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I am using the cmprsk package to create a series of regressions. In the real models I used, I specified my models in the same way that is shown in the example that produces mel2 below. My problem is, I want the Melanoma$ in front of the coefficients to go away, as happens if I had specified the model like in mel1. Is there a way to delete that data frame prefix out of the object without re-running it?
library(cmprsk)
data(Melanoma, package = "MASS")
head(Melanoma)
mel1 <- crr(ftime = Melanoma$time, fstatus = Melanoma$status, cov1 = Melanoma[, c("sex", "age")], cencode = 2)
covs2 <- model.matrix(~ Melanoma$sex + Melanoma$age)[, -1]
mel2 <- crr(ftime = Melanoma$time, fstatus = Melanoma$status, cov1 = covs2, cencode = 2)
What I want:
What I have:
You could use the data argument in model.matrix, and wrap the crr call in with(Melanoma, ...)
covs2 <- model.matrix(~ sex + age, data = Melanoma)[, -1]
mel2 <- with(Melanoma, crr(ftime = time, fstatus = status,
cov1 = covs2, cencode = 2))
mel2$coef
#> sex age
#> 0.58838573 0.01259388
If you are stuck with existing models like this:
covs2 <- model.matrix(~ Melanoma$sex + Melanoma$age)[, -1]
mel2 <- crr(ftime = Melanoma$time, fstatus = Melanoma$status,
cov1 = covs2, cencode = 2)
You could simply rename the coefficients like this
names(mel2$coef) <- c("sex", "age")
mel2
#> convergence: TRUE
#> coefficients:
#> sex age
#> 0.58840 0.01259
#> standard errors:
#> [1] 0.271800 0.009301
#> two-sided p-values:
#> sex age
#> 0.03 0.18
I want to model insurance claim count using a Poisson glmnet. The data I have at hand contains the number of claims for each policy (which is the response variable), some features about the policy (gender, region, etc.) as well as the duration of the policy (in years). I want to include the log-duration as an offset term, as we usually do in actuarial science. With the cv.glmnet function of the glmnet package, it is straightforward:
library(tidyverse)
library(glmnet)
n <- 100
dat <- tibble(
nb_claims = rpois(n, lambda = 0.5),
duration = runif(n),
x1 = runif(n),
x2 = runif(n),
x3 = runif(n)
)
fit <- cv.glmnet(
x = dat %>% dplyr::select(x1, x2, x3) %>% as.matrix(),
y = dat %>% pull(nb_claims),
family = "poisson",
offset = dat %>% pull(duration) %>% log()
)
fit
However, my goal is to train this model using the train function of the caret package, because of the many advantages it gives. Indeed, validation, preprocessing as well as feature selection is much better with this package. It is straightforward to train a basic glmnet (without an offset term) with caret:
library(caret)
fit <- caret::train(
x = dat %>% dplyr::select(x1, x2, x3) %>% as.matrix(),
y = dat %>% pull(nb_claims),
method = "glmnet",
family = "poisson"
)
fit
Naively, we could try to add the offset argument in the train function:
fit <- caret::train(
x = dat %>% dplyr::select(x1, x2, x3) %>% as.matrix(),
y = dat %>% pull(nb_claims),
method = "glmnet",
family = "poisson",
offset = dat %>% pull(duration) %>% log()
)
fit
Unfortunately, this code throws the error Error : No newoffset provided for prediction, yet offset used in fit of glmnet. This error occurs because the caret::train function doesn't take care to give a value for the newoffset argument in predict.glmnet function.
In this book, they show how to add an offset term to a GLM model by modifying the source code of the caret::train function. It works perfectly. However, the predict.glm function is quite different from the predict.glmnet function, because it does not have the newoffset argument. I tried to modify the source code of the caret::train function, but I am having some trouble because I do not know well enough how this function works.
A simple way to perform this is pass the offset column as part of x and in each fit and predict call pass as x columns of x which are not the offset. While as offset/newoffset pass the x column corresponding to the offset.
