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In practice there is little match of empirical parameters in modern models (level 3 was the last one).
The best bet is to edit the model name in the transistor symbol and provide the model in the .lib later inluded in the spice command file. Hopefully the vendor can provide this model file. For a simple empirical model some basic parameters can be extracted. I believe Baker’s book has some pointers on doing this. Vt can be defined as the Vgs where you get 1uA of current, or 0.1uA, as you prefer, under the particular conditions of Vdd, Temp, etc. gm is roughly the derivative of the id curves when the transistor is operating in saturation, as Vgs is changed. Lambda can be derived from the x-axis intercept (as the Early voltage for a bjt). Gamma is a bit more difficult to derive, but it’s effect is inverse quadratic anyway.