Joel,
The following should answer most of your questions:
time <- c(seq(0,10),seq(0,10),seq(0,10))
plant <- c(rep(1,11),rep(2,11),rep(3,11))
severity <- c(
42,51,59,64,76,93,106,125,149,171,199,
40,49,58,72,84,103,122,138,162,187,209,
41,49,57,71,89,112,146,174,218,250,288)/288
# Suggestion: you don't need cbind() to make a dataframe:
data1 <- data.frame(time, plant, severity)
# Plot severity versus time
# you can avoid the awkward ..$.. by using with():
with(data1, plot(time, severity, type="n"))
with(data1, text(time, severity, plant))
title(main="Graph of severity vs time")
# Now you use either the 'getInitial' approach and
# transform your parameter estimates to your
# preferred ones, or you can use SSlogis for your
# model and transform the parameter estimates
# afterwards:
# Method 1:
# --------
ini <- getInitial(
severity ~ SSlogis(time, alpha, xmid, scale),
data = data1
)
ini <- unname(ini) ##to get rid of names
# start vector in terms of alpha, beta, gamma:
para0.st <- c(
alpha = ini[1],
beta = ini[2]/ini[3],
gamma = 1/ini[3]
)
fit0 <- nls(
severity~alpha/(1+exp(beta-gamma*time)),
data1,
start=para0.st,
trace=T
)
# logistic curve on the scatter plot
co <- coef(fit0) ##get the parameter estimates
curve(co[1]/(1+exp(co[2]-co[3]*x)), add=TRUE)
# you don't need from, to, since the plot is already
# set up and you don't want to restrict the curve;
# personally, I prefer defining the function to be plotted:
f <- function(x, abc){
alpha <- abc[1]
beta <- abc[2]
gamma <- abc[3]
alpha / (1 + exp(beta - gamma * x))
}
# then you can plot the curve with:
curve(f(x, coef(fit0)), add = TRUE)
# Method 2:
# --------
fit2 <- nls(severity ~ SSlogis(time, Asym, xmid, scal), data = data1)
co <- unname(coef(fit2))
abc <- c(co[1], co[2]/co[3], 1/co[3])
with(data1, plot(time, severity, type="n"))
with(data1, text(time, severity, plant))
title(main="Graph of severity vs time")
curve(f(x, abc), add = TRUE)
Cheers,
-Peter Ehlers
Joel F?rstenberg-H?gg wrote:> Hi everybody,
>
>
>
> I'm using the method described here to make a linear regression:
>
>
>
>
http://www.apsnet.org/education/advancedplantpath/topics/Rmodules/Doc1/05_Nonlinear_regression.html
>
>
>
>> ## Input the data that include the variables time, plant ID, and
severity
>> time <- c(seq(0,10),seq(0,10),seq(0,10))
>> plant <- c(rep(1,11),rep(2,11),rep(3,11))
>>
>> ## Severity represents the number of
>> ## lesions on the leaf surface, standardized
>> ## as a proportion of the maximum
>> severity <- c(
> + 42,51,59,64,76,93,106,125,149,171,199,
> + 40,49,58,72,84,103,122,138,162,187,209,
> + 41,49,57,71,89,112,146,174,218,250,288)/288
>> data1 <- data.frame(
> + cbind(
> + time,
> + plant,
> + severity
> + )
> + )
>> ## Plot severity versus time
>> ## to see the relationship between## the two variables for each plant
>> plot(
> + data1$time,
> + data1$severity,
> + xlab="Time",
> + ylab="Severity",
> + type="n"
> + )
>> text(
> + data1$time,
> + data1$severity,
> + data1$plant
> + )
>> title(main="Graph of severity vs time")
>>
>> getInitial(
> + severity ~ SSlogis(time, alpha, xmid, scale),
> + data = data1
> + )
> alpha xmid scale
> 2.212468 12.506960 4.572391
>>
>> ## Using the initial parameters above,
>> ## fit the data with a logistic curve.
>> para0.st <- c(
> + alpha=2.212,
> + beta=12.507/4.572, # beta in our model is xmid/scale
> + gamma=1/4.572 # gamma (or r) is 1/scale
> + )
>> fit0 <- nls(
> + severity~alpha/(1+exp(beta-gamma*time)),
> + data1,
> + start=para0.st,
> + trace=T
> + )
> 0.1621433 : 2.2120000 2.7355643 0.2187227
> 0.1621427 : 2.2124095 2.7352979 0.2187056
>> ## Plot to see how the model fits the data; plot the
>> ## logistic curve on a scatter plot
>> plot(
> + data1$time,
> + data1$severity,
> + type="n"
> + )
>> text(
> + data1$time,
> + data1$severity,
> + data1$plant
> + )
>> title(main="Graph of severity vs time")
>>
>> curve(
> + 2.21/(1+exp(2.74-0.22*x)),
> + from=time[1],
> + to=time[11],
> + add=TRUE
> + )
>
>
> As you can see I have to do some work manually, such as setting the numbers
to be used for calculation of alpha, beta and gamma. I wonder if you might have
an idea how to automatize this? I suppose it should be possible to save the
output from getInitial() and reach the elements via index or something, but how?
>
>
>
> I guess a similar approach could be used for the values of fit0?
>
>
>
> Or even better, if the variables alpha, beta and gamma could be used right
away for instance in curve(), instead of adding the values manually. But just
exchanging the values with the varables (alpha instead of 2.21 etc) doesn't
seem to work. What is the reason for that? Any solution?
>
>
>
> A last, general but somewhat related question. If I set variables in a
function such as para0.st <- c(alpha=2.212, ...), is it just stored locally,
or can it be used globally, I mean, can I use the variable anywhere (for
instance in curve()) or just in the function where it was created? I'm
asking because I'm used to Java, where the life time of local variabels only
extends to the closing braces, while global variables can be reached everywhere.
>
>
>
> The reason for automatization is that I'll have to repeat the procedure
more than a hundred times, while making overview pair waise plots of my data,
with both this logaritmic regression and several others (exponential,
monomoelcular, logistic, Gompertz and Weibull).
>
>
>
>
>
> Wish you all the best,
>
>
>
> Joel
>
> _________________________________________________________________
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>
>
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