What are practically useful ways of modelling the effect of liquidity on options?
In general liquidity is most often modeled, for most types of instruments, via proxy by the 'bid-ask spread' (wider = less liquid, narrower = more liquid)
You can choose to model the bid-ask spread in dollars, or what is often most helpful, for options, is to model the bid-ask spread in terms of implied volatility (of the difference between the bid and ask prices). This lets you make consistent cross-sectional comparisons of liquidity, and do hypothesis testing.
here's a sample paper that uses the implied vol appraoch: http://www.ccfr.org.cn/cicf2010/papers/20091215131015.pdf