FlexParamCurve (version 1.3)

posnegRichards_eqn: Equations of the FlexParamCurve Family

Description

Function to solve any of the equations in the FlexParamCurve family, depending on user-specified parameters and model choice

Usage

posnegRichards_eqn(x,

Asym = NA,

K = NA,

Infl = NA,

M = NA,

RAsym = NA,

Rk = NA,

Ri = NA,

RM = NA,

modno)

Arguments

x

a numeric vector of the primary predictor variable

Asym

a numeric value for the asymptote of the positive (increasing) curve

K

a numeric value for the rate parameter of the positive (increasing) curve

Infl

a numeric value for the point of inflection of the positive (increasing) curve

M

a numeric value for the shape parameter of the positive (increasing) curve

RAsym

a numeric value for the asymptote of the negative (decreasing) curve

Rk

a numeric value for the rate parameter of the negative (decreasing) curve

Ri

a numeric value for the point of inflection of the negative (decreasing) curve

RM

a numeric value for the shape parameter of the negative (decreasing) curve

modno

a numeric value (currently integer only) between 1 and 36 specifying the identification number of the equation to be fitted

Value

• the solution of the equation specified (by modno), given the user-entered parameters

Details

This function fits 1 of 36 possible FlexParamCurve equations. All equations are biomodal, in that they have a positive (increasing) trajectory followed by a negative (decreasing) trajectory. These equations have also been described as double-Richards curves, or positive-negative Richards curves. From version 1.2 onwards this function can fit curves that exhibit negative followed by positive trajectories or double positive or double negative trajectories. This function can now also fit two component models, where the first curve is used up to the age of intersection and the second curve is used afterwards, thus the curves are not joined as in standard models (see SSposnegRichards for details. The 36 possible equations are all based on the subtraction of one Richards curve from another, producing: $y = A / ([1+ m exp(-k (t-i))]1/m) - A' / ([1+ m' exp(-k' (t-i' ))]1/m' )$, where A=Asym, k=K, i=Infl, m=M, A'=RAsym, k'=Rk, i'=Ri, m'=RM; as described in the Arguments section above. All 36 possible equations are simply reformulations of this equation, in each case fixing a parameter or multiple parameters to the mean parameter across all individuals in the dataset (such as produced by a nls model). All models are detailed in the SSposnegRichards help file. Any models that require parameter fixing (i.e. all except R1) extract appropriate values from the object $pnmodelparams$ for the fixed parameters. This object is created by running modpar and can be adjusted manually or by using change.pnparameters to user required specification.

See Also

SSposnegRichards modpar

Examples

require(graphics)

# calculate y from an 8-parameter model

   	 data(posneg_data)

   	 modpar(posneg_data$age, posneg_data$mass) #create pnmodelparams for fixed parameters

   	 y <- posnegRichards_eqn(10, 1000, 0.5, 25, 1, 100, 0.5, 125, 

   	 1, modno = 1)



# calculate y from a 4-parameter positive only model, note that second curve parameters are unneeded

# and replaced with value from pnmodelparams

   	 y <- posnegRichards_eqn(10, 1000, 0.5, 25, 1, 

   	 1, modno = 12)

   	 

# plot a logistic curve (M=1),  note that second curve parameters are unneeded 	     

   	 plot(1:200, posnegRichards_eqn(1:200, 1000, 0.5, 25, 1, 

   	  modno = 12), xlim = c(1, 200), xlab = "x", 

   		 ylab = "y", pch = 1, cex = 0.7)