Sounds like you need 'growthmodels' in R.

Here's the link: https://github.com/drodriguezperez/growthmodels

I don't know whether five is enough. In the example, they used ten. 

If chosen wisely, five time intervals should be good. If you choose poorly, even ten is not enough. It all depends on the shape of the growth curve. That will be determined by intrinsic rate of increase, as well as resource availability and competition factors. Unfortunately, if you don't have preliminary data, then you may need to repeat your experiment. This also assumes that the underlying curve has two inflexion points. Exponential growth that curves to become asymptotic to some stable proportion of the population would be a good example.

If there is no equilibrium, then you may need more time intervals.

Also, one could get exponential growth that slows to some equilibrium that lasts for 24H after which time available resources are depleted (or toxins accumulate) and the population declines. Now you will need more time intervals.

Hi,

I will answer the 2nd question only. For growth models, Gompertz or other models, U can fit it using a non-linear mixed model. You can use the package minpack.lm, with the function nlsLM. This package, with my experience, better compared to gnm package as it less likely produces error of not being able to fit.

You also want to look at the package growthmodels  as well.

Another suggestion is that you can fit the model in SAS using PROC NLMIXED where U easily get the estimate, predictions and their 95% CI which I could not obtain from that R pacakge. (Any one who knows how to do it might help). Also, you will usually face the problem with finding the appropriate starting values. I found that the paper  "Parameter Estimation of Nonlinear Growth Models in Forestry" of Fekedulegn D. et al. is a good start to guide you how to choose appropriate starting values for fitting these non-linear model.

Hope it help. 

You can use the package ‘grofit’ in R which fits Gompertz. If you want a smoother curve, you will need more than 5-time intervals for your model. 

Any example for this?

Hi Jack,

Here is an example of the R-code I used to fit Gompertz model to my data (number of cases of Ebola in Liberia):

################################### ### GOMPERTZ

alpha = 9526 beta = 9.1618 k = 0.0028

nls.gompertz

@ Thao Mai Phuong Tran

How did you choose alpha, beta and K at first place?

Hi Shabnam Salimi ,

It is indeed difficult to choose starting values for such kinds of model.

I tried to find some "good"starting values based on the "interpretation" of those parameters in the model.

It was based on this paper: Article Parameter Estimation of Nonlinear Growth Models in Forestry

Hope it helps.

Someone have an example or tutorial ? Because until today I have no idea of how to do it.

Hello to all and @ Jack Andrés Rincón Pérez

I also want to use the Gompertz or Weibull model for non-linear regression analysis of my data (survival of bacteria in water over time). I found a nice document: https://www.jstatsoft.org/article/view/v066i05 where they use the nlstools package. Maybe it is helpful for someone?

There, they are using a self-starting Gompertz model where the starting values are automatically choosen. Also, they demonstrate how you can check if your model fits well. An example is included.

see also: Non-linear modelling, Duursma (2017) http://www.hiercourse.com/docs/Rnotes_nonlinear.pdf

Now I am trying to use it for my own data.. let's see how it goes XD

Cheers, Carina

Carina Eisfeld Thanks a lot. Actually, I have read that document but I didn't fully understand it. Would you be so kind to give me an example or tutorial so I can have a better understanding? I would appreciate it.

Dear Jack Andrés Rincón Pérez , I am afraid I cannot help you with that at the moment because I am also still learning and trying to apply the code. Try to make the example in the PDF (there is somewhere the link with example data as well). And try to write the code by yourself even if it will take some time, following the protocol. That really helps to understand the steps in between and what the commands mean. Also, in youtube you can find useful videos, but you won't find the whole script explained. But parts of it (depends also on what you know already).

When I get further and have a working code, I can write you again.

Good luck!

Carina Eisfeld thanks a lot, you are so kind.

We keeping in contact

I found the following R package that can estimate the coefficients in Gompertz. https://cran.r-project.org/web/packages/growthrates/vignettes/Introduction.html

Hope it will help.

Haifeng Zhang Do you have an especific example?

@Jack: I do not have my own example. But, page 16 of the documentation below has an example. I guess what you need to do is to use "FUN=grow_gompertz" (when call fit_growthmodel) instead of "FUN=grow_logistic".

https://cran.r-project.org/web/packages/growthrates/growthrates.pdf

Haifeng Zhang thank you very much

Use gompertz function i regression model. For example in gretl kod look like this

genr a=0.8

genr b=2

genr c=0.4

nls var=a*exp(-b*exp(-c*time))

params a b c

end nls

LI if You like I may help You. Please send me data and I send You estimated data in Gompertz model. My mail is [email protected]

Jan Grzegorek : Dear Jan, could you help me fit the data for Gompertz?

Jiri.

excel solver for LSQ may be sufficient

You can use excel Solver to calculate Gompertz parameters by minimizing the sum of square residus (residus : difference between Experimental value and Gompertz model value

This has been very helpful. Many thanks

You are welcome Olayemi

Hassan

Here a nice video link on how to use Excel Solver for no linear regression to calculate Gompertz three parameters :

https://www.youtube.com/watch?v=Ewp5CF5ba_w

Hassan

Hi everyone, I am trying to fit a gombertz model as in the question of Li Zhou.. I tried the code below and I got an error message as in below. My data is not so good. It is GDP versus motorization rate and has some fluctuations in it.

The video that I have learnt the method and code is https://www.youtube.com/watch?v=0ifT-7K68sk&ab_channel=mathetal.

I am using easynls library. If you could help me, I will be very happy.

model5= nlsfit(MREST, model = 10, start =c(a = 120, b= 45, c=0.1))

Error in numericDeriv(form[[3L]], names(ind), env) :

Missing value or an infinity produced when evaluating the model

Dear Gulcin

Here a nice video link on how to use Excel Solver for no linear regression to calculate Gompertz three parameters :

https://www.youtube.com/watch?v=Ewp5CF5ba_w

Hassan

Thank you, I have watched this video but excel solver did not work for my data as well :(

Dear Gulcin

You have to add your model theoric equation in Excel sheet

thank you so much for your answers.

Hi, dear Gulcin Dalkic did you get answer for your question? I have a annual data of GDP per capita and annual data of registered. I want to forecast registered vehicles for the next 10 years from GDP per capita. if you have got the answer for your question let me know

Dear Abrha, I used excel solver and found some meaningful results. You can check the video above.

Gulcin Dalkic do you mean the video from Hassan El Bari ? if so, I am a bit confused about that.

I used this in R:

Gompertz

Yes Abrha, i mean that video, but then i used an R code..

Thanks so much Katja for sharing your code, i am gonna try it as well.

Formula: V2 ~ a * exp(-b * exp(-c * V1))

Please check this, it might be useful

https://encyclopedia.pub/entry/626#:~:text=Gompertz%20Function%20with%20R%20%7C%20Encyclopedia%20MDPI&text=The%20Gompertz%20function%20is%20a,is%20now%20used%20in%20biology.

https://www.youtube.com/watch?v=0ifT-7K68sk