <- c(rep(1, round(line[i]) ), rep(0, round(cnt-line[i]) ))
}
# delete sentinel column
mat$toDelete123 <- NULL
mat
}
addBSfcStructure <- function(mat, bs) {
# adds to the mat the between-subject group(s)
if (!is.null(bs)) {
for (i in names(bs) )
mat[[i]] <- rep( bs[[i]], dim(mat)[1])
}
mat
}
doONEline <- function(lineno, DF, BSfacts, WSfacts, CountCol, AlphaCol) {
oneBScd <- DF[lineno, BSfacts, drop=FALSE]
oneline <- DF[lineno, WSfacts]
onecnt <- DF[lineno, CountCol]
oneual <- DF[lineno, AlphaCol]
mat1 <- getBaseStructure(oneline, onecnt)
mat2 <- getCorrStructure(mat1, oneual )
mat3 <- addBSfcStructure(mat2, oneBScd)
mat3
}
##############################################################################
# Subfunctions for recognizing formats
##############################################################################
getAfterNested <- function(frm) {
# There are three possible cases?
# frm1 <- b ~ BSFactors * WSConditions | Id
# frm2 <- b ~ WSConditions | Id * BSFactors
# frm3 <- b ~ (WSConditions | Id) * BSFactors
f <- sub.formulas(frm, "|")[[1]]
if (length(f[[3]]) == 1) {
v1 <- f[[3]]
} else {
if (f[[3]][[1]] == "*") {
v1 <- f[[3]][[2]]
} else {
stop("ANOPA::internal(-1): Case non-existant: That should never happen")
}
}
return( paste(v1) )
}
getAroundNested <- function(frm) {
# There are three possible cases?
# frm1 <- b ~ BSFactors * WSConditions | Id
# frm2 <- b ~ WSConditions | Id * BSFactors
# frm3 <- b ~ (WSConditions | Id) * BSFactors
f <- sub.formulas(frm, "|")[[1]]
if (length(f[[3]]) == 1) {
v1 <- f[[3]]
if (length(f[[2]]) == 1) {
v2 <- f[[2]]
} else {
v2 <- f[[2]][[length(f[[2]])]]
}
} else {
if (f[[3]][[1]] == "*") {
v1 <- f[[3]][[2]]
if (length(f[[2]]) == 1) {
v2 <- f[[2]]
} else {
v2 <- f[[2]][[length(f[[2]])]]
}
} else {
stop("ANOPA::internal (-2): Case non-existant: That should never happen")
}
}
return( c( paste(v1), paste(v2)) )
}
checkforZeros <- function( cData, ss) {
# Are there emtpy cells, i.e. where the proportion is 0 on 0?
# These must be imputed to avoid Undetermined scores
# Adjust ANOPA.zeros vector for a different imputation strategy
# DISCLAIMER: I did not validate if this is a sensible strategy. Do your homework.
res <- cData
repl <- as.list(unlist(options("ANOPA.zeros"))) # niaisage...
for (i in ss) {
if (any(mapply(\(x,y){(x==0)&&(y==0)}, res[[i]], res[["n"]]) ) ) {
ANOPAwarning("ANOPA::warning(1): Some cells have zero over zero data. Imputing...")
res[ res[[i]] == 0 & res[["n"]] == 0, c(i,"n")] <- repl
}
}
return( res )
}
checkmissingcellsBSFactors <- function( cData, BSFactors, ss) {
# all the combination of the levels of the factors
a <- prod(unlist(lapply(BSFactors, \(x) length(unique(cData[,x])))))
b <- dim(cData)[1]
if (a != b) {
# there are missing cases
lvls <- lapply(BSFactors, \(x) unique(cData[,x]))
cmbn <- expand.grid(lvls)
names(cmbn) <- BSFactors
notthere <- linesA1notInA2( cmbn, cData )
for ( m in ss ) {notthere[[m]] <- 0}
notthere[["n"]] <- 0
cData <- rbind(cData, notthere)
ANOPAmessage(paste("ANOPA::fyi(1): Combination of cells missing. Adding: "))
temp <- paste0(capture.output(print(notthere, row.names=FALSE)),collapse="\n")
ANOPAmessage(temp)
}
return( cData )
}
cleanWSFactors <- function(WSFactors, ss) {
# Unpack the WS factors and run a fyi if not inhibited...
WSLevels <- c(1)
WSDesign <- data.frame()
if (!is.null(WSFactors)) {
# separate name from nLevel
for (i in 1:length(WSFactors)) {
WSLevels[i] <- as.integer(unlist(strsplit(WSFactors[i], '[()]'))[2])
WSFactors[i] <- unlist(strsplit(WSFactors[i], '[()]'))[1]
}
combinaisons <- expand.grid(lapply(WSLevels, seq))
WSDesign <- cbind(combinaisons, ss)
colnames(WSDesign)[1:length(WSFactors)] <- WSFactors
colnames(WSDesign)[length(WSFactors)+1] <- "Variable"
if ( (!is.null(WSFactors)) & ('design' %in% getOption("ANOPA.feedback") ) ) {
ANOPAmessage("ANOPA::fyi: Here is how the within-subject variables are understood:")
temp <- paste0(capture.output(print(WSDesign[,c(WSFactors, "Variable") ], row.names=FALSE)),collapse="\n")
ANOPAmessage(temp)
}
}
return( list(WSFactors, WSLevels, WSDesign ) )
}
# disjonction of two data.frames
linesA1notInA2 <- function( a1, a2 ) {
# adds dummy columns
a1$included_a1 <- TRUE
a2$included_a2 <- TRUE
res <- merge(a1, a2, all=TRUE)
res <- res[ is.na(res$included_a2), ]
# removes the dummy columns
res$included_a1 <- NULL
res$included_a2 <- NULL
return( res )
}
# harmonic mean
hmean <- function(v) (length(v)/ sum(1/v))
##############################################################################
##############################################################################
# Analyses functions per se
##############################################################################
##############################################################################
anopa1way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, unneeded ) {
# One-way ANOPA (either within- or between-subject design)
# The observations are compiled into success (s) and number (n) per group and uAlpha when relevant
if (length(wsfacts) == 1) { # within-subject design
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
facts <- wsfacts
corlt <- cData[[acol]]
} else { # between-subject design
s <- cData[[ss]]
n <- cData[[ncol]]
facts <- bsfacts
corlt <- 0
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
p <- length(As)
# compute mean square of effect P, mean square of error
msP <- var(As)
msE <- mean(Vs) * (1-corlt)
# compute F ratio or chi-square test statistic
F <- msP / msE
g <- (p-1) * F
# compute p value from the latter (the former has infinite df on denominator)
pval <- 1 - pchisq(g, df = (p-1) )
# the corrections
cf <- 1+ (p^2-1)/(6 * hmean(n) * (p-1) )
pvaladj <- 1 - pchisq(g/cf, df = (p-1) )
# keep the results
results <- data.frame(
MS = c(msP, msE),
df = c(p-1,Inf),
F = c(F, NA),
p = c(pval, NA),
correction = c(cf,NA),
Fcorr = c(g/cf/(p-1),NA),
pvalcorr = c(pvaladj, NA)
)
rownames(results) <- c(facts, "Error")
return(results)
}
