  The scale-dependent galaxy bias generated by primordial non-Gaussianity (PNG)
can be used to detect and constrain deviations from standard single-field
inflation. The strongest signal is expected in the local model for PNG, where
the amplitude of non-Gaussianity can be expressed by a set of parameters (fnl,
gnl, ...). Current observational constraints from galaxy clustering on fnl and
gnl assume that the others PNG parameters are vanishing. Using two sets of
cosmological N-body simulations where both fnl and gnl are non-zero, we show
that this strong assumption generally leads to biased estimates and spurious
redshift dependencies of the parameters. Additionally, if the signs of fnl and
gnl are opposite, the amplitude of the scale-dependent bias is reduced,
possibly leading to a false null detection. Finally we show that model
selection techniques like the Bayesian evidence can (and should) be used to
determine if more than one PNG parameter is required by the data.
