BNSP (version 2.2.3)

sinusoid: Sinusoid terms in mvrm formulae

Description

Function used to define sinusoidal curves in the mean formula of function mvrm. The function is used internally to construct design matrices.

Usage

sinusoid(..., harmonics = 1, amplitude = 1, period = 0, periodRange = NULL, 
breaks = NULL, knots = NULL)

Value

Specifies the design matrices of an mvrm call

Arguments

...

a single covariate that the sinusoid term is a function of.

harmonics

an integer value that denotes the number of sins and cosines to be utilized in the representation of a sinusoidal curve.

amplitude

a positive integer. If set equal to one, it denotes a fixed amplitude. Otherwise, if set to an integer that is greater than one, it denotes the number of knots to be utilized in the representation of the time-varying amplitude.

period

the period of the sinusoidal wave. Values less than or equal to zero signify that the period is unknown. Positive values signify that the period is known and fixed.

periodRange

a vector of length two with the range of possible period values. It is required when the period is unknown.

breaks

the growth break points.

knots

the knots to be utilized in the representation of the time-varying amplitude. Relevant only when amplitude is greater than 1.

Author

Georgios Papageorgiou

Details

Use this function within calls to function mvrm to specify sinusoidal waves in the mean function of a regression model.

Consider the sinusoidal curve $$ y_t = \beta_0 + A(t) \sin(2\pi t/\omega+\varphi) + \epsilon_t,$$ where \(y_t\) is the response at time \(t\), \(\beta_0\) is an intercept term, \(A(t)\) is a time-varying amplitude, \(\varphi \in [0,2\pi]\) is the phase shift parameter, \(\omega\) is the period taken to be known, and \(\epsilon_t\) is the error term.

The period \(\omega\) is defined by the argument period.

The time-varying amplitude is represented using \(A(t) = \sum_{j=1}^{K} \beta_{Aj} \phi_{Aj}(t)\), where \(K\), the number of knots, is defined by argument amplitude. If amplitude = 1, then the amplitude is taken to be fixed: \(A(t)=A\).

Further, \(\sin(2\pi t/\omega+\varphi)\) is represented utilizing \(\sin(2\pi t/\omega+\varphi) = \sum_{k=1}^{L} a_k \sin(2k\pi t/\omega) + b_k \cos(2k\pi t/\omega)\), where \(L\), the number of harmonics, is defined by argument harmonics.

See Also

mvrm

Examples

# Simulate and fit a sinusoidal curve
# First load releveant packages
require(BNSP)
require(ggplot2)
require(gridExtra)
require(Formula)
# Simulate the data 
mu <- function(u) {cos(0.5 * u) * sin(2 * pi * u + 1)}
set.seed(1)
n <- 100
u <- sort(runif(n, min = 0, max = 2*pi))
y <- rnorm(n, mu(u), 0.1)
data <- data.frame(y, u)
# Define the model and call function \code{mvrm} that perfomes posterior sampling for the given 
# dataset and defined model 
model <- y ~ sinusoid(u, harmonics = 2, amplitude = 20, period = 1)
if (FALSE) {
m1 <- mvrm(formula = model, data = data, sweeps = 10000, burn = 5000, thin = 2, seed = 1, 
           StorageDir = getwd())
# Plot
x1 <- seq(min(u), max(u), length.out = 100)
plotOptionsM <- list(geom_line(aes_string(x = x1, y = mu(x1)), col = 2, alpha = 0.5, lty = 2),
                     geom_point(data = data, aes(x = u, y = y)))
plot(x = m1, term = 1, plotOptions = plotOptionsM, intercept = TRUE, 
     quantiles = c(0.005, 0.995), grid = 100, combine = 1)
}