  We construct a simple multicomponent lattice gas model in one dimension in
which each site can either be empty or occupied by at most one particle of any
one of $D$ species. Particles interact with a nearest neighbor interaction
which depends on the species involved. This model is capable of reproducing the
relations between factorial moments observed in high--energy scattering
experiments for moderate values of $D$. The factorial moments of the negative
binomial distribution can be obtained exactly in the limit as $D$ becomes
large, and two suitable prescriptions involving randomly drawn nearest neighbor
interactions are given. These results indicate the need for considerable care
in any attempt to extract information regarding possible critical phenomena
from empirical factorial moments.