anopa2way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
# Two-way ANOPA (within, between, or mixed design)
# the observations are compiled into success (s) and number (n) per group and uAlpha when relevant
#print("Begin anopa2way")
if (length(wsfacts) == 2) { # both within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- wsfacts
f1levl <- wslevls[2]
} else if (length(wsfacts) == 1) { # mixed, within-between, design
s <- unlist(cData[ss]) # i.e., flatten
n <- rep(cData[[ncol]], length(ss))
corlt <- rep(cData[[acol]], wslevls[1])
facts <- c(wsfacts, bsfacts)
f1levl <- wslevls
} else { # both between-subject factors
s <- cData[[ss]]
n <- cData[[ncol]]
corlt <- 0
facts <- bsfacts
f1levl <- length(unique(cData[[bsfacts[1]]]))
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
# fold the scores into a matrix
Af <- matrix( As, ncol = f1levl)
Vf <- matrix( Vs, ncol = f1levl)
ns <- matrix( n, ncol = f1levl)
# compute marginal means (P is "column" factor, Q is "row" factor) and grand mean
AP <- colMeans(Af) # marginal mean along Q factor
AQ <- rowMeans(Af) # marginal mean along P factor
Ag <- mean(As) # grand mean
nP <- colSums(ns) # sample size across all Q levels
nQ <- colSums(t(ns)) # sample size across all P levels
p <- length(AP)
q <- length(AQ)
# compute mean square of effects P, Q and PxQ
msP <- q * var( AP )
msQ <- p * var( AQ )
msPQ <- 1/((p-1)*(q-1)) * sum((As - outer(AQ, AP, `+`) + mean(As) )^2 )
# get mean squared of error for within and between respectively
msEintra <- 1/(p*q) * sum( (1-corlt)/(4*(ns+1/2) ) )
msEinter <- 1/(p*q) * sum( 1 / (4*(ns+1/2)) )
# assign error terms to each factor based on design
msEp <- if (facts[1] %in% wsfacts) msEintra else msEinter
msEq <- if (facts[2] %in% wsfacts) msEintra else msEinter
msEpq <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)) msEintra else msEinter
# compute F ratio or chi-square test statistic
FP <- msP/msEp
FQ <- msQ/msEq
FPQ <- msPQ/msEpq
gP <- (p-1) * FP
gQ <- (q-1) * FQ
gPQ <- (p-1) * (q-1) * FPQ
# compute p value from the latter (the former has infinite df on denominator)
pvalP <- 1 - pchisq(gP, df = (p-1) )
pvalQ <- 1 - pchisq(gQ, df = (q-1) )
pvalPQ <- 1 - pchisq(gPQ, df = (p-1) * (q-1) )
# If you want to apply the corrections
cfP <- 1 + (p^2-1)/(6 * hmean(nP) * (p-1) )
cfQ <- 1 + (q^2-1)/(6 * hmean(nQ) * (q-1) )
cfPQ <- 1 + ((p * q)^2-1)/(6 * hmean(ns) * (p-1)*(q-1) )
pvalPadj <- 1 - pchisq(gP/cfP, df = (p-1) )
pvalQadj <- 1 - pchisq(gQ/cfQ, df = (q-1) )
pvalPQadj <- 1 - pchisq(gPQ/cfPQ, df = (p-1)*(q-1) )
# keep the results
results <- data.frame(
MS = c(msP, msQ, msPQ, msEintra, msEinter ),
df = c(p-1, q-1, (p-1)*(q-1), Inf, Inf ),
F = c(FP, FQ, FPQ, NA, NA ),
pvalue = c(pvalP, pvalQ, pvalPQ, NA, NA ),
correction = c(cfP, cfQ, cfPQ, NA, NA ),
Fcorr = c(FP/cfP, gQ/cfQ/(q-1), gPQ/cfPQ/((p-1)*(q-1)), NA, NA ),
pvalcorr = c(pvalPadj, pvalQadj, pvalPQadj, NA, NA)
)
rownames(results) <- c(facts, paste(facts, collapse=":"),
"Error(within)", "Error(between)" )
if (length(bsfacts) == 0) results <- results[-5,] #remove 5th line
if (length(wsfacts) == 0) results <- results[-4,] #remove 4th line
return(results)
}
anopa3way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
# Three-way ANOPA (any design with within or between subject factors)
# the observations are compiled into success (s) and number (n) per group and uAlpha when relevant
if (length(wsfacts) == 3) { # entirely within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- wsfacts
lvlp <- 1:wslevls[1] # first is always within
lvlq <- 1:wslevls[2]
lvlr <- 1:wslevls[3]
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
} else if (length(wsfacts) == 2) { # mixed, 2 within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- c(wsfacts, bsfacts)
lvlp <- 1:wslevls[1]
lvlq <- 1:wslevls[2]
lvlr <- unique(cData[[bsfacts[1]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
corlt <- array(unlist(lapply( corlt, rep, p*q)), dim = c(r,q,p))
} else if (length(wsfacts) == 1) { # mixed, 1 within-subject factor
s <- c(t(cData[ss])) # i.e., flatten
n <- rep(cData[[ncol]], length(ss))
corlt <- rep(cData[[acol]], wslevls[1])
facts <- c(wsfacts, bsfacts)
lvlp <- 1:wslevls[1]
lvlq <- unique(cData[[bsfacts[1]]])
lvlr <- unique(cData[[bsfacts[2]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
corlt <- array(unlist(lapply( corlt, rep, p)), dim = c(r,q,p))
} else { # entirely between-subject factors
s <- cData[[ss]]
n <- cData[[ncol]]
corlt <- 0
facts <- bsfacts
lvlp <- unique(cData[[bsfacts[1]]])
lvlq <- unique(cData[[bsfacts[2]]])
lvlr <- unique(cData[[bsfacts[3]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
# fold the scores into an array
# for between-subject design: https://stackoverflow.com/a/52435862/5181513
namesOfDim <- list( lvlr, lvlq, lvlp )
Af <- array(As, dim = c(r, q, p), dimnames = namesOfDim)
Vf <- array(Vs, dim = c(r, q, p), dimnames = namesOfDim)
ns <- array(n, dim = c(r, q, p), dimnames = namesOfDim)
# compute marginal means (P is "column" factor, Q is "row" factor) and grand mean
AP <- apply(Af, 3, mean)
AQ <- apply(Af, 2, mean)
AR <- apply(Af, 1, mean)
APQ <- apply( Af, c(3,2), mean ) ## Les dimensions sont inversées
APR <- apply( Af, c(3,1), mean )
AQR <- apply( Af, c(2,1), mean )
nP <- apply( ns, 3, sum ) # sample size across all R levels
nQ <- apply( ns, 2, sum ) # sample size across all R levels
nR <- apply( ns, 1, sum ) # sample size across all R levels
nPQ <- apply( ns, c(3,2), sum ) # sample size across all R levels
nPR <- apply( ns, c(3,1), sum ) # sample size across all R levels
nQR <- apply( ns, c(2,1), sum ) # sample size across all R levels
# compute mean square of effects P, Q and PxQ; Keppel, 1978
msP <- q*r * var( AP )
msQ <- p*r * var( AQ )
msR <- p*q * var( AR )
msPQ <- ((p*q-1) * r * var( c(APQ) ) - (p-1)*msP - (q-1)*msQ)/((p-1)*(q-1))
msPR <- ((p*r-1) * q * var( c(APR) ) - (p-1)*msP - (r-1)*msR)/((p-1)*(r-1))
msQR <- ((q*r-1) * p * var( c(AQR) ) - (q-1)*msQ - (r-1)*msR)/((q-1)*(r-1))
