I want to fit my data (50 samples so that each of them contains 100 data points) with Gompertz curve. After that, I want to check whether the fitting is appropriate. Here, low bias and variance is meant by appropriate fitting. I’m looking for some implementation for this purpose. I found the distfit function in Matlab for fitting, but it doesn’t support Gompertz distribution. So, what is your suggestion?
SAS would offer Gompertz in PROC Probit - and if you activate the lackfit option, it performs two goodness-of-fit tests (a Pearson chi-square test and a log-likelihood ratio chisquare test) for the fitted model.
You will also get confidence limits displayed for the model.
I will suggest that you do all the diagnostics for the data before you go ahead in fitting you curve. that is, QQ plot for normality of the data, cummulative periodogram for independence of errors, box-pierce for normality and test for homoskedasticity.
Dear Negin,
I'm not sure if I understand you correctly. But I would say that you just want to fit a Gompertz distribution to your data. I don't know how this works in Matlab, but in R you could use e.g. the flexsurv package, see first link. Also the vglm() function from the VGAM package seems to support the Gompertz distribution. Or you use the makeham() function, which is also contained in the VGAM pacakge, see second link.
Best, Stephan
http://stackoverflow.com/questions/17718566/gompertz-aging-analysis-in-r
http://www.inside-r.org/packages/cran/vgam/docs/Makeham
I think Stephan gave a hint.
Another option is here.
If you need just to find the inflection point, then package 'inflection' will help for that task.
See how:
> library(inflection)
> library(nlme)
> gomp=function(x,L,b,k)
+ {
+ L*exp(-b*exp(-k*x))
+ }
> xy xysol summary(xysol)
Formula: V2 ~ gomp(V1, L, b, k)
Parameters:
Estimate Std. Error t value Pr(>|t|)
L 0.82096 0.01230 66.75 bb=findiplist(cbind(xy$V1),cbind(xy$V2),0)
> abline(v=bb[,3],col='blue')
> title('[email protected], example of inflection for Gompertz')
>
The result is attached plot.
Data and Code is also attached.
Good luck!
Data Find inflection point using R
Thanks all,
Let me be clearer about my question:
Now, I want to use the chi-square test. I have 50 samples so that each of them contains 100 data points and want to see if the 100 data points have the Gompertz distribution. The point is, the chi-square test just take one sample (in my case, the 100 data points) as an input. So, do you have any solutions?
Dear Negin,
so let's assume you have fitted a Gompertz distribution to one of the data sets. Then you could use e.g. ks.gompertz(), see link, to perform a Kolmogorov Smirnov test and judge the goodness of fit based on this result
You could of course repeat this procedure for all 50 data sets. This would make sense if you want to judge the goodness of fit for all 50 data sets separately.
If this is not the case and you want to make simultaneous statements about all 50 data sets, then you must apply a multiple testing procedure and there the dependence between the samples will be important.
Best, Stephan
http://www.inside-r.org/packages/cran/reliaR/docs/ks.gompertz
Dear Stephan,
I don’t want to measure the goodness of fitting a single sample, separately. Actually, I want to measure the overall goodness of fitting samples to the Gompertz curve. But, I don’t know how to do this! One easy way coming to my mind is to average over 30 samples and use the average data to learn the fitting parameters, then, average over remaining 20 samples and use this average to measure the error! What is your idea about that? Do you think it is true?
In the regards of “multiple testing procedure”, could you possibly explain more, please.
Thanks,
Negin
Dear Negin,
I would say that it depends very much on how the sample are created and what the relationship between the samples is. As long as there is no direct connection between the samples (like first observation in the first sample "belongs" to first observation in the second sample and so on), averaging makes not so much sense to me.
I would say that you want to consider the 50 hypotheses
H0: sample 1 has a Gompertz distribution
...
H0: sample 50 has a Gompertz distribution
simultaneously and therefore you have a multiple comparisons problem. See the wikipedia link for more details about multiple comparisons procedures. In R the sgof package might be helpful for your problem. But I have to say that I'm not familiar with this package.
Best, Stephan
https://en.wikipedia.org/wiki/Multiple_comparisons_problem
https://cran.r-project.org/web/packages/sgof/
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis