  We calculate the shape correlations between trispectra in various equilateral
non-Gaussian models, including DBI inflation, ghost inflation and Lifshitz
scalars, using the full trispectrum as well as the reduced trispectum. We find
that most theoretical models are distinguishable from the shapes of primordial
trispectra except for several exceptions where it is difficult to discriminate
between the models, such as single field DBI inflation and a Lifshitz scalar
model. We introduce an estimator for the amplitude of the trispectrum, $g_{\rm
NL} ^{equil}$ and relate it to model parameters in various models. Using
constraints on $g_{\rm NL} ^{equil}$ from WMAP5, we give constraints on the
model parameters.
