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Sequential analysis for Informed Bayesian Multinomial and Multi-Binomial Tests #176

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Feb 1, 2024
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Sequential analysis for Informed Bayesian Multinomial and Multi-Binomial Tests #176

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8a45a99
qml changes
FBartos May 14, 2023
bc9339d
update InformedMultinomialTestBayesian
FBartos May 15, 2023
9286207
update InformedMultinomialTestBayesian
FBartos May 25, 2023
7f637a1
fix bfComparison selection
FBartos May 31, 2023
9447a5a
fix sequential plot updating
FBartos May 31, 2023
7175993
better crash check?
FBartos May 31, 2023
c0dfbcd
Merge remote-tracking branch 'upstream/master' into mult-sequential
FBartos Nov 17, 2023
adc0851
add sequential analysis to multibinomial test
FBartos Nov 20, 2023
442db8e
Apply suggestions from code review
FBartos Feb 1, 2024
c6a470f
add attributes and rowSums
FBartos Feb 1, 2024
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311 changes: 302 additions & 9 deletions R/informedbinomialtestbayesian.R
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Original file line number Diff line number Diff line change
Expand Up @@ -19,6 +19,9 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,

dataset <- .informedBinReadData(dataset, options)
.informedBinCheckErrors(dataset, options)
options <- .informedBayesParsePriorModelProbability(options)
dataset <- .binomialAggregateData(dataset, options)

.computeInformedBinResults(jaspResults, dataset, options)
.createInformedBayesMainTable(jaspResults, options, type = "binomial")

Expand All @@ -31,6 +34,9 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,
if (options[["posteriorPlot"]])
.createInformedBinBayesPosteriorPlot(jaspResults, dataset, options)

if (options[["sequentialAnalysisPlot"]])
.createInformedBinSequentialAnalysisPlot(jaspResults, dataset, options)

return()
}

Expand Down Expand Up @@ -79,9 +85,38 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,

return(dataset)
}
.binomialAggregateData <- function(dataset, options) {

if (length(dataset[[options[["factor"]]]]) != length(levels(dataset[[options[["factor"]]]])) && options[["successes"]] != "") {

if (options[["sampleSize"]] != "")
.quitAnalysis("No `Sample Size` should be provided in case the individual successes for a given factor level are specified.")

individualDataFactor <- dataset[[options[["factor"]]]]
individualDataSuccesses <- dataset[[options[["successes"]]]]

if (length(unique(individualDataSuccesses)) != 2)
.quitAnalysis(gettext("The `Success` must have two levels if the `Sample Size` is not specified."))

frequencies <- table(individualDataFactor, individualDataSuccesses)
sampleSize <- rowSums(frequencies)
dataset <- data.frame(factor(rownames(frequencies), levels = levels(dataset[[options[["factor"]]]])))
colnames(dataset) <- options[["factor"]]

attr(dataset, "individual") <- TRUE
attr(dataset, "successes") <- frequencies[,2]
attr(dataset, "sampleSize") <- sampleSize
attr(dataset, "individualDataFactor") <- individualDataFactor
attr(dataset, "individualDataSuccesses") <- individualDataSuccesses
} else {
attr(dataset, "individual") <- FALSE
}

return(dataset)
}
.informedBinCheckErrors <- function(dataset, options) {

if (options[["factor"]] == "" || options[["successes"]] == "" || options[["sampleSize"]] == "")
if (options[["factor"]] == "" || options[["successes"]] == "" || (options[["sampleSize"]] == "" && is.null(attr(dataset, "sampleSize"))))
return()

customChecks <- list(
Expand Down Expand Up @@ -121,7 +156,7 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,
return()

# skip if the input is not specified
if (options[["factor"]] == "" || options[["successes"]] == "" || options[["sampleSize"]] == "")
if (options[["factor"]] == "" || options[["successes"]] == "" || (options[["sampleSize"]] == "" && is.null(attr(dataset, "sampleSize"))))
return()

models <- createJaspState()
Expand All @@ -137,8 +172,8 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,
# fit an overall unrestricted model (for plotting the posterior)
modelsList[[1]] <- list(
"model" = try(multibridge::binom_bf_informed(
x = dataset[[options[["successes"]]]],
n = dataset[[options[["sampleSize"]]]],
x = .informedExtractSuccesses(dataset, options),
n = .informedExtractSampleSize(dataset, options),
Hr = paste0(levels(dataset[[options[["factor"]]]]), collapse = ","),
a = options[["priorCounts"]][[1]][["values"]],
b = options[["priorCounts"]][[2]][["values"]],
Expand Down Expand Up @@ -166,8 +201,8 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,