msPQR <- ((p*q*r-1)*var( c(Af) ) -(p-1)*(q-1)*msPQ -(p-1)*(r-1)*msPR -(q-1)*(r-1)*msQR -(p-1)*msP -(q-1)*msQ -(r-1)*msR )/ ((p-1)*(q-1)*(r-1))
# get mean squared of error for within and between respectively
msEintra <- 1/(p*q*r)*sum( (1-corlt)/ (4*ns+1/2))
msEinter <- 1/(p*q*r)*sum( 1 / (4*ns+1/2))
# assign error terms to each factor based on design
msEp <- if (facts[1] %in% wsfacts) msEintra else msEinter
msEq <- if (facts[2] %in% wsfacts) msEintra else msEinter
msEr <- if (facts[3] %in% wsfacts) msEintra else msEinter
msEpq <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)) msEintra else msEinter
msEpr <- if ((facts[1] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
msEqr <- if ((facts[2] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
msEpqr <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
# compute F ratio or chi-square test statistic
FP <- msP/msEp
FQ <- msQ/msEq
FR <- msR/msEr
FPQ <- msPQ/msEpq
FPR <- msPR/msEpr
FQR <- msQR/msEqr
FPQR <- msPQR/msEpqr
gP <- (p-1) * FP
gQ <- (q-1) * FQ
gR <- (r-1) * FR
gPQ <- (p-1) * (q-1) * FPQ
gPR <- (p-1) * (r-1) * FPR
gQR <- (q-1) * (r-1) * FQR
gPQR <- (p-1) * (q-1) * (r-1) * FPQR
# compute p value from the latter (the former has infinite df on denominator)
pvalP <- 1 - pchisq(gP, df = (p-1) )
pvalQ <- 1 - pchisq(gQ, df = (q-1) )
pvalR <- 1 - pchisq(gR, df = (r-1) )
pvalPQ <- 1 - pchisq(gPQ, df = (p-1) * (q-1) )
pvalPR <- 1 - pchisq(gPR, df = (p-1) * (r-1) )
pvalQR <- 1 - pchisq(gQR, df = (q-1) * (r-1) )
pvalPQR <- 1 - pchisq(gPQR, df = (p-1) * (q-1) * (r-1) )
# If you want to apply the corrections; we remove the imputed cells...
cfP <- 1 + (p^2-1)/(6 * hmean(nP) * (p-1) )
cfQ <- 1 + (q^2-1)/(6 * hmean(nQ) * (q-1) )
cfR <- 1 + (r^2-1)/(6 * hmean(nR) * (r-1) )
cfPQ <- 1 + ((p * q)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(q-1) )
cfPR <- 1 + ((p * r)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(r-1) )
cfQR <- 1 + ((q * r)^2-1)/(6 * hmean(ns[ns>1]) * (q-1)*(r-1) )
cfPQR <- 1 + ((p * q * r)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(q-1)*(r-1) )
pvalPadj <- 1 - pchisq(gP/cfP, df = (p-1) )
pvalQadj <- 1 - pchisq(gQ/cfQ, df = (q-1) )
pvalRadj <- 1 - pchisq(gR/cfR, df = (r-1) )
pvalPQadj <- 1 - pchisq(gPQ/cfPQ, df = (p-1)*(q-1) )
pvalPRadj <- 1 - pchisq(gPR/cfPR, df = (p-1)*(r-1) )
pvalQRadj <- 1 - pchisq(gQR/cfQR, df = (q-1)*(r-1) )
pvalPQRadj <- 1 - pchisq(gPQR/cfPQR, df = (p-1)*(q-1)*(r-1) )
# keep the results
results <- data.frame(
MS = c(msP, msQ, msR, msPQ, msPR, msQR, msPQR, msEintra, msEinter ),
df = c(p-1, q-1, r-1, (p-1)*(q-1), (p-1)*(r-1), (q-1)*(r-1), (p-1)*(q-1)*(r-1), Inf, Inf ),
F = c(FP, FQ, FR, FPQ, FPR, FQR, FPQR, NA, NA ),
pvalue = c(pvalP, pvalQ, pvalR, pvalPQ, pvalPR, pvalQR, pvalPQR, NA, NA ),
correction = c(cfP, cfQ, cfR, cfPQ, cfPR, cfQR, cfPQR, NA, NA ),
Fcorr = c(FP/cfP, gQ/cfQ/(q-1), gR/cfR/(r-1),
gPQ/cfPQ/((p-1)*(q-1)), gPR/cfPR/((p-1)*(r-1)), gQR/cfQR/((q-1)*(r-1)),
gPQR/cfPQR/((p-1)*(q-1)*(r-1)),
NA, NA ),
pvalcorr = c(pvalPadj, pvalQadj, pvalRadj, pvalPQadj, pvalPRadj, pvalQRadj, pvalPQRadj, NA, NA)
)
rownames(results) <- c(facts,
apply(data.frame(utils::combn(facts,2)), 2, paste, collapse = ":"),
paste(facts, collapse=":"),
"Error(within)", "Error(between)" )
if (length(bsfacts) == 0) results <- results[-9,] #remove between-error line
if (length(wsfacts) == 0) results <- results[-8,] #remove within-error line
return(results)
}
anopa4way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
return("Not programmed so far. Contact Denis Cousineau if needed.")
}
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Defines functions anopa4way anopa3way anopa2way anopa1way hmean linesA1notInA2 cleanWSFactors checkmissingcellsBSFactors checkforZeros getAroundNested getAfterNested doONEline addBSfcStructure getBaseStructure getCorrStructure anopa
Documented in anopa
####################################################################################
#' @name anopafct
#'
#' @title ANOPA: analysis of proportions using Anscombe transform.
#'
#' @md
#'
#' @description The function `anopa()` performs an ANOPA for designs with up to 4 factors
#' according to the ANOPA framework. See \insertCite{lc23;textual}{ANOPA} for more.
#'
#'
#' @param formula A formula with the factors on the left-hand side. See below for writing the
#' formula to match the data format.
#'
#' @param data Dataframe in one of wide, long, or compiled format;
#'
#' @param WSFactors For within-subject designs, provide the factor names and their number of levels.
#' This is expressed as a vector of strings such as "Moment(2)".
#'
#' @return An omnibus analyses of the given proportions. Each factor's significance is
#' assessed, as well as their interactions when there is more than one factor.
#' The results are obtained with `summary()` or `summarize()` as usual. If desired,
#' the corrected-only statistics can be presented \insertCite{w76}{ANOPA} using
#' `corrected()`; the uncorrected statistics only are obtained with `uncorrected()`.
#' For decomposition of the main analyses, follow the main analysis with `emProportions()`,
#' `contrastProportions()`, or `posthocProportions()`)
#'
#' @details Note the following limitations:
#' 1. The main analysis performed by `anopa()` is currently restricted to three
#' factors in total (between and/or within). Contact the author if you plan to analyze
#' more complex designs.
#' 2. If you have repeated-measure design, the data *must* be provided in wide or
#' long format. The correlation between successes cannot be assessed once the data are
#' in a compiled format.
#' 3. The data can be given in three formats:
#' * `wide`: In the wide format, there is one line for each participant, and
#' one column for each between-subject factors in the design. In the column(s), the level
#' of the factor is given (as a number, a string, or a factor). For within-subject
#' factors, the columns contains 0 or 1 based on the status of the measurement.
