surveillance: addSeason2formula – R documentation

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addSeason2formula

Function that adds a sine-/cosine formula to an existing formula.

Description

This function helps to construct a formula object that can be used in a call to hhh4 to model seasonal variation via a sum of sine and cosine terms.

Usage

addSeason2formula(f = ~1, S = 1, period = 52, timevar = "t")

Arguments

`f`	formula that the seasonal terms should be added to, defaults to an intercept `~1`.
`S`	number of sine and cosine terms. If `S` is a vector, unit-specific seasonal terms are created.
`period`	period of the season, defaults to 52 for weekly data.
`timevar`	the time variable in the model. Defaults to `"t"`.

Details

The function adds the seasonal terms

sum_s gamma_s * sin(2*pi*s/period * t) + delta_s * cos(2*pi*s/period * t),

where gamma_s and delta_s are the unknown parameters and t, t = 1, 2, … denotes the time variable timevar, to an existing formula f.

Note that the seasonal terms can also be expressed as

γ_s sin(2*pi*s/period * t) + δ_s cos2*pi*s/period * t) = A_s sin(2*pi*s/period * t + ε_s)

with amplitude A_s=sqrt{γ_s^2 +δ_s^2} and phase shift \tan(ε_s) = δ_s / γ_s. The amplitude and phase shift can be obtained from a fitted hhh4 model via coef(..., amplitudeShift = TRUE), see coef.hhh4.

Value

Returns a formula with the seasonal terms added and its environment set to .GlobalEnv. Note that to use the resulting formula in hhh4, a time variable named as specified by the argument timevar must be available.

Author(s)

M. Paul, with contributions by S. Meyer

Examples

# add 2 sine/cosine terms to a model with intercept and linear trend
addSeason2formula(f = ~ 1 + t, S = 2)

# the same for monthly data
addSeason2formula(f = ~ 1 + t, S = 2, period = 12)

# different number of seasons for a bivariate time series
addSeason2formula(f = ~ 1, S = c(3, 1), period = 52)

surveillance

Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

v1.19.1

GPL-2

Authors

Michael H<f6>hle [aut, ths] (<https://orcid.org/0000-0002-0423-6702>), Sebastian Meyer [aut, cre] (<https://orcid.org/0000-0002-1791-9449>), Michaela Paul [aut], Leonhard Held [ctb, ths], Howard Burkom [ctb], Thais Correa [ctb], Mathias Hofmann [ctb], Christian Lang [ctb], Juliane Manitz [ctb], Andrea Riebler [ctb], Daniel Saban<e9>s Bov<e9> [ctb], Ma<eb>lle Salmon [ctb], Dirk Schumacher [ctb], Stefan Steiner [ctb], Mikko Virtanen [ctb], Wei Wei [ctb], Valentin Wimmer [ctb], R Core Team [ctb] (A few code segments are modified versions of code from base R)

Initial release

2021-03-30