diagnosticTest {biclust}

Testing Procedure for Bicluster Diagnostics

Description

Calculate the statistical value of the row, column and multiplicative effect based on discovered biclusters in the data. Additionally multiple sampling methods are available to compute the statistical significance through p-values.

Usage

diagnosticTest(BCresult, data, number = 1:BCresult@Number, verbose = TRUE,
  statistics = c("F", "Tukey"), sampling = TRUE, samplingtypes = NULL,
  nSim = 1000, alpha = 0.05, save_F = FALSE)

Arguments

BCresult

An object of class biclust containing the result of a biclustering algorithm

data

data matrix, which biclust function was applied to

number

Vector of bicluster numbers of which the diagnostics should be calculated. (default = all available biclusters)

verbose

Boolean value to print progression of computed statistics.

statistics

Vector select which statistics to compute. (default = c("F","Tukey"))

• "F" (Row and column F statistics of two-way ANOVA with one replicate for cell)

• "Tukey" (Tukey's test for non-additivity)

• "ModTukey" (mtukey.test)

• "Tusell" (tusell.test)

• "Mandel" (mandel.test)

• "LBI" (lbi.test)

• "JandG" (johnson.graybill.test)

sampling

Boolean value to apply sampling methods to compute statistical significance (default=TRUE). If FALSE only the "Theoretical" p-values are computed. If TRUE, both the "Theoretical" and samplingtypes p-values are computed.

samplingtypes

Vector of sampling methods for sampling=TRUE. (default=NULL=c("Permutation","SemiparPerm"))

• "Permutation"

• "SemiparPerm"

• "SemiparBoot"

• "PermutationCor"

• "SamplingCor"

• "NormSim"

See Details for more info.

nSim

Number of permutations/bootstraps.

alpha

Significance level (default=0.05)

save_F

Option to save the permuted/bootstraped statistics. This is necessary for diagnosticPlot2

Details

Due to the uncertainty of discovering the true bicluster(s) in the data, it's often advisable to not rely on the theoretical p-values but instead retrieve the p-values through a sampling procedure.

Available p-values/sampling types for each statistical method:

• "F": "Theoretical" and "Permutation" for both row and column effect.

• "Tukey": "Theoretical", "SemiparPerm" and "SemiparBoot".

• "ModTukey": "Theoretical", "SemiparPerm", "SemiparBoot", "PermutationCor" and "SamplingCor".

• "Tusell": "SemiparPerm", "SemiparBoot" and "NormSim".

• "Mandel": "Theoretical", "SemiparPerm" and "SemiparBoot".

• "LBI": "SemiparPerm", "SemiparBoot" and "NormSim".

• "JandG": "SemiparPerm", "SemiparBoot" and "NormSim".

More info on the sampling types can be found in the secion below. If available, the "Theoretical" will always be computed. By default when sampling=TRUE, a sampling method without replacement is chosen, namely "Permutation" and "SemiparPerm".

When save_F=TRUE, the null distributions of the statistics can be visualised with diagnosticPlot2.

Disclaimer: While their functionality did not change, some functions of the additivityTests package were altered in order to be able to return the permuted/bootstrapped statistics and p-values.

Value

Returns a list with length(number) elements. Each element corresponds with the requested biclusters and is a list containing:

• table: a data frame where each row is statistics and samplingtypes (including Theoretical) combination. The data frame contains the Method, Type (p-value type), StatVal (statistical value), CritVal (critical value), pVal and Sign (0/1 significance indicator based on alpha).

• save_F: if save_F=TRUE, a (nSim x number of permuted/bootstrapped p-values) matrix contained the sampled statistics.

Sampling Types

For each sampling type a permuted/bootstrapped BC is created as following:

• "Permutation": Sample a BC from the entire dataset with replacement.

• "SemiparPerm": A semi-parametric permutation procedure. Two-way ANOVA is applied on the original BC and the residual matrix extracted. A new residual matrix is created by sampling without replacement from the original residual matrix. The sampled BC is then generated by adding this sampled residual matrix on top the mean, row and column effect of the ANOVA procedure of the original BC.

• "SemiparBoot": A semi-parametric bootstrapping procedure. Two-way ANOVA is applied on the original BC and the residual matrix extracted. A new residual matrix is created by sampling with replacement from the original residual matrix. The sampled BC is then generated by adding this sampled residual matrix on top the mean, row and column effect of the ANOVA procedure of the original BC.

• "PermutationCor": See correction=1 parameter of mtukey.test. More info in Simecek and Simeckova (2012).

• "SamplingCor": See correction=2 parameter of mtukey.test. More info in Simecek and Simeckova (2012).

• "NormSim": Sample a BC from a standard normal distribution. This sampling procedure is used for some methods in the additivityTests package.

Author(s)

Ewoud De Troyer

References

Tukey, J.W.: One Degree of Freedom for Non-additivity, Biometrics 5, pp. 232-242, 1949.

Simecek, Petr, and Simeckova, Marie. "Modification of Tukey's additivity test." Journal of Statistical Planning and Inference, 2012.

Examples

## Not run: 
#Random matrix with embedded bicluster (with multiplicative effect)
test <- matrix(rnorm(5000),100,50)
roweff <- sample(1:5,10,replace=TRUE)
coleff <- sample(1:5,10,replace=TRUE)
test[11:20,11:20] <- test[11:20,11:20] +
  matrix(coleff,nrow=10,ncol=10,byrow=TRUE) +
  matrix(roweff,nrow=10,ncol=10) +
  roweff %*% t(coleff)


#Apply Plaid Biclustering
res <- biclust(test, method=BCPlaid())

#Apply default diagnosticTest
out <- diagnosticTest(BCresult=res, data=test, save_F=TRUE, number=1,
                      statistics=c("F","Tukey","ModTukey","Tusell","Mandel","LBI","JandG"),
                      samplingtypes=c("Permutation","SemiparPerm","SemiparBoot",
                      "PermutationCor","SamplingCor","NormSim"))

out[[1]]$table

## End(Not run)