#' * `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.
#' * `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 \code{vignette("B-DataFormatsForProportions", package = "ANOPA")}
#' for more on data format and how to write their formula.
#'
#'
#' @references
#' \insertAllCited
#'
#' @examples
#' # -- FIRST EXAMPLE --
#' # Basic example using a single between-subject factor design with the data in compiled format.
#' # Ficticious data present success (1) or failure (0) of the observation according
#' # to the state of residency (three levels: Florida, Kentucky or Montana) for
#' # 3 possible cells. There are 175 observations (with unequal n, Montana having only)
#' # 45 observations).
#' minimalBSExample
#' # The data are in compiled format, consequently the data frame has only three lines.
#' # The complete data frame in wide format would be composed of 175 lines, one per participant.
#'
#' # The following formula using curly braces is describing this data format
#' # (note the semicolon to separate the number of successes from the number of observations):
#' formula <- {s; n} ~ state
#'
#' # The analysis is performed using the function `anopa()` with a formula and data:
#' w <- anopa(formula, minimalBSExample)
#' summary(w)
#' # As seen, the proportions of success do not differ across states.
#'
#' # To see the proportions when the data is in compiled format, simply divide the
#' # number of success (s) by the total number of observations (n):
#' minimalBSExample$s / minimalBSExample$n
#'
#' # A plot of the proportions with error bars (default 95% confidence intervals) is
#' # easily obtained with
#' anopaPlot(w)
#'
#' # The data can be re-formated into different formats with,
#' # e.g., `toRaw()`, `toLong()`, `toWide()`
#' head(toWide(w))
#' # In this format, only 1s and 0s are shown, one participant per line.
#' # See the vignette `DataFormatsForFrequencies` for more.
#'
#' # -- SECOND EXAMPLE --
#' # Real-data example using a three-factor design with the data in compiled format:
#' ArringtonEtAl2002
#'
#' # This dataset, shown in compiled format, has three cells missing
#' # (e.g., fishes whose location is African, are Detrivore, feeding Nocturnally)
#' w <- anopa( {s;n} ~ Location * Trophism * Diel, ArringtonEtAl2002 )
#'
#' # The function `anopa()` generates the missing cells with 0 success over 0 observations.
#' # Afterwards, cells with missing values are imputed based on the option:
#' getOption("ANOPA.zeros")
#' # where 0.05 is 1/20 of a success over one observations (arcsine transforms allows
#' # fractions of success; it remains to be studied what imputation strategy is best...)
#'
#' # The analysis suggests a main effect of Trophism (type of food ingested)
#' # but the interaction Trophism by Diel (moment of feeding) is not to be neglected...
#' summary(w) # or summarize(w)
#'
#' # The above presents both the uncorrected statistics as well as the corrected
#' # ones for small samples (Williams, 1976). You can obtain only the uncorrected...
#' uncorrected(w)
#'
#' #... or the corrected ones
#' corrected(w)
#'
#' # Finally, the data may have repeated measures and still be accessible in a compiled
#' # format, as is the case of this short example:
#' minimalMxExampleCompiled
#'
#' # As seen, it has one "group" factor (between) and two repeated measures (under the
#' # "foraging" or "frg" within factor). The groups are unequal, ranging form 16 to 81.
#' # Finally, as this is repeated measures, there are correlations in each group
#' # (generally weak except possibly for the "treatment3" group).
#'
#' # Such a compiled structure can be provided to anopa() by specifying the
#' # repeated measures first (within cbind()), next the number of observation column,
#' # and finally, the column containing the measure of correlation (any names can be used):
#' v <- anopa( {cbind(frg.before,frg.after); Count; uAlpha} ~ group,
#' minimalMxExampleCompiled,
#' WSFactors = "foraging(2)")
#' anopaPlot(v)
#' summary(v)
#'
#'
#' # You can also ask easier outputs with:
#' explain(w) # human-readable ouptut NOT YET DONE
#'
####################################################################################
#'
#' @importFrom stats pchisq as.formula
#' @importFrom utils combn
#' @importFrom utils capture.output
#' @export anopa
#' @importFrom Rdpack reprompt
#' @importFrom utils compareVersion packageVersion
#'
####################################################################################
anopa <- function(
formula = NULL, #mandatory: the design of the data
data = NULL, #mandatory: the data itself
WSFactors = NULL #optional: if the data are in raw format, name the factors
) {
##############################################################################
## NB. Herein, the following abbreviations are used
## WS: Within-subject design
## BS: Between-subject design
## MX: Mixed, within+between, design
##############################################################################
##############################################################################
# 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("ANOPA::error(11): Argument `formula` is not a legitimate formula. Exiting...")
# 1.1b: if the formula has crange, replace with cbind
if (has.crange.terms(formula)) {
#print("testing crange")
range <- sub.formulas(formula, "crange")[[1]]
beg <- match(paste(range[[2]]), names(data))
end <- match(paste(range[[3]]), names(data))
tmp <- paste("cbind(", paste(names(data)[beg:end],collapse=","),")", sep="")
#print(tmp)
pos <- sub.formula.locations(formula,"crange")
if (length(pos)>1)
stop("ANOPA::error(11.1): crange is found in more than one location. Existing...")
formula[[pos[[1]]]] <- as.formula(paste(tmp,"~whatever"))[[2]]
ANOPAmessage(paste("ANOPA::fyi: Here is how the crange is unpacked: ", tmp))
}
# 1.2: has the formula 1 or more DV?
if (is.one.sided( formula )) {
stop("ANOPA::error(12): Argument `formula` has no DV. Exiting...")
}
# 1.3: are the data actually data?
if( (!is.data.frame(data)) || (dim(data)[2] <= 1))
stop("ANOPA::error(13): Argument `data` 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, cbind and nested alike
vars <- vars[!(vars == ".")] # remove .
if (!(all(vars %in% names(data))))
stop("ANOPA::error(14): Variables in `formula` are not all in `data`. Exiting...")
# 1.5: If wide format with repeated-measures, are the WSFactors given?
if ((has.cbind.terms(formula)) && is.null(WSFactors))
stop("ANOPA::error(15): Argument `WSFactors` must be defined in wide format with repeated measures. Exiting...")
# 1.6: correct version of superb?
version_above <- function(pkg, than) {
as.logical(compareVersion(as.character(packageVersion(pkg)), than))
}
if (!version_above("superb","0.95.22"))
stop("ANOPA::error(16): superb version installed is prior to 0.95.23. Update package superb. Exiting...")