modelsList[[i+1]] <- list(
"model" = try(multibridge::binom_bf_informed(
x = dataset[[options[["successes"]]]],
n = dataset[[options[["sampleSize"]]]],
x = .informedExtractSuccesses(dataset, options),
n = .informedExtractSampleSize(dataset, options),
Hr = options[["models"]][[i]][["syntax"]],
a = options[["priorCounts"]][[1]][["values"]],
b = options[["priorCounts"]][[2]][["values"]],
Expand All @@ -189,6 +224,139 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,

return()
}
.computeInformedBinSequentialResults <- function(jaspResults, dataset, options) {

# skip if there is nothing new
if (!is.null(jaspResults[["sequentialAnalysisResults"]]))
return()

# skip if the input is not specified
# skip if the input is not specified
if (options[["factor"]] == "" || options[["successes"]] == "" || (options[["sampleSize"]] == "" && is.null(attr(dataset, "sampleSize"))))
return()

# skip if the data are only aggregated
if (!attr(dataset, "individual"))
return()

sequential <- createJaspState()
sequential$dependOn(c(.informedMultDependency, "sequentialAnalysisNumberOfSteps"))
jaspResults[["sequentialAnalysisResults"]] <- sequential

# extract data
individualDataFactor <- attr(dataset, "individualDataFactor")
individualDataSuccesses <- attr(dataset, "individualDataSuccesses")

# specify sequential steps (do all if 0)
if(options[["sequentialAnalysisNumberOfSteps"]] == 0)
steps <- 1:length(individualDataFactor)
else
steps <- unique(round(c(seq.int(0, length(individualDataFactor), length.out = options[["sequentialAnalysisNumberOfSteps"]]), length(individualDataFactor))))[-1]

startProgressbar(length(steps), label = gettext("Performing sequential analysis."))

out <- list()
for (step in steps){

tempOutput <- list()

### prepare data
frequencies <- table(individualDataFactor[1:step], individualDataSuccesses[1:step])
sampleSize <- rowSums(frequencies)
seqDataset <- data.frame(factor(rownames(frequencies), levels = levels(dataset[[options[["factor"]]]])), frequencies[,2], sampleSize)
colnames(seqDataset) <- c(options[["factor"]], "successes", "sampleSize")


### fit models & extract margliks
# fit an overall unrestricted model (for plotting the posterior)
model0 <- try(multibridge::binom_bf_informed(
x = seqDataset[["successes"]],
n = seqDataset[["sampleSize"]],
Hr = paste0(levels(dataset[[options[["factor"]]]]), collapse = ","),
a = options[["priorCounts"]][[1]][["values"]],
b = options[["priorCounts"]][[2]][["values"]],
factor_levels = seqDataset[[options[["factor"]]]],
bf_type = "BF0r",
nburnin = options[["mcmcBurnin"]],
niter = options[["mcmcBurnin"]] + options[["mcmcSamples"]],
maxiter = options[["bridgeSamples"]],
seed = if (options[["setSeed"]]) .getSeedJASP(options) else sample.int(.Machine$integer.max, 1),
))

# extract margliks
if (jaspBase::isTryError(model0)) {
tempOutput[[1]] <- data.frame(
model = "Null",
marglik = NA
)
tempOutput[[2]] <- data.frame(
model = "Encompassing",
marglik = NA
)
} else {
tempOutput[[1]] <- data.frame(
model = "Null",
marglik = model0$logml[["logmlH0"]]
)
tempOutput[[2]] <- data.frame(
model = "Encompassing",
marglik = model0$logml[["logmlHe"]]
)
}


# estimate the restricted models & extract margliks
for(i in seq_along(options[["models"]])) {

if (nchar(options[["models"]][[i]][["syntax"]]) == 0) {

next

} else {

model1 <- try(multibridge::binom_bf_informed(
x = seqDataset[["successes"]],
n = seqDataset[["sampleSize"]],
Hr = options[["models"]][[i]][["syntax"]],
a = options[["priorCounts"]][[1]][["values"]],
b = options[["priorCounts"]][[2]][["values"]],
factor_levels = seqDataset[[options[["factor"]]]],
bf_type = "BF0r",
nburnin = options[["mcmcBurnin"]],
niter = options[["mcmcBurnin"]] + options[["mcmcSamples"]],
maxiter = options[["bridgeSamples"]],
seed = if (options[["setSeed"]]) .getSeedJASP(options) else sample.int(.Machine$integer.max, 1),
))

