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,

pn.options,

Envir = .GlobalEnv)

Value

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

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
pn.options: a character vector specifying a list of parameters and options for plotting
Envir: a valid R environment to find pn.options, by default this is the global environment

Author

Stephen Oswald <steve.oswald@psu.edu>

Details

This function fits 1 of 32 possible FlexParamCurve equations (plus custon model #17). Equations

can fit both monotonic and non-monotonic curves (two different trajectories).

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 (biphasic) models, where the first curve is used up to the x-value (e.g. 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 32 possible equations are all based on the subtraction of one Richards curve from another, producing:

$y = A / ([1 + m e x p (- k (t - i))] 1 / m) - A^{'} / ([1 + m^{'} e x p (- k^{'} (t - i^{'}))] 1 / m^{'})$ , 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 32 possible equations are simply reformulations of this equation, in each case fixing a parameter or

multiple parameters to (by default) 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 model #1) extract appropriate values from the specified list passed by name to pn.options for the fixed parameters.

This object is most easily created by running modpar and can be adjusted manually or by using

change.pnparameters to user required specification.

If parameters are omitted in the call but required by the $m o d n o$ specified in the call, then they will be automatically extracted

from the pn.options object supplied, with the appropriate warning. Thus, it is not necessary to list out parameters and modno but is

a useful exercise if you are unfamiliar or in doubt of exactly which model is being specified by $m o d n o$ , see SSposnegRichards

for a list. If a parameter is supplied separately with the call then this value will override those stored in for the same parameter in $m o d n o$ :

see examples below.

Examples

Run this code



require(graphics)


# calculate y (dependent variable) for a given x for an 8-parameter double-Richards model


         #create pnmodelparams for fixed parameters 


   	 modpar(posneg.data$age, posneg.data$mass, pn.options = "myoptions")


   	 x = 10


   	 y <- posnegRichards.eqn(x, 1000, 0.5, 25, 1, 100, 0.5, 125, 


   	 1, modno = 1, pn.options = "myoptions")


   	 print( c(x = x, y = y) )


   	 


# plot 8-parameter model using saved parameter values from modpar


	 plot(posneg.data$age, posneg.data$mass, pch = ".")


	 curve(posnegRichards.eqn(x,modno = 1, pn.options = "myoptions"), add = TRUE, lwd = 3)


	 


# plot 3-parameter model using saved parameter values from modpar


         curve(posnegRichards.eqn(x,modno = 32, pn.options = "myoptions"), add = TRUE, col =2


               , lwd = 3)


	 


# tweak the plot of a 3-parameter model by user specifying a lower asymptote:


#      ie give some parameter values


# directly and others through pn.options by default


         curve(posnegRichards.eqn(x,modno = 32, Asym = 3200, pn.options = "myoptions"),


               add = TRUE, col = 5, lwd = 3)


	 


# calculate y (dependent variable) for a given x for a 4-parameter Richards model 


# (note that second curve parameters are unneeded) and replaced with value from pn.options.


# User-supplied variables over-ride those stored in pn.options object


	 x = 10


   	 y <- posnegRichards.eqn(x, 1000, 0.5, 25, 1, 


   	 1, modno = 12, pn.options = "myoptions")


   	 print( c(x = x, y = y) )


   	 


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


         plot(1:200, posnegRichards.eqn(1:200, Asym = 1000, K = 0.5, Infl = 25, M = 1, 


   	         modno = 12, pn.options = "myoptions"), xlim = c(1, 200), xlab = "x", 


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





# plot a double-logistic curve (M=1, RM=1),  


#note that second curve parameters are unneeded 	     


   	 plot(1:200, posnegRichards.eqn(1:200, Asym = 1000, K = 0.5, Infl = 25, M = 1,


   	      RAsym = -100, Rk = 0.5, Ri = 125, RM = 1,


   	      modno = 1, pn.options = "myoptions"), xlim = c(1, 200), xlab = "x", 


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

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