Is GAMLSS a good choice to quantify association of paternal and maternal vitamin levels (continuous variables, biologically correlated) on the risk of offspring autism(binary vaiable)? It this better than using GAM model or GAM model in testing nonlinear association and interactions?
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For a binary response variable, gam and gamlss are essentially the same. I would recommend gam for a binary response variable (the mgcv package is specifically designed for generalized additive models).