# extract margliks
if (jaspBase::isTryError(model1)) {
tempOutput[[i+2]] <- data.frame(
model = options[["models"]][[i]][["modelName"]],
marglik = NA
)
} else {
tempOutput[[i+2]] <- data.frame(
model = options[["models"]][[i]][["modelName"]],
marglik = model1$logml[["logmlHr"]]
)
}
}
}

### store sequential summary
tempOutput <- do.call(rbind, tempOutput)
tempOutput$step <- step
out[[step]] <- tempOutput

progressbarTick()
}

out <- do.call(rbind, out)
sequential$object <- out

return()

}
.createInformedBinBayesDescriptivesTable <- function(jaspResults, dataset, options) {

if (!is.null(jaspResults[["descriptivesTable"]]))
Expand Down Expand Up @@ -260,18 +428,128 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,
if (is.null(jaspResults[["models"]]) || jaspBase::isTryError(jaspResults[["models"]]$object[[1]]$model))
return()

successes <- .informedExtractSuccesses(dataset, options)
sampleSize <- .informedExtractSampleSize(dataset, options)
priorAlpha <- options[["priorCounts"]][[1]][["values"]]
priorBeta <- options[["priorCounts"]][[2]][["values"]]

# extract posterior summary from the unrestricted model and format it for the plotting function
tempSummary <- data.frame(
fact = levels(dataset[[options[["factor"]]]]),
observed = (options[["priorCounts"]][[1]][["values"]] + dataset[[options[["successes"]]]]) / (options[["priorCounts"]][[1]][["values"]] + dataset[[options[["successes"]]]] + options[["priorCounts"]][[2]][["values"]] + (dataset[[options[["sampleSize"]]]]-dataset[[options[["successes"]]]])),
lowerCI = stats::qbeta(p = (1-options[["posteriorPlotCiCoverage"]])/2, shape1 = options[["priorCounts"]][[1]][["values"]] + dataset[[options[["successes"]]]], shape2 = options[["priorCounts"]][[2]][["values"]] + (dataset[[options[["sampleSize"]]]]-dataset[[options[["successes"]]]])),
upperCI = stats::qbeta(p = 1-(1-options[["posteriorPlotCiCoverage"]])/2, shape1 = options[["priorCounts"]][[1]][["values"]] + dataset[[options[["successes"]]]], shape2 = options[["priorCounts"]][[2]][["values"]] + (dataset[[options[["sampleSize"]]]]-dataset[[options[["successes"]]]]))
observed = (priorAlpha + successes) / (priorAlpha + successes + priorBeta + (sampleSize-successes)),
lowerCI = stats::qbeta(p = (1-options[["posteriorPlotCiCoverage"]])/2, shape1 = priorAlpha + successes, shape2 = priorBeta + (sampleSize-successes)),
upperCI = stats::qbeta(p = 1-(1-options[["posteriorPlotCiCoverage"]])/2, shape1 = priorAlpha + successes, shape2 = priorBeta + (sampleSize-successes))
)

posteriorPlot$plotObject <- .createInformedBinBayesPlot(tempSummary, options, descriptives = FALSE)

return()
}
.createInformedBinSequentialAnalysisPlot <- function(jaspResults, dataset, options) {

if (!is.null(jaspResults[["sequentialAnalysisPlot"]]))
return()


# create/obtain sequential analysis
.computeInformedBinSequentialResults(jaspResults, dataset, options)
sequentialAnalysisResults <- jaspResults[["sequentialAnalysisResults"]]$object

# create an empty plot in case the selection is restricted
if (is.null(jaspResults[["models"]]$object) || .informedBayesNumberOfModels(jaspResults, options) < 2) {
tempPlot <- createJaspPlot(title = gettext("Sequential analysis"), width = 480, height = 320)
tempPlot$dependOn(c(.informedMultDependency, "includeNullModel", "includeEncompassingModel"))
tempPlot$position <- 5
jaspResults[["sequentialAnalysisPlot"]] <- tempPlot
tempPlot$setError(gettext("At least two models need to be specified."))
return()
}