In the following example the offest column of x needs to be named "offset" too. This can be changed relatively easy
To create the function we will just use lots of parts from: https://github.com/topepo/caret/blob/master/models/files/glmnet.R
glmnet is peculiar since it needs a loop, the rest is just rinse and reapeat from https://topepo.github.io/caret/using-your-own-model-in-train.html#illustrative-example-1-svms-with-laplacian-kernels
family = "poisson" will be specified throughout, to change this adopt code from https://github.com/topepo/caret/blob/master/models/files/glmnet.R
glmnet_offset <- list(type = "Regression",
library = c("glmnet", "Matrix"),
loop = function(grid) {
alph <- unique(grid$alpha)
loop <- data.frame(alpha = alph)
loop$lambda <- NA
submodels <- vector(mode = "list", length = length(alph))
for(i in seq(along = alph)) {
np <- grid[grid$alpha == alph[i],"lambda"]
loop$lambda[loop$alpha == alph[i]] <- np[which.max(np)]
submodels[[i]] <- data.frame(lambda = np[-which.max(np)])
}
list(loop = loop, submodels = submodels)
})
glmnet_offset$parameters <- data.frame(parameter = c('alpha', 'lambda'),
class = c("numeric", "numeric"),
label = c('Mixing Percentage', 'Regularization Parameter'))
glmnet_offset$grid <- function(x, y, len = NULL, search = "grid") {
if(search == "grid") {
init <- glmnet::glmnet(Matrix::as.matrix(x[,colnames(x) != "offset"]), y,
family = "poisson",
nlambda = len+2,
alpha = .5,
offset = x[,colnames(x) == "offset"])
lambda <- unique(init$lambda)
lambda <- lambda[-c(1, length(lambda))]
lambda <- lambda[1:min(length(lambda), len)]
out <- expand.grid(alpha = seq(0.1, 1, length = len),
lambda = lambda)
} else {
out <- data.frame(alpha = runif(len, min = 0, 1),
lambda = 2^runif(len, min = -10, 3))
}
out
}
So x[,colnames(x) != "offset"] is x while offset is x[,colnames(x) == "offset"]
glmnet_offset$fit <- function(x, y, wts, param, last, ...) {
theDots <- list(...)
## pass in any model weights
if(!is.null(wts)) theDots$weights <- wts
if(!(class(x)[1] %in% c("matrix", "sparseMatrix")))
x <- Matrix::as.matrix(x)
modelArgs <- c(list(x = x[,colnames(x) != "offset"],
y = y,
alpha = param$alpha,
family = "poisson",
offset = x[,colnames(x) == "offset"]),
theDots)
out <- do.call(glmnet::glmnet, modelArgs)
if(!is.na(param$lambda[1])) out$lambdaOpt <- param$lambda[1]
out
}
glmnet_offset$predict <- function(modelFit, newdata, submodels = NULL) {
if(!is.matrix(newdata)) newdata <- Matrix::as.matrix(newdata)
out <- predict(modelFit,
newdata[,colnames(newdata) != "offset"],
s = modelFit$lambdaOpt,
newoffset = newdata[,colnames(newdata) == "offset"],
type = "response") #important for measures to be appropriate
if(is.matrix(out)) out <- out[,1]
out
if(!is.null(submodels)) {
tmp <- as.list(as.data.frame(predict(modelFit,
newdata[,colnames(newdata) != "offset"],
s = submodels$lambda,
newoffset = newdata[,colnames(newdata) == "offset"],
type = "response"),
stringsAsFactors = TRUE))
out <- c(list(out), tmp)
}
out
}
For some reason which I don't understand yet it does not work without the prob slot
glmnet_offset$prob <- glmnet_offset$predict
glmnet_offset$tags = c("Generalized Linear Model", "Implicit Feature Selection",
"L1 Regularization", "L2 Regularization", "Linear Classifier",
"Linear Regression")
glmnet_offset$sort = function(x) x[order(-x$lambda, x$alpha),]
glmnet_offset$trim = function(x) {
x$call <- NULL
x$df <- NULL
x$dev.ratio <- NULL
x
}
library(tidyverse)
library(caret)
library(glmnet)
n <- 100
set.seed(123)
dat <- tibble(
nb_claims = rpois(n, lambda = 0.5),
duration = runif(n),
x1 = runif(n),
x2 = runif(n),
x3 = runif(n)
)
x = dat %>%
dplyr::select(-nb_claims) %>%
mutate(offset = log(duration)) %>%
dplyr::select(-duration) %>%
as.matrix
fit <- caret::train(
x = x,
y = dat %>% pull(nb_claims),
method = glmnet_offset,
)
fit
100 samples
4 predictor
No pre-processing
Resampling: Bootstrapped (25 reps)
Summary of sample sizes: 100, 100, 100, 100, 100, 100, ...
