DESeq2 (version 1.12.3)

nbinomWaldTest: Wald test for the GLM coefficients


This function tests for significance of coefficients in a Negative Binomial GLM, using previously calculated sizeFactors (or normalizationFactors) and dispersion estimates. See DESeq for the GLM formula.


nbinomWaldTest(object, betaPrior, betaPriorVar, modelMatrix = NULL, modelMatrixType, maxit = 100, useOptim = TRUE, quiet = FALSE, useT = FALSE, df, useQR = TRUE)


a DESeqDataSet
whether or not to put a zero-mean normal prior on the non-intercept coefficients
a vector with length equal to the number of model terms including the intercept. betaPriorVar gives the variance of the prior on the sample betas on the log2 scale. if missing (default) this is estimated from the data
an optional matrix, typically this is set to NULL and created within the function. only can be supplied if betaPrior=FALSE
either "standard" or "expanded", which describe how the model matrix, X of the formula in DESeq, is formed. "standard" is as created by model.matrix using the design formula. "expanded" includes an indicator variable for each level of factors in addition to an intercept. betaPrior must be set to TRUE in order for expanded model matrices to be fit.
the maximum number of iterations to allow for convergence of the coefficient vector
whether to use the native optim function on rows which do not converge within maxit
whether to print messages at each step
whether to use a t-distribution as a null distribution, for significance testing of the Wald statistics. If FALSE, a standard normal null distribution is used.
the degrees of freedom for the t-distribution
whether to use the QR decomposition on the design matrix X while fitting the GLM


a DESeqDataSet with results columns accessible with the results function. The coefficients and standard errors are reported on a log2 scale.


The fitting proceeds as follows: standard maximum likelihood estimates for GLM coefficients (synonymous with "beta", "log2 fold change", "effect size") are calculated. A zero-centered Normal prior distribution is assumed for the coefficients other than the intercept. The variance of the prior distribution for each non-intercept coefficient is calculated using the observed distribution of the maximum likelihood coefficients. The final coefficients are then maximum a posteriori estimates using this prior (Tikhonov/ridge regularization). See below for details on the prior variance and the Methods section of the DESeq2 manuscript for more detail. The use of a prior has little effect on genes with high counts and helps to moderate the large spread in coefficients for genes with low counts. For calculating Wald test p-values, the coefficients are scaled by their standard errors and then compared to a standard Normal distribution.

The prior variance is calculated by matching the 0.05 upper quantile of the observed MLE coefficients to a zero-centered Normal distribution. In a change of methods since the 2014 paper, the weighted upper quantile is calculated using the wtd.quantile function from the Hmisc package. The weights are the inverse of the expected variance of log counts, so the inverse of $1/mu-bar + alpha_tr$ using the mean of normalized counts and the trended dispersion fit. The weighting ensures that noisy estimates of log fold changes from small count genes do not overly influence the calculation of the prior variance. See estimateBetaPriorVar. The final prior variance for a factor level is the average of the estimated prior variance over all contrasts of all levels of the factor. Another change since the 2014 paper: when interaction terms are present in the design, the prior on log fold changes is turned off (for more details, see the vignette section, "Methods changes since the 2014 DESeq2 paper").

When a log2 fold change prior is used (betaPrior=TRUE), then nbinomWaldTest will by default use expanded model matrices, as described in the modelMatrixType argument, unless this argument is used to override the default behavior. This ensures that log2 fold changes will be independent of the choice of reference level. In this case, the beta prior variance for each factor is calculated as the average of the mean squared maximum likelihood estimates for each level and every possible contrast. The results function without any arguments will automatically perform a contrast of the last level of the last variable in the design formula over the first level. The contrast argument of the results function can be used to generate other comparisons. The Wald test can be replaced with the nbinomLRT for an alternative test of significance.

See Also

DESeq, nbinomLRT


Run this code

dds <- makeExampleDESeqDataSet()
dds <- estimateSizeFactors(dds)
dds <- estimateDispersions(dds)
dds <- nbinomWaldTest(dds)
res <- results(dds)

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