# remove unused hypotheses
if (!options[["includeNullModel"]])
sequentialAnalysisResults <- sequentialAnalysisResults[sequentialAnalysisResults$model != "Null",]
if (!options[["includeEncompassingModel"]])
sequentialAnalysisResults <- sequentialAnalysisResults[sequentialAnalysisResults$model != "Encompassing",]

if (options[["sequentialAnalysisPlotType"]] == "bayesFactor") {

# create plot container
sequentialAnalysisPlot <- createJaspContainer(gettext("Sequential analysis"))
sequentialAnalysisPlot$dependOn(c(.informedBinDependency, "bayesFactorType", "bfComparison", "bfVsHypothesis",
"sequentialAnalysisPlot", "sequentialAnalysisPlotType", "sequentialAnalysisNumberOfSteps",
"includeNullModel", "includeEncompassingModel"))
sequentialAnalysisPlot$position <- 5
jaspResults[["sequentialAnalysisPlot"]] <- sequentialAnalysisPlot

# extract BF type and Bayes factor comparison
bfTypeIgnoreLog <- if (options[["bayesFactorType"]] == "BF01") "BF01" else "BF10"
bfComparison <- .selectAvailableBfComparison(options, unique(sequentialAnalysisResults$model))

for (hypothesis in unique(sequentialAnalysisResults$model)) {

if (hypothesis == bfComparison)
next

# create sequential figures for individual hypotheses
tempPlot <- createJaspPlot(title = gettext(paste0(hypothesis, " vs. ", bfComparison)), width = 480, height = 320)
sequentialAnalysisPlot[[hypothesis]] <- tempPlot

tempData <- data.frame(
x = c(0, sequentialAnalysisResults$step[sequentialAnalysisResults$model == bfComparison]),
y = c(0, sequentialAnalysisResults$marglik[sequentialAnalysisResults$model == hypothesis] -
sequentialAnalysisResults$marglik[sequentialAnalysisResults$model == bfComparison])
)
if (bfTypeIgnoreLog == "BF01")
tempData$y <- - tempData$y

tempPlot$plotObject <- jaspGraphs::PlotRobustnessSequential(
dfLines = tempData,
xName = "n",
BF = exp(tempData$y[nrow(tempData)]),
bfType = bfTypeIgnoreLog,
hypothesis = "equal")
}

return()

} else if(options[["sequentialAnalysisPlotType"]] == "posteriorProbability") {

# compute posterior probabilities
priorProb <- options[["priorModelProbability"]][[1]][["valuesParsed"]][options[["priorModelProbability"]][[1]][["levels"]] %in% unique(sequentialAnalysisResults$model)]
priorProb <- priorProb / sum(priorProb)
postProb <- do.call(rbind, lapply(unique(sequentialAnalysisResults$step), function(step) {

logLik <- sequentialAnalysisResults$marglik[sequentialAnalysisResults$step == step]
postProb <- bridgesampling::post_prob(logLik, prior_prob = priorProb)

return(data.frame(
model = sequentialAnalysisResults$model[sequentialAnalysisResults$step == step],
step = step,
postProb = postProb
))
}))
postProb <- rbind(
data.frame(
model = unique(sequentialAnalysisResults$model),
step = 0,
postProb = priorProb
),
postProb
)

# create plot
tempPlot <- createJaspPlot(title = gettext("Sequential analysis"), width = 480, height = 320)
tempPlot$dependOn(c(.informedMultDependency, "bayesFactorType", "bfComparison", "bfVsHypothesis",
"sequentialAnalysisPlot", "sequentialAnalysisPlotType", "priorModelProbability", "sequentialAnalysisNumberOfSteps",
"includeNullModel", "includeEncompassingModel"))
tempPlot$position <- 5
jaspResults[["sequentialAnalysisPlot"]] <- tempPlot
tempPlot$plotObject <- .createInformedMultPlotSequentialProb(postProb)


return()
}
}
.createInformedBinBayesDescriptivesData <- function(jaspResults, options) {

model <- jaspResults[["models"]]$object[[1]]$model
Expand Down Expand Up @@ -364,3 +642,18 @@ InformedBinomialTestBayesianInternal <- function(jaspResults, dataset, options,

return(ciDf)
}
.informedExtractColumn <- function(dataset, options, column) {
if (attr(dataset, "individual"))
return(attr(dataset, column))
else
return(dataset[[options[[column]]]])
}
.informedExtractSampleSize <- function(dataset, options) {
.informedExtractColumn(dataset, options, "sampleSize")
}
.informedExtractSuccesses <- function(dataset, options) {
.informedExtractColumn(dataset, options, "successes")
}
.informedExtractCount <- function(dataset, options) {
.informedExtractColumn(dataset, options, "count")
}
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