Resampling results across tuning parameters:
alpha lambda RMSE Rsquared MAE
0.10 0.0001640335 0.7152018 0.01805762 0.5814200
0.10 0.0016403346 0.7152013 0.01805684 0.5814193
0.10 0.0164033456 0.7130390 0.01798125 0.5803747
0.55 0.0001640335 0.7151988 0.01804917 0.5814020
0.55 0.0016403346 0.7150312 0.01802689 0.5812936
0.55 0.0164033456 0.7095996 0.01764947 0.5783706
1.00 0.0001640335 0.7152033 0.01804795 0.5813997
1.00 0.0016403346 0.7146528 0.01798979 0.5810811
1.00 0.0164033456 0.7063482 0.01732168 0.5763653
RMSE was used to select the optimal model using the smallest value.
The final values used for the model were alpha = 1 and lambda = 0.01640335.
predict(fit$finalModel, x[,1:3], newoffset = x[,4]) #works
This will not work with preprocessing in caret since we pass offset as one of the features. However it will work with recipes since you can define columns on which preprocessing functions will be performed via selections. Se article for details: https://tidymodels.github.io/recipes/articles/Selecting_Variables.html
I haven't had time to error check my code. If any problems occur or if there is a mistake somewhere please comment. Thanks.
You can also post an issue in caret github asking this feature (offset/newoffset) to be added to the model
I tried to change the model info a lot of ways, but it was failing miserably. Below I can propose one solution, may not be the best, but will get you somewhere if your data is sensible.
In the poisson / negative binom .. regression, the offset in factor gets introduced into the regression, you can read more here and here:
where tx is the offset. In glmnet, there is a penalty factor you can introduce for each term, and if you let that be 0 for a term, basically you are not penalizing it and it's always included. We can use that for the offset, and you can see this effect only if you use a dataset that makes some sense (note that in your example dataset, the offsets are numbers that make no sense).
Below I use the insurance claims dataset from MASS:
library(tidyverse)
library(glmnet)
library(MASS)
dat <- Insurance
X = model.matrix(Claims ~ District + Group + Age,data=dat)
Y = dat$Claims
OFF = log(dat$Holders)
fit_cv <- cv.glmnet(
x = X,
y = Y,
family = "poisson",
offset = OFF
)
Now using caret, I will fit it without any training, and using the same lambda obtained from the fit in cv.glmnet. One thing you should note too is that cv.glmnet often uses lambda.1se instead of lambda.min:
fit_c <- caret::train(
x = cbind(X,OFF),
y = Y,
method = "glmnet",
family = "poisson",
tuneGrid=data.frame(lambda=fit_cv$lambda.1se,alpha=1),
penalty=c(rep(1,ncol(X)),0),
trControl = trainControl(method="none")
)
We can see how different are the predictions:
p1 = predict(fit_cv,newx=X,newoffset=OFF)
p2 = predict(fit_c,newx=cbind(X,OFF))
plot(p1,p2)
I am trying to make the prediction of three variables (retweets,media,content) in my dataset (df_22) to choose between Poisson, Negative binomial and Zero-inflated Poisson. One of the three variables is the response variable (retweets) and the other two the predictive variables (media,content).