##############################################################################
# STEP 2: Manage WS factors
##############################################################################
# 2.0: Keep only the columns named
data <- data[, names(data) %in% vars]
# 2.1: get cbind/crange variables if Wide (WS or MX) formats
if (!in.formula(formula, "{") && has.cbind.terms(formula)) {
# extract vars from cbind
bvars <- c()
for (i in 2:length(formula[[2]]))
bvars <- c(bvars, paste(formula[[2]][[i]]))
cleanedWSF <- cleanWSFactors(WSFactors, bvars)
}
# 2.2: get cbind variables if Compiled (WS or MX)
if (in.formula(formula, "{") && has.cbind.terms(formula)) {
# extract vars from cbind
bvars <- c()
for (i in 2:length(formula[[2]][[2]]))
bvars <- c(bvars, paste(formula[[2]][[2]][[i]]))
cleanedWSF <- cleanWSFactors(WSFactors, bvars)
}
# 2.3: get WSfactors in Long format before they are erased
if (has.nested.terms(formula)) {
tmp <- getAroundNested(formula)
wsvars <- unique(data[[paste(tmp[[2]])]])
cleanedWSF <- cleanWSFactors(WSFactors, wsvars)
}
##############################################################################
# STEP 3: Harmonize the data format to wide
##############################################################################
# 3.1: Set defaults
uAlpha <- -99.9 # no correlation
BSFactors <- WSFactors <- c()
WSLevels <- BSLevels <- 1
WSDesign <- data.frame()
compData <- NULL
countCol <- "n"
alphaCol <- "uAlpha"
# 3.2: Convert data to wide format based on the format as infered from the formula
if (in.formula(formula, "{") && has.cbind.terms(formula)) {
# Case 1: Compiled (WS or MX) template: {cbind(b1,..,bm);n;r} ~ Factors
bracedvars <- c(paste(bvars), paste(formula[[2]][[3]]), paste(formula[[2]][[4]]))
BSFactors <- complement(vars, bracedvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(data[,x])) ))
DVvars <- bvars # ??
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
countCol <- paste(formula[[2]][[3]])
alphaCol <- paste(formula[[2]][[4]])
compData <- data # data are in compiled format
wideData <- lapply(1:(dim(data)[1]), doONEline,
DF = data,
BSfacts = BSFactors,
WSfacts = bvars,
CountCol = paste(formula[[2]][[3]]),
AlphaCol = paste(formula[[2]][[4]])
)
wideData <- do.call(rbind, wideData)
} else if (in.formula(formula, "{")) {
#case 1: Compiled (BS only) template: {s;n} ~ Factors
bracedvars <- c(paste(formula[[2]][[2]]), paste(formula[[2]][[3]]))
wideData <- ctow(data, bracedvars[1], bracedvars[2] )
BSFactors <- complement(vars, bracedvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ))
DVvars <- paste(formula[[2]][[2]])
} else if (has.cbind.terms(formula)) {
#case 2: Wide (WS or MX)
# 2.1: Wide (WS) template: cbind(b1,...,bm) ~ .
# 2.2: Wide (MX) template: cbind(b1,...,bm) ~ Factors
BSFactors <- complement(vars, bvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(data[,x])) ))
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
WSDesign <- cleanedWSF[[3]]
DVvars <- bvars
wideData <- data # nothing to do, already correct format
# computes correlation with unitaryAlpha
factors <- names(data)[!(names(data) %in% bvars )]
if (length(factors) == 0) {
# adds a dummy BS factor
data[["dummyBSfactor"]] <- 1; factors <- "dummyBSfactor"
}
uAlpha <- plyr::ddply(data, factors, function(x) {unitaryAlpha(as.matrix(x[bvars]))} )$V1
} else if (has.nested.terms(formula)) {
#case 3: long (BS or WS or MX)
# 3.1: long (BS) template: b ~ BSFactors | Id
# 3.2: long (WS) template: b ~ WSConditions | Id
# 3.3: long (MX) template: b ~ BSFactors * WSConditions | Id
idvar <- getAfterNested( formula )
DVvars <- paste(formula[[2]])
# get vars that are changing for a given Id
Factors <- names(data)[ !(names(data) %in% c(idvar, DVvars))]
BSFactors <- c()
WSFactors <- c()
for (i in Factors) {
if (dim(unique(data[data[[idvar]] == 1,][c(idvar, i)]))[1] > 1) {
WSFactors <- c(WSFactors, i)
} else {
BSFactors <- c(BSFactors, i)
}
}
wideData <- ltow(data, idvar, tmp[[2]], DVvars )
# take the success name under Variable
DVvars <- names(wideData)[!(names(wideData) %in% c( all.vars(formula[[3]]), "n"))]
BSFactors <- complement(names(wideData), DVvars)
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ) )
WSFactors <- cleanedWSF[[1]]
WSLevels <- cleanedWSF[[2]]
WSDesign <- cleanedWSF[[3]]
# computes correlation with unitaryAlpha
if (!is.null(WSFactors)) {
factors <- names(wideData)[!(names(wideData) %in% wsvars )]
if (length(factors) == 0) {
# adds a dummy BS factor
wideData[["dummyBSfactor"]] <- 1; factors <- "dummyBSfactor"
}
uAlpha <- plyr::ddply(wideData, factors,
function(x) {unitaryAlpha(as.matrix(x[wsvars]))}
)$V1
wideData[["dummyBSfactor"]] <- NULL
}
} else if (length(formula[[1]]) == 1) {
#case 2.3: Wide (BS) template: b ~ Factors
wideData <- data # nothing to do, already correct format
# extract vars from rhs formula
BSFactors <- all.vars(formula[[3]])
BSLevels <- unlist(lapply(BSFactors, \(x) length(unique(wideData[,x])) ) )
WSLevels <-1
DVvars <- paste(formula[[2]])
} else {
# error...
stop("ANOPA::error(17): Unrecognized data format. Exiting...")
}
# 3.3: Keep the factor names
allFactors <- c(WSFactors, BSFactors)
# 3.4: Acknolwedge limitations of the present package
if( (length(allFactors) < 1) )
stop("ANOPA::error(18a): No factor provided. Exiting...")
if( (length(allFactors)>4) || (length(allFactors) < 1) )
stop("ANOPA::error(18b): Too many factors. Exiting...")
if( length(allFactors)==4 )
stop("ANOPA::error(18c): Four factors; contact the author. Exiting...")
##############################################################################
# STEP 4: run the analysis, depending on the number of factors
##############################################################################
# 4.0: additional checks on within...
if (prod(WSLevels) != length(DVvars))
stop("ANOPA::error(19): There are missing within-subject level columns. Exiting...")
# 4.1: to avoid integer overflow, convert integers to num
for (i in DVvars)
wideData[[i]] <- as.numeric( wideData[[i]] )
# 4.2: compile the data if was not given compiled
if (is.null(compData))
compData <- wtoc(wideData, DVvars, "n")
# 4.3: check for all sorts of missing (not there or there with zeros...)
compData <- checkmissingcellsBSFactors(compData, BSFactors, DVvars)
compData <- checkforZeros(compData, DVvars)
# 4.4: sort the data
if (length(BSFactors) > 0)
compData <- compData[ do.call(order, data.frame(compData[,BSFactors]) ), ]
# 4.4: perform the analysis based on the number of factors
analysis <- switch( length(allFactors),
anopa1way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa2way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa3way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels),
anopa4way(compData, DVvars, countCol, alphaCol, BSFactors, WSFactors, WSLevels)
)
##############################################################################
# STEP 5: return the object
##############################################################################
# 5.1: preserve everything in an object of class ANOPAobject
res <- list(
type = "ANOPAomnibus",
formula = as.formula(formula),
BSfactColumns = BSFactors,
BSfactNlevels = BSLevels,
WSfactColumns = WSFactors,
WSfactDesign = WSDesign,
WSfactNlevels = WSLevels,
DVvariables = DVvars,
AlphaVariable = alphaCol,
NVariable = countCol,
wideData = wideData, # raw data are absolutely needed for plot only
compData = compData, # compiled data are used for analyzes
omnibus = analysis # results of the omnibus analysis
)
class(res) <- c("ANOPAobject", class(res) )
return( res )
