cycleRtools (version 1.0.0)

Pt_model: Power-time modelling.

Description

Model the Power-time (Pt) relationship for a set of data. This is done via nonlinear least squares regression of four models: an inverse model; an exponential model; a bivariate power function model; and a three parameter inverse model. An S3 object of class "Ptmodels" is returned, which currently has methods for print, coef, summary, and predict. If inputs do not conform well to the models, a warning message is generated. This function can make use of minpack.lm::nlsLM.

Usage

Pt_model(P, tsec)

Arguments

P

a numeric vector of maximal mean power values for time periods given in the tsec argument.

tsec

a numeric vector of time values that (positionally) correspond to elements in P.

Value

• returns an S3 object of class "Ptmodels".

References

R. Hugh Morton (1996) A 3-parameter critical power model, Ergonomics, 39:4, 611-619, http://dx.doi.org/10.1080/00140139608964484{DOI}.

Examples

data(Pt_prof)
P    <- unname(Pt_prof)
tsec <- as.numeric(names(Pt_prof))
# Generate model object
m <- Pt_model(P, tsec)
# View
print(m)
# Plot
plot(P ~ tsec, cex = 0.2)
with(m$Pfn, curve(inv(x), add = TRUE, col = "red"))
with(m$Pfn, curve(exp(x), add = TRUE, col = "blue"))
with(m$Pfn, curve(pwr(x), add = TRUE, col = "purple"))
with(m$Pfn, curve(thrp(x), add = TRUE, col = "green"))
legend("topright", legend = round(m$table$RSE, 2),
       text.col = c("red", "blue", "purple", "green"),
       title = "RSE",title.col = "black",
       bty = "n")