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Details of formula specifications in mvgam

Details

mvgam will accept an observation model formula and an optional process model formula (via the argument trend_formula). Neither of these formulae can be specified as lists, contrary to the accepted behaviour in some mgcv or brms models.

Note that it is possible to supply an empty formula where there are no predictors or intercepts in the observation model (i.e. y ~ 0 or y ~ -1). In this case, an intercept-only observation model will be set up but the intercept coefficient will be fixed at zero. This can be handy if you wish to fit pure State-Space models where the variation in the dynamic trend controls the average expectation, and/or where intercepts are non-identifiable.

The formulae supplied to mvgam are exactly like those supplied to glm except that smooth terms, s, te, ti and t2, time-varying effects using dynamic, monotonically increasing (using s(x, bs = 'moi')) or decreasing splines (using s(x, bs = 'mod'); see smooth.construct.moi.smooth.spec for details), as well as Gaussian Process functions using gp, can be added to the right hand side (and . is not supported in mvgam formulae).

Further details on specifying different kinds of smooth functions, and how to control their behaviours by modifying their potential complexities and / or how the penalties behave, can be found in the extensive documentation for the mgcv package.

Author

Nicholas J Clark