}
##############################################################################
# Subfunctions to generate long from compiled
##############################################################################
getCorrStructure <- function(mat, targetUA) {
# This function is used when the design has repeated measures
# and the data are provided as compiled. In that case,
# the exact dispositions of 1s and 0s cannot be determined and
# so random rearrangments are tested to get uAlpha as close as possible.
bestDiff = 999
ncol = dim(mat)[2]
for (seed in 1:2000) {
set.seed(seed)
for (col in 2:ncol) {
mat[,col] = sample(mat[,col])
}
currentUA = unitaryAlpha(mat)
if (abs(currentUA - targetUA) < .0001) {
# close enough!
bestmat = mat
break
}
if (abs(currentUA - targetUA) < bestDiff) {
bestDiff = abs(currentUA - targetUA)
bestmat = mat
}
}
# check that correlation are not too far from target
if (abs(targetUA-unitaryAlpha(bestmat)) > 0.25) {
ANOPAwarning("ANOPA::warning(111): Cannot reconstitute the correlation structure. Consider using raw (wide or long) data...")
}
return(bestmat)
}
getBaseStructure <- function(line, cnt) {
# expand a line of the compiled data into a matrix
mat <- data.frame( toDelete123 = 1:cnt )
for (i in names(line)) {
mat[[i]] <- c(rep(1, round(line[i]) ), rep(0, round(cnt-line[i]) ))
}
# delete sentinel column
mat$toDelete123 <- NULL
mat
}
addBSfcStructure <- function(mat, bs) {
# adds to the mat the between-subject group(s)
if (!is.null(bs)) {
for (i in names(bs) )
mat[[i]] <- rep( bs[[i]], dim(mat)[1])
}
mat
}
doONEline <- function(lineno, DF, BSfacts, WSfacts, CountCol, AlphaCol) {
oneBScd <- DF[lineno, BSfacts, drop=FALSE]
oneline <- DF[lineno, WSfacts]
onecnt <- DF[lineno, CountCol]
oneual <- DF[lineno, AlphaCol]
mat1 <- getBaseStructure(oneline, onecnt)
mat2 <- getCorrStructure(mat1, oneual )
mat3 <- addBSfcStructure(mat2, oneBScd)
mat3
}
##############################################################################
# Subfunctions for recognizing formats
##############################################################################
getAfterNested <- function(frm) {
# There are three possible cases?
# frm1 <- b ~ BSFactors * WSConditions | Id
# frm2 <- b ~ WSConditions | Id * BSFactors
# frm3 <- b ~ (WSConditions | Id) * BSFactors
f <- sub.formulas(frm, "|")[[1]]
if (length(f[[3]]) == 1) {
v1 <- f[[3]]
} else {
if (f[[3]][[1]] == "*") {
v1 <- f[[3]][[2]]
} else {
stop("ANOPA::internal(-1): Case non-existant: That should never happen")
}
}
return( paste(v1) )
}
getAroundNested <- function(frm) {
# There are three possible cases?
# frm1 <- b ~ BSFactors * WSConditions | Id
# frm2 <- b ~ WSConditions | Id * BSFactors
# frm3 <- b ~ (WSConditions | Id) * BSFactors
f <- sub.formulas(frm, "|")[[1]]
if (length(f[[3]]) == 1) {
v1 <- f[[3]]
if (length(f[[2]]) == 1) {
v2 <- f[[2]]
} else {
v2 <- f[[2]][[length(f[[2]])]]
}
} else {
if (f[[3]][[1]] == "*") {
v1 <- f[[3]][[2]]
if (length(f[[2]]) == 1) {
v2 <- f[[2]]
} else {
v2 <- f[[2]][[length(f[[2]])]]
}
} else {
stop("ANOPA::internal (-2): Case non-existant: That should never happen")
}
}
return( c( paste(v1), paste(v2)) )
}
checkforZeros <- function( cData, ss) {
# Are there emtpy cells, i.e. where the proportion is 0 on 0?
# These must be imputed to avoid Undetermined scores
# Adjust ANOPA.zeros vector for a different imputation strategy
# DISCLAIMER: I did not validate if this is a sensible strategy. Do your homework.
res <- cData
repl <- as.list(unlist(options("ANOPA.zeros"))) # niaisage...
for (i in ss) {
if (any(mapply(\(x,y){(x==0)&&(y==0)}, res[[i]], res[["n"]]) ) ) {
ANOPAwarning("ANOPA::warning(1): Some cells have zero over zero data. Imputing...")
res[ res[[i]] == 0 & res[["n"]] == 0, c(i,"n")] <- repl
}
}
return( res )
}
checkmissingcellsBSFactors <- function( cData, BSFactors, ss) {
# all the combination of the levels of the factors
a <- prod(unlist(lapply(BSFactors, \(x) length(unique(cData[,x])))))
b <- dim(cData)[1]
if (a != b) {
# there are missing cases
lvls <- lapply(BSFactors, \(x) unique(cData[,x]))
cmbn <- expand.grid(lvls)
names(cmbn) <- BSFactors
notthere <- linesA1notInA2( cmbn, cData )
for ( m in ss ) {notthere[[m]] <- 0}
notthere[["n"]] <- 0
cData <- rbind(cData, notthere)
ANOPAmessage(paste("ANOPA::fyi(1): Combination of cells missing. Adding: "))
temp <- paste0(capture.output(print(notthere, row.names=FALSE)),collapse="\n")
ANOPAmessage(temp)
}
return( cData )
