# Specify Formulae in a Random Effects HHH Model

`hhh4_formula.Rd`

The special functions `fe`

and `ri`

are used to specify
unit-specific effects of covariates and random intercept terms,
respectively, in the component formulae of `hhh4`

.

## Arguments

- x
an expression like

`sin(2*pi*t/52)`

involving the time variable`t`

, or just`1`

for an intercept. In general this covariate expression might use any variables contained in the`control$data`

argument of the parent`hhh4`

call.- unitSpecific
logical indicating if the effect of

`x`

should be unit-specific. This is a convenient shortcut for`which = rep(TRUE, nUnits)`

, where`nUnits`

is the number of units (i.e., columns of the`"sts"`

object).- which
vector of logicals indicating which unit(s) should get an unit-specific parameter. For units with a

`FALSE`

value, the effect term for`x`

will be zero in the log-linear predictor. Note especially that setting a`FALSE`

value for the intercept term of a unit, e.g.,`ar = list(f = ~-1 + fe(1, which=c(TRUE, FALSE)))`

in a bivariate`hhh4`

model, does*not*mean that the (autoregressive) model component is omitted for this unit, but that \(\log(\lambda_1) = \alpha_1\) and \(\log(\lambda_2) = 0\), which is usually not of interest. ATM, omitting an autoregressive effect for a specific unit is not possible.

If`which=NULL`

, the parameter is assumed to be the same for all units.- initial
initial values (on internal scale!) for the fixed effects used for optimization. The default (

`NULL`

) means to use zeroes.- type
random intercepts either follow an IID or a CAR model.

- corr
whether random effects in different components (such as

`ar`

and`end`

) should be correlated or not.- initial.fe
initial value for the random intercept mean.

- initial.var
initial values (on internal scale!) for the variance components used for optimization.

- initial.re
initial values (on internal scale!) for the random effects used for optimization. The default

`NULL`

are random numbers from a normal distribution with zero mean and variance 0.001.

## See also

`hhh4`

model specifications in `vignette("hhh4")`

,
`vignette("hhh4_spacetime")`

or on the help page of
`hhh4`

.