I realize the generalized linear models and without problem.
Zero-inflated Poisson data
library("pscl")
summary( m0 <- zeroinfl(retweets ~ media + content, data=df_22,dist="poisson") )
Poisson
summary( m1 <- glm(formula=retweets ~ media + content, data=df_22, family="poisson"(link=log)))
Negative binomial
library (MASS)
summary( m2 <- glm.nb(retweets ~ media + content, data=df_22) )
However, when I create the new database to make the prediction. I check it levels.
> levels(df_22$media)
[1] "other" "pic" "pw" "text" "web"
> levels(df_22$content)
[1] "cultura" "employ" "environment" "other" "security" "sport" "transport"
I have a problem. And it is that the rows of both columns is different.
newmedia = c("other","pic","pw","text", "web")
newcontent = c("cultura","employ","environment","other","security","sport","transport")
nd = data.frame(media = newmedia, content = newcontent)
Error in data.frame(media = newmedia, content = newcontent) : arguments imply differing number of rows: 5, 7
What should I do to solve these problems?
I want to solve this problem in order to be able to make these predictions so that I can choose which of the three models is better for my data.
p0 <- cbind(nd, Count = predict(m0, newdata = nd, type = "count"), Zero = predict(m0, newdata = nd, type = "zero"))
p1 <- cbind(nd, Mean = predict(m1, newdata = nd, type="response"), SE = predict(m1, newdata = nd, type="response", se.fit=T)$se.fit)
p2 <- cbind(nd, Mean = predict(m2, newdata = nd, type="response"), SE = predict(m2, newdata = nd, type="response", se.fit=T)$se.fit)
In the code below a sample data set is created and it computes the p0, p1, p2. The nb dataframe was created differently as a test dataframe.
Import libraries
library(pscl)
library (MASS)
Create sample data set
media <- c("other", "pic", "pw", "text", "web")
content <- c("cultura", "employ", "environment", "other", "security", "sport", "transport")
set.seed(1)
retweets <- floor(abs(1e4*rnorm(1000)))
temp_index <- which(retweets %in% sample(retweets, 20)) # sample indexes
retweets[temp_index] <- 0 # set some retweets to zero to run zeroinfl()
df <- data.frame(retweets)
df$media <- sample(media, 1000, replace = TRUE)
df$content <- sample(content, 1000, replace = TRUE)
head(df)
unique(df$media)
unique(df$content)
Create a test data set
Note: Here, test data set is drawn from the training data for illustration purpose only. Ideally, it should be a new set of data.
nd = df[sample(nrow(df), 300), ] # ideally this should not be from the train data, this is just for an example code
nd_X <- test[,c('media', 'content')]
nd_Y <- test[,c('retweets')]
Fit models: zeroinf(dist='poisson'), glm(family='poisson'), glm.nb()
# Poisson
summary( m0 <- zeroinfl(retweets ~ media + content, data=df, dist="poisson") )
# Binomial
summary( m1 <- glm(formula=retweets ~ media + content, data=df, family="poisson"(link=log)))
# glm()
#summary( m2 <- glm.nb(retweets ~ media + content, data=df) ) # gives error in summary due to zeros
summary( m2 <- glm.nb(retweets ~ media + content, data=df[df$retweets!=0,]) ) # no error without zeros
Predict using test data set
p0 <- cbind(nd, Count = predict(m0, newdata = nd_X, type = "count"), Zero = predict(m0, newdata = nd, type = "zero"))
p1 <- cbind(nd, Mean = predict(m1, newdata = nd_X, type="response"), SE = predict(m1, newdata = nd, type="response", se.fit=T)$se.fit)
p2 <- cbind(nd, Mean = predict(m2, newdata = nd_X, type="response"), SE = predict(m2, newdata = nd, type="response", se.fit=T)$se.fit)
Output:
I'm running into an error that I can't find any documentation on when I try to bootstrap a glmer object:
glm2 <- glmer(RT~valence+location+first_location+Trial_num +
(1+Trial_num|id)+(1|Trial_num),
family=inverse.gaussian(log),
control = glmerControl(optimizer = "nloptwrap",
calc.derivs = FALSE), data=df_long)
The error is:
Error in lme4::.simulateFun(object = , :
could not find function "sfun
This is regardless of whether I try bootMer or confint:
bootMer_out <- bootMer(glm2,FUN=fixef, nsim=300)
confint_out <- confint(glm2, method="boot")
When I run as an lmer object I don't have the issue with bootstrapping. i.e.