}
cleanWSFactors <- function(WSFactors, ss) {
# Unpack the WS factors and run a fyi if not inhibited...
WSLevels <- c(1)
WSDesign <- data.frame()
if (!is.null(WSFactors)) {
# separate name from nLevel
for (i in 1:length(WSFactors)) {
WSLevels[i] <- as.integer(unlist(strsplit(WSFactors[i], '[()]'))[2])
WSFactors[i] <- unlist(strsplit(WSFactors[i], '[()]'))[1]
}
combinaisons <- expand.grid(lapply(WSLevels, seq))
WSDesign <- cbind(combinaisons, ss)
colnames(WSDesign)[1:length(WSFactors)] <- WSFactors
colnames(WSDesign)[length(WSFactors)+1] <- "Variable"
if ( (!is.null(WSFactors)) & ('design' %in% getOption("ANOPA.feedback") ) ) {
ANOPAmessage("ANOPA::fyi: Here is how the within-subject variables are understood:")
temp <- paste0(capture.output(print(WSDesign[,c(WSFactors, "Variable") ], row.names=FALSE)),collapse="\n")
ANOPAmessage(temp)
}
}
return( list(WSFactors, WSLevels, WSDesign ) )
}
# disjonction of two data.frames
linesA1notInA2 <- function( a1, a2 ) {
# adds dummy columns
a1$included_a1 <- TRUE
a2$included_a2 <- TRUE
res <- merge(a1, a2, all=TRUE)
res <- res[ is.na(res$included_a2), ]
# removes the dummy columns
res$included_a1 <- NULL
res$included_a2 <- NULL
return( res )
}
# harmonic mean
hmean <- function(v) (length(v)/ sum(1/v))
##############################################################################
##############################################################################
# Analyses functions per se
##############################################################################
##############################################################################
anopa1way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, unneeded ) {
# One-way ANOPA (either within- or between-subject design)
# The observations are compiled into success (s) and number (n) per group and uAlpha when relevant
if (length(wsfacts) == 1) { # within-subject design
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
facts <- wsfacts
corlt <- cData[[acol]]
} else { # between-subject design
s <- cData[[ss]]
n <- cData[[ncol]]
facts <- bsfacts
corlt <- 0
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
p <- length(As)
# compute mean square of effect P, mean square of error
msP <- var(As)
msE <- mean(Vs) * (1-corlt)
# compute F ratio or chi-square test statistic
F <- msP / msE
g <- (p-1) * F
# compute p value from the latter (the former has infinite df on denominator)
pval <- 1 - pchisq(g, df = (p-1) )
# the corrections
cf <- 1+ (p^2-1)/(6 * hmean(n) * (p-1) )
pvaladj <- 1 - pchisq(g/cf, df = (p-1) )
# keep the results
results <- data.frame(
MS = c(msP, msE),
df = c(p-1,Inf),
F = c(F, NA),
p = c(pval, NA),
correction = c(cf,NA),
Fcorr = c(g/cf/(p-1),NA),
pvalcorr = c(pvaladj, NA)
)
rownames(results) <- c(facts, "Error")
return(results)
}
anopa2way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
# Two-way ANOPA (within, between, or mixed design)
# the observations are compiled into success (s) and number (n) per group and uAlpha when relevant
#print("Begin anopa2way")
if (length(wsfacts) == 2) { # both within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- wsfacts
f1levl <- wslevls[2]
} else if (length(wsfacts) == 1) { # mixed, within-between, design
s <- unlist(cData[ss]) # i.e., flatten
n <- rep(cData[[ncol]], length(ss))
corlt <- rep(cData[[acol]], wslevls[1])
facts <- c(wsfacts, bsfacts)
f1levl <- wslevls
} else { # both between-subject factors
s <- cData[[ss]]
n <- cData[[ncol]]
corlt <- 0
facts <- bsfacts
f1levl <- length(unique(cData[[bsfacts[1]]]))
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
# fold the scores into a matrix
Af <- matrix( As, ncol = f1levl)
Vf <- matrix( Vs, ncol = f1levl)
ns <- matrix( n, ncol = f1levl)
# compute marginal means (P is "column" factor, Q is "row" factor) and grand mean
AP <- colMeans(Af) # marginal mean along Q factor
AQ <- rowMeans(Af) # marginal mean along P factor
Ag <- mean(As) # grand mean
nP <- colSums(ns) # sample size across all Q levels
nQ <- colSums(t(ns)) # sample size across all P levels
p <- length(AP)
q <- length(AQ)
# compute mean square of effects P, Q and PxQ
msP <- q * var( AP )
msQ <- p * var( AQ )
msPQ <- 1/((p-1)*(q-1)) * sum((As - outer(AQ, AP, `+`) + mean(As) )^2 )
# get mean squared of error for within and between respectively
msEintra <- 1/(p*q) * sum( (1-corlt)/(4*(ns+1/2) ) )
msEinter <- 1/(p*q) * sum( 1 / (4*(ns+1/2)) )
# assign error terms to each factor based on design
msEp <- if (facts[1] %in% wsfacts) msEintra else msEinter
msEq <- if (facts[2] %in% wsfacts) msEintra else msEinter
msEpq <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)) msEintra else msEinter
# compute F ratio or chi-square test statistic
FP <- msP/msEp
FQ <- msQ/msEq
FPQ <- msPQ/msEpq
gP <- (p-1) * FP
gQ <- (q-1) * FQ
gPQ <- (p-1) * (q-1) * FPQ
# compute p value from the latter (the former has infinite df on denominator)
pvalP <- 1 - pchisq(gP, df = (p-1) )
pvalQ <- 1 - pchisq(gQ, df = (q-1) )
pvalPQ <- 1 - pchisq(gPQ, df = (p-1) * (q-1) )
# If you want to apply the corrections
cfP <- 1 + (p^2-1)/(6 * hmean(nP) * (p-1) )
cfQ <- 1 + (q^2-1)/(6 * hmean(nQ) * (q-1) )
cfPQ <- 1 + ((p * q)^2-1)/(6 * hmean(ns) * (p-1)*(q-1) )
pvalPadj <- 1 - pchisq(gP/cfP, df = (p-1) )
pvalQadj <- 1 - pchisq(gQ/cfQ, df = (q-1) )
pvalPQadj <- 1 - pchisq(gPQ/cfPQ, df = (p-1)*(q-1) )
# keep the results
results <- data.frame(
MS = c(msP, msQ, msPQ, msEintra, msEinter ),
df = c(p-1, q-1, (p-1)*(q-1), Inf, Inf ),
F = c(FP, FQ, FPQ, NA, NA ),
pvalue = c(pvalP, pvalQ, pvalPQ, NA, NA ),
correction = c(cfP, cfQ, cfPQ, NA, NA ),
Fcorr = c(FP/cfP, gQ/cfQ/(q-1), gPQ/cfPQ/((p-1)*(q-1)), NA, NA ),
pvalcorr = c(pvalPadj, pvalQadj, pvalPQadj, NA, NA)
)
rownames(results) <- c(facts, paste(facts, collapse=":"),
"Error(within)", "Error(between)" )
if (length(bsfacts) == 0) results <- results[-5,] #remove 5th line
if (length(wsfacts) == 0) results <- results[-4,] #remove 4th line
return(results)
}
anopa3way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
# Three-way ANOPA (any design with within or between subject factors)
# the observations are compiled into success (s) and number (n) per group and uAlpha when relevant
if (length(wsfacts) == 3) { # entirely within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- wsfacts
