Why are necessity theories and models simple?

Why are sufficiency theories and models complex?

Why are necessity theory/conceptual model unaffected by omitted variable bias?

Why does a necessity theory/conceptual model not need control variables?

Why are necessity theories and models simple?

Necessary conditions theories are simple (parsimonious) because even a single factor can explain the absence of the outcome if the necessary condition is absent. This contrasts sufficiency theories and models (e.g., as with structural equation models) where a many factors together predict the presence of the outcome.

Why are sufficiency theories and models complex?

One reason for the complexity of sufficiency theories and models is that for multi-causal phenomena the outcome can only be properly explained when many factors that help to produce the outcome are included. Furthermore, when population parameters are estimated with regression models, not including relevant variables (confounders) may cause “omitted variable bias” (incorrect estimation of the regression coefficients of the variables that are included in the model). This bias occurs when variables that correlate with other variables in the model and with the outcome are omitted. By adding “control” variables, the explanatory power of the model can be improved, and omitted variable bias can be reduced. As a result sufficiency models can become complex.

Why are necessity theory/conceptual model unaffected by omitted variable bias?

Necessity theory and necessity conceptual models are unaffected by omitted variable bias because the necessary condition operates in isolation from the rest of the causal structure. The NCA parameters of the necessary condition are unaffected by adding or deleting other variables from the theory/conceptual model. One reason is that NCA takes the projections of the ceiling surface in  XY planes, rather than that it estimates the multidimensional ceiling surface. NCA estimates the 'absolute necessity' rather than 'necessity dependent on other variables'.

Why does a necessity theory/conceptual model not need control variables?  

Necessity theory and necessity conceptual models do not need control variables because the NCA parameters are the same with and without having control variables in the theory/model.