lm2 <- glmer(RT~valence+location+first_location+Trial_num + (1+Trial_num|id)+(1|Trial_num), family=inverse.gaussian(log), control = glmerControl(optimizer = "nloptwrap", calc.derivs = FALSE), data=df_long))
Does it have to do with the link function? Is there a workaround? I couldn't find function 'sfun' in the simulateFun documentation either. I could always just do the transformation on the data separately and use lmer instead of glmer, but if anyone has some insight that would be great (since I'm curious now).
As pointed out by #user20650, you'll need to add a simulation method for the inverse gaussian family.
For example, I added these to a branch on my lme4 fork under predict.R:
rinvgauss <- function(n, mu, lambda) {
# transcribed from https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution
nu <- rnorm(n)
y <- nu^2
x <- mu + (mu^2 * y)/(2*lambda) - (mu/(2*lambda)) * sqrt(4*mu*lambda*y + mu^2*y^2)
z <- runif(n)
ifelse(z <= mu/(mu + x), x, mu^2/x)
}
inverse.gaussian_simfun <- function(object, nsim, ftd = fitted(object),
wts = weights(object)) {
if (any(wts != 1)) message("using weights as inverse variances")
dispersion <- sum((weights(object, 'working') *
resid(object, 'working')^2)[weights(object, 'working')>0])/df.residual(object)
rinvgauss(nsim * length(ftd), mu = ftd,
lambda = wts/dispersion)
}
# ... skip a few
simfunList <- list(gaussian = gaussian_simfun,
binomial = binomial_simfun,
poisson = poisson_simfun,
Gamma = Gamma_simfun,
negative.binomial = negative.binomial_simfun,
inverse.gaussian = inverse.gaussian_simfun)
Here's an example:
# devtools::install_github('aforren1/lme4', ref = 'add_invgauss_simulate')
library(lme4)
set.seed(1)
dat <- data.frame(y = lme4:::rinvgauss(1000, 3, 4),
x = runif(1000),
subj = factor(rep(1:10, 100)))
mod <- glmer(y ~ x + (1|subj),
data = dat,
family = inverse.gaussian(link='log'))
# ~60 secs on my laptop
(boots <- confint(mod, method = 'boot', nsim = 100, parm = 'beta_'))
2.5 % 97.5 %
(Intercept) 1.0044813 1.248774
x -0.2158155 0.161213
(walds <- confint(mod, method = 'Wald', parm = 'beta_'))
2.5 % 97.5 %
(Intercept) 1.000688 1.2289971
x -0.205546 0.1644621
You can see that the bootstrap method gives (roughly) the same results as the Wald method.
I have some difficulties getting a specific curve to fit in R, while it works perfectly fine in a commercial curve-fitting program.
