Perform multiscale test of independence for multivariate vectors. See vignettes for further examples.
MultiFIT(xy, x = NULL, y = NULL, p_star = NULL, R_max = NULL,
R_star = 1, rank.transform = TRUE, ranking.approximation = FALSE,
M = 10, apply.stopping.rule = FALSE, alpha = 0.05,
test.method = "Fisher", correct = TRUE, min.tbl.tot = 25L,
min.row.tot = 10L, min.col.tot = 10L, p.adjust.methods = c("H",
"Hcorrected"), compute.all.holm = TRUE, return.all.pvs = TRUE,
verbose = FALSE)A list, whose first element corresponds to the matrix x as below, and
its second element corresponds to the matrix y as below. If xy is not
specified, x and y need to be assigned.
A matrix, number of columns = dimension of random vector, number of rows = number of observations.
A matrix, number of columns = dimension of random vector, number of rows = number of observations.
Numeric, cuboids associated with tests whose p-value is below p_star
will be halved and further tested.
A positive integer (or Inf), the maximal number of
resolutions to scan (algorithm will stop at a lower resolution if
all tables in it do not meet the criteria specified at min.tbl.tot,
min.row.tot and min.col.tot)
A positive integer, if set to an integer
between 0 and R_max, all tests up to and including resolution R_star
will be performed (algorithm will stop at a lower resolution than requested if
all tables in it do not meet the criteria specified at min.tbl.tot,
min.row.tot and min.col.tot). For higher resolutions only the children of
tests with p-value lower than p_star will be considered.
Logical, if TRUE, marginal rank transform is
performed on all margins of x and y. If FALSE, all
margins are scaled to 0-1 scale. When FALSE, the average and top
statistics of the negative logarithm of the p-values are only computed
for the univariate case.
Logical, if FALSE, select only tests with p-values
more extreme than p_star to halve and further test. FWER control not guaranteed.
If TRUE, choose at each resolution the M tests with the most extreme
p-values to further halve and test.
A positive integer (or Inf), the number of top ranking tests to continue to split at each resolution. FWER control not guaranteed for this method.
Logical. If TRUE, an adjusted p-value is computed for each resolution,
Numeric. Threshold below which resolution-specific p-values trigger early stopping.
String, choose "Fisher" for Fisher's exact test (slowest), "chi.sq" for Chi-squared test, "LR" for likelihood-ratio test and "norm.approx" for approximating the hypergeometric distribution with a normal distribution (fastest).
Logical, if TRUE compute mid-p corrected p-values for
Fisher's exact test, or Yates corrected p-values for the Chi-squared test,
or Williams corrected p-values for the likelihood-ratio test.
Non-negative integer, the minimal number of observations
per table below which a p-value for a given table will not be computed.
Non-negative integer, the minimal number of observations for row totals in the 2x2 contingency tables below which a contingency table will not be tested.
Non-negative integer, the minimal number of observations for column totals in the 2x2 contingency tables below which a contingency table will not be tested.
String, choose between "H" for Holm, "Hcorrected" for Holm with
the correction as specified in correct.
Logical, if FALSE, only global p-value is
computed (may be a little faster when any tests are performed). If TRUE
adjusted p-values are computed for all tests.
Logical, if TRUE, a data frame with all p-values
is returned (not applicable when stopping rule is applied)
Logical.
p.values.holistic, a named numerical vector containing the holistic p-values of
for the global null hypothesis (i.e. x independent of y).
p.values.resolution.specific, a named numerical vector containing the
reslution specific p-values of for the global null hypothesis (i.e. x independent of y).
res.by.res.pvs, a dta frame that contains the raw and Bonferroni adjusted
resolution specific p-values.
all.pvs, a data frame that contains all p-values and adjusted
p-values that are computed. Returned if return.all.pvs is TRUE.
all, a nested list. Each entry is named and contains data about a resolution
that was tested. Each resolution is a list in itself, with cuboids, a summary of
all tested cuboids in a resolution, tables, a summary of all 2x2
contingency tables in a resolution, pv, a numerical vector containing the
p-values from the tests of independence on 2x2 contingency table in tables
that meet the criteria defined by min.tbl.tot, min.row.tot and min.col.tot.
The length of pv is equal to the number of rows of tables. pv.correct,
similar to the above pv, corrected p-values are computed and returned when
correct is TRUE. rank.tests, logical vector that indicates
whether or not a test was ranked among the top M tests in a resolution. The
length of rank.tests is equal to the number of rows of tables. parent.cuboids,
an integer vector, indicating which cuboids in a resolution are associated with
the ranked tests, and will be further halved in the next higher resolution.
parent.tests, a logical vector of the same length as the
number of rows of tables, indicating whether or not a test was chosen as a parent
test (same tests may have multiple children).
# NOT RUN {
set.seed(1)
n = 300
Dx = Dy = 2
x = matrix(0, nrow = n, ncol = Dx)
y = matrix(0, nrow = n, ncol = Dy)
x[,1] = rnorm(n)
x[,2] = runif(n)
y[,1] = rnorm(n)
y[,2] = sin(5 * pi * x[ , 2]) + 1 / 5 * rnorm(n)
fit = MultiFIT(x = x, y = y, verbose = TRUE)
w = MultiSummary(x = x, y = y, fit = fit, alpha = 0.0001)
# }
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