lvlp <- 1:wslevls[1] # first is always within
lvlq <- 1:wslevls[2]
lvlr <- 1:wslevls[3]
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
} else if (length(wsfacts) == 2) { # mixed, 2 within-subject factors
s <- cData[ss]
n <- rep(cData[[ncol]], length(ss))
corlt <- cData[[acol]]
facts <- c(wsfacts, bsfacts)
lvlp <- 1:wslevls[1]
lvlq <- 1:wslevls[2]
lvlr <- unique(cData[[bsfacts[1]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
corlt <- array(unlist(lapply( corlt, rep, p*q)), dim = c(r,q,p))
} else if (length(wsfacts) == 1) { # mixed, 1 within-subject factor
s <- c(t(cData[ss])) # i.e., flatten
n <- rep(cData[[ncol]], length(ss))
corlt <- rep(cData[[acol]], wslevls[1])
facts <- c(wsfacts, bsfacts)
lvlp <- 1:wslevls[1]
lvlq <- unique(cData[[bsfacts[1]]])
lvlr <- unique(cData[[bsfacts[2]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
corlt <- array(unlist(lapply( corlt, rep, p)), dim = c(r,q,p))
} else { # entirely between-subject factors
s <- cData[[ss]]
n <- cData[[ncol]]
corlt <- 0
facts <- bsfacts
lvlp <- unique(cData[[bsfacts[1]]])
lvlq <- unique(cData[[bsfacts[2]]])
lvlr <- unique(cData[[bsfacts[3]]])
p <- length(lvlp)
q <- length(lvlq)
r <- length(lvlr)
}
# apply the transform to all the pairs (s, n)
As <- mapply(A, s, n)
Vs <- mapply(varA, s, n)
# fold the scores into an array
# for between-subject design: https://stackoverflow.com/a/52435862/5181513
namesOfDim <- list( lvlr, lvlq, lvlp )
Af <- array(As, dim = c(r, q, p), dimnames = namesOfDim)
Vf <- array(Vs, dim = c(r, q, p), dimnames = namesOfDim)
ns <- array(n, dim = c(r, q, p), dimnames = namesOfDim)
# compute marginal means (P is "column" factor, Q is "row" factor) and grand mean
AP <- apply(Af, 3, mean)
AQ <- apply(Af, 2, mean)
AR <- apply(Af, 1, mean)
APQ <- apply( Af, c(3,2), mean ) ## Les dimensions sont inversées
APR <- apply( Af, c(3,1), mean )
AQR <- apply( Af, c(2,1), mean )
nP <- apply( ns, 3, sum ) # sample size across all R levels
nQ <- apply( ns, 2, sum ) # sample size across all R levels
nR <- apply( ns, 1, sum ) # sample size across all R levels
nPQ <- apply( ns, c(3,2), sum ) # sample size across all R levels
nPR <- apply( ns, c(3,1), sum ) # sample size across all R levels
nQR <- apply( ns, c(2,1), sum ) # sample size across all R levels
# compute mean square of effects P, Q and PxQ; Keppel, 1978
msP <- q*r * var( AP )
msQ <- p*r * var( AQ )
msR <- p*q * var( AR )
msPQ <- ((p*q-1) * r * var( c(APQ) ) - (p-1)*msP - (q-1)*msQ)/((p-1)*(q-1))
msPR <- ((p*r-1) * q * var( c(APR) ) - (p-1)*msP - (r-1)*msR)/((p-1)*(r-1))
msQR <- ((q*r-1) * p * var( c(AQR) ) - (q-1)*msQ - (r-1)*msR)/((q-1)*(r-1))
msPQR <- ((p*q*r-1)*var( c(Af) ) -(p-1)*(q-1)*msPQ -(p-1)*(r-1)*msPR -(q-1)*(r-1)*msQR -(p-1)*msP -(q-1)*msQ -(r-1)*msR )/ ((p-1)*(q-1)*(r-1))
# get mean squared of error for within and between respectively
msEintra <- 1/(p*q*r)*sum( (1-corlt)/ (4*ns+1/2))
msEinter <- 1/(p*q*r)*sum( 1 / (4*ns+1/2))
# assign error terms to each factor based on design
msEp <- if (facts[1] %in% wsfacts) msEintra else msEinter
msEq <- if (facts[2] %in% wsfacts) msEintra else msEinter
msEr <- if (facts[3] %in% wsfacts) msEintra else msEinter
msEpq <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)) msEintra else msEinter
msEpr <- if ((facts[1] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
msEqr <- if ((facts[2] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
msEpqr <- if ((facts[1] %in% wsfacts)|(facts[2] %in% wsfacts)|(facts[3] %in% wsfacts)) msEintra else msEinter
# compute F ratio or chi-square test statistic
FP <- msP/msEp
FQ <- msQ/msEq
FR <- msR/msEr
FPQ <- msPQ/msEpq
FPR <- msPR/msEpr
FQR <- msQR/msEqr
FPQR <- msPQR/msEpqr
gP <- (p-1) * FP
gQ <- (q-1) * FQ
gR <- (r-1) * FR
gPQ <- (p-1) * (q-1) * FPQ
gPR <- (p-1) * (r-1) * FPR
gQR <- (q-1) * (r-1) * FQR
gPQR <- (p-1) * (q-1) * (r-1) * FPQR
# compute p value from the latter (the former has infinite df on denominator)
pvalP <- 1 - pchisq(gP, df = (p-1) )
pvalQ <- 1 - pchisq(gQ, df = (q-1) )
pvalR <- 1 - pchisq(gR, df = (r-1) )
pvalPQ <- 1 - pchisq(gPQ, df = (p-1) * (q-1) )
pvalPR <- 1 - pchisq(gPR, df = (p-1) * (r-1) )
pvalQR <- 1 - pchisq(gQR, df = (q-1) * (r-1) )
pvalPQR <- 1 - pchisq(gPQR, df = (p-1) * (q-1) * (r-1) )
# If you want to apply the corrections; we remove the imputed cells...
cfP <- 1 + (p^2-1)/(6 * hmean(nP) * (p-1) )
cfQ <- 1 + (q^2-1)/(6 * hmean(nQ) * (q-1) )
cfR <- 1 + (r^2-1)/(6 * hmean(nR) * (r-1) )
cfPQ <- 1 + ((p * q)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(q-1) )
cfPR <- 1 + ((p * r)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(r-1) )
cfQR <- 1 + ((q * r)^2-1)/(6 * hmean(ns[ns>1]) * (q-1)*(r-1) )
cfPQR <- 1 + ((p * q * r)^2-1)/(6 * hmean(ns[ns>1]) * (p-1)*(q-1)*(r-1) )
pvalPadj <- 1 - pchisq(gP/cfP, df = (p-1) )
pvalQadj <- 1 - pchisq(gQ/cfQ, df = (q-1) )
pvalRadj <- 1 - pchisq(gR/cfR, df = (r-1) )
pvalPQadj <- 1 - pchisq(gPQ/cfPQ, df = (p-1)*(q-1) )
pvalPRadj <- 1 - pchisq(gPR/cfPR, df = (p-1)*(r-1) )
pvalQRadj <- 1 - pchisq(gQR/cfQR, df = (q-1)*(r-1) )
pvalPQRadj <- 1 - pchisq(gPQR/cfPQR, df = (p-1)*(q-1)*(r-1) )
# keep the results
results <- data.frame(
MS = c(msP, msQ, msR, msPQ, msPR, msQR, msPQR, msEintra, msEinter ),
df = c(p-1, q-1, r-1, (p-1)*(q-1), (p-1)*(r-1), (q-1)*(r-1), (p-1)*(q-1)*(r-1), Inf, Inf ),
F = c(FP, FQ, FR, FPQ, FPR, FQR, FPQR, NA, NA ),
pvalue = c(pvalP, pvalQ, pvalR, pvalPQ, pvalPR, pvalQR, pvalPQR, NA, NA ),
correction = c(cfP, cfQ, cfR, cfPQ, cfPR, cfQR, cfPQR, NA, NA ),
Fcorr = c(FP/cfP, gQ/cfQ/(q-1), gR/cfR/(r-1),
gPQ/cfPQ/((p-1)*(q-1)), gPR/cfPR/((p-1)*(r-1)), gQR/cfQR/((q-1)*(r-1)),
gPQR/cfPQR/((p-1)*(q-1)*(r-1)),
NA, NA ),
pvalcorr = c(pvalPadj, pvalQadj, pvalRadj, pvalPQadj, pvalPRadj, pvalQRadj, pvalPQRadj, NA, NA)
)
rownames(results) <- c(facts,
apply(data.frame(utils::combn(facts,2)), 2, paste, collapse = ":"),
paste(facts, collapse=":"),
"Error(within)", "Error(between)" )
if (length(bsfacts) == 0) results <- results[-9,] #remove between-error line
if (length(wsfacts) == 0) results <- results[-8,] #remove within-error line
return(results)
}
anopa4way <- function( cData, ss, ncol, acol, bsfacts, wsfacts, wslevls ) {
return("Not programmed so far. Contact Denis Cousineau if needed.")
}
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