The formula that the data should fit to is:
y(t) = A * exp(-a*(t)) + B * exp(-b*(t)) - (A+B) * exp(-c*(t))
So for this I want to use the nonlinear regression built into R. I've been at this for a day on-and-off now and just can't get it to function. The issue lies entirely with the initial values, so I'm using NLS2 to brute-force find the initial values.
y <- c(0,0.01377,0.01400875,0.0119175,0.00759375,0.00512125,0.004175,0.00355375,
0.00308875,0.0028925,0.00266375)
t <- c(0,3,6,12,24,48,72,96,120,144,168)
df <- data.frame(t,y)
plot(t,y);
#Our model:
fo <- y ~ f1*exp(-k1*t)+f2*exp(-k2*t)-(f1+f2)*exp(-k3*t);
#Define the outer boundaries to search for initial values
grd <- data.frame(f1=c(0,1),
f2=c(0,1),
k1=c(0,2),
k2=c(0,2),
k3=c(0,0.7));
#Do the brute-force
fit <- nls2(fo,
data=df,
start = grd,
algorithm = "brute-force",
control=list(maxiter=20000))
fit
coef(fit)
final <- nls(fo, data=df, start=as.list(coef(fit)))
The values it should give are:
f1 0.013866
f2 0.005364
k1 0.063641
k2 0.004297
k3 0.615125
Though even with quite high iteration values, I'm just getting nonsense returns. I'm clearly doing something wrong, but I cannot see it
Edit based on #Roland 's comment:
The method you propose with the approximation of k1-3 with a linear approach seems to work on some datasets, but not on all of them. Below is the code I'm using now based on your input.
#Oral example:
y <- c(0,0.0045375,0.0066325,0.00511375,0.00395875,0.003265,0.00276,
0.002495,0.00231875);
t <- c(0,12,24,48,72,96,120,144,168);
#IV example:
#y <- c(0,0.01377,0.01400875,0.0119175,0.00759375,0.00512125,0.004175,
#0.00355375,0.00308875,0.0028925,0.00266375)
#t <- c(0,3,6,12,24,48,72,96,120,144,168)
DF <- data.frame(y, t)
fit1 <- nls(y ~ cbind(exp(-k1*t), exp(-k2*t), exp(-k3*t)), algorithm = "plinear", data = DF,
start = list(k1 = 0.002, k2 = 0.02, k3= 0.2))
k1_predict <-summary(fit1)$coefficients[1,1]
k2_predict <-summary(fit1)$coefficients[2,1]
k3_predict <-summary(fit1)$coefficients[3,1]
fo <- y ~ f1*exp(-k1*t)+f2*exp(-k2*t)-(f1+f2)*exp(-k3*t);
fit2 <- nls(fo, data = DF,
start = list(k1 = k1_predict, k2 = k2_predict, k3 = k3_predict, f1 = 0.01, f2 = 0.01))
summary(fit2);
plot(t,y);
curve(predict(fit2, newdata = data.frame(t = x)), 0, 200, add = TRUE, col = "red")
oral_example fit
#G. Grothendieck
Similar to Roland's suggestion, your suggestion is also excellent in that it is capable of fitting some datasets but struggles with others. The code below is based on your input, and exits with a singular gradient matrix.
#Oral example:
y <- c(0,0.0045375,0.0066325,0.00511375,0.00395875,0.003265,0.00276,
0.002495,0.00231875);
t <- c(0,12,24,48,72,96,120,144,168);
#IV example:
#y <- c(0,0.01377,0.01400875,0.0119175,0.00759375,0.00512125,0.004175,
#0.00355375,0.00308875,0.0028925,0.00266375)
#t <- c(0,3,6,12,24,48,72,96,120,144,168)
df <- data.frame(y, t)
grd <- data.frame(f1=c(0,1),
f2=c(0,1),
k1=c(0,2),
k2=c(0,2),
k3=c(0,0.7));
set.seed(123)
fit <- nls2(fo,
data=df,
start = grd,
algorithm = "random",
control = nls.control(maxiter = 100000))
nls(fo, df, start = coef(fit), alg = "port", lower = 0)
plot(t,y);
curve(predict(nls, newdata = data.frame(t = x)), 0, 200, add = TRUE, col = "red")
