  Probe-level microarray data are usually stored in matrices, where the row and
column correspond to array and probe, respectively. Scientists routinely
summarize each array by a single index as the expression level of each probe
set (gene). We examine the adequacy of a unidimensional summary for
characterizing the data matrix of each probe set. To do so, we propose a
low-rank matrix model for the probe-level intensities, and develop a useful
framework for testing the adequacy of unidimensionality against targeted
alternatives. This is an interesting statistical problem where inference has to
be made based on one data matrix whose entries are not i.i.d. We analyze the
asymptotic properties of the proposed test statistics, and use Monte Carlo
simulations to assess their small sample performance. Applications of the
proposed tests to GeneChip data show that evidence against a unidimensional
model is often indicative of practically relevant features of a probe set.
