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.

## See also

`mvgam`

,
`formula.gam`

,
`gam.models`

,
`jagam`

,
`gam`

,
`s`

,
`formula`