I would first do a partially linear fit with no constraints on the linear parameters to get good starting values for the exponential parameters and some idea regarding the magnitude of the linear parameters:
DF <- data.frame(y, t)
fit1 <- nls(y ~ cbind(exp(-k1*t), exp(-k2*t), exp(-k3*t)), algorithm = "plinear", data = DF,
start = list(k1 = 0.002, k2 = 0.02, k3= 0.2))
summary(fit1)
#Formula: y ~ cbind(exp(-k1 * t), exp(-k2 * t), exp(-k3 * t))
#
#Parameters:
# Estimate Std. Error t value Pr(>|t|)
#k1 0.0043458 0.0010397 4.180 0.008657 **
#k2 0.0639379 0.0087141 7.337 0.000738 ***
#k3 0.6077646 0.0632586 9.608 0.000207 ***
#.lin1 0.0053968 0.0006637 8.132 0.000457 ***
#.lin2 0.0139231 0.0008694 16.014 1.73e-05 ***
#.lin3 -0.0193145 0.0010631 -18.168 9.29e-06 ***
Then you can fit your actual model:
fit2 <- nls(fo, data = DF,
start = list(k1 = 0.06, k2 = 0.004, k3 = 0.6, f1 = 0.01, f2 = 0.01))
summary(fit2)
#Formula: y ~ f1 * exp(-k1 * t) + f2 * exp(-k2 * t) - (f1 + f2) * exp(-k3 * t)
#
#Parameters:
# Estimate Std. Error t value Pr(>|t|)
#k1 0.0639344 0.0079538 8.038 0.000198 ***
#k2 0.0043456 0.0009492 4.578 0.003778 **
#k3 0.6078929 0.0575616 10.561 4.24e-05 ***
#f1 0.0139226 0.0007934 17.548 2.20e-06 ***
#f2 0.0053967 0.0006059 8.907 0.000112 ***
curve(predict(fit2, newdata = data.frame(t = x)), 0, 200, add = TRUE, col = "red")
Note that this model can easily be re-parameterized by switching the exponential terms (i.e., the order of the kn starting values), which could result in different estimates for f1 and f2, but basically the same fit.
With this many parameters I would use algorithm = "random" rather than "brute". If we do that then the following gives a result close to the one in the question (up to permutation of the arguments due to the symmetry of the model parameters):
set.seed(123)
fit <- nls2(fo,
data=df,
start = grd,
algorithm = "random",
control = nls.control(maxiter = 20000))
nls(fo, df, start = coef(fit), alg = "port", lower = 0)
giving:
Nonlinear regression model
model: y ~ f1 * exp(-k1 * t) + f2 * exp(-k2 * t) - (f1 + f2) * exp(-k3 * t)
data: df
f1 f2 k1 k2 k3
0.005397 0.013923 0.004346 0.063934 0.607893
residual sum-of-squares: 2.862e-07
Algorithm "port", convergence message: relative convergence (4)
ADDED
A variation of the above is to use nlsLM in the minpack.lm package instead of nls and to use splines to get more points in the data set. In place of the nls line try the following. It still gives convergence:
library(minpack.lm)
t_s <- with(df, min(t):max(t))
df_s <- setNames(data.frame(spline(df$t, df$y, xout = t_s)), c("t", "y"))
nlsLM(fo, df_s, start = coef(fit), lower = rep(0,5), control = nls.control(maxiter = 1024))
and it also does in the Oral example:
set.seed(123)
y <- c(0,0.0045375,0.0066325,0.00511375,0.00395875,0.003265,0.00276,
0.002495,0.00231875);
t <- c(0,12,24,48,72,96,120,144,168)
DF <- data.frame(y, t)
grd <- data.frame(f1=c(0,1), f2=c(0,1), k1=c(0,2), k2=c(0,2), k3=c(0,0.7))
fit <- nls2(fo,
data=DF,
start = grd,
algorithm = "random",
control = nls.control(maxiter = 20000))
library(minpack.lm)
t_s <- with(DF, min(t):max(t))
df_s <- setNames(data.frame(spline(DF$t, DF$y, xout = t_s)), c("t", "y"))
nlsLM(fo, df_s, start = coef(fit), lower = rep(0,5), control = nls.control(maxiter = 1024))