Distribution of Area Estimates

49 views
Skip to first unread message

Odd Jacobson

unread,
Mar 17, 2022, 10:24:13 AMMar 17
to ctmm R user group
Hi Chris,

I hope you are well.

I was wondering if it was possible to extract the distribution of possible akde area estimates from the summary function instead of just the estimate (mean) and the CIs? 

Also, I read that when you do the summary function on the model fits, then you should get the Gaussian area estimates. However, it seems that I am not getting Gaussian CIs in my case. Why might this be the case? and is there another way to get the Gaussian estimate?

For context, I am trying to do a measurement error model with both the predictor and outcome variable being area estimates with uncertainty.

Thanks in advance!

All the best,
Odd

Christen Fleming

unread,
Mar 17, 2022, 3:56:58 PMMar 17
to ctmm R user group
Hi Odd,

Do you mean the approximated sampling distribution / posterior distribution? This is approximated as a gamma distribution with mean given by the point estimate and variance given by (point estimate)^2/DOF[area].

I'm not clear on your second question. Are you not getting outputs like in the vignette: https://ctmm-initiative.github.io/ctmm/articles/variogram.html#cb16

If I understand, you will likely want to log transform the areas to be closer to normal, in which case the quantities you need are given by

log.area = log(area)
var.log.area = 1/DOF

for the point estimates and variance estimates.

Best,
Chris

Odd Jacobson

unread,
Mar 18, 2022, 7:05:01 AMMar 18
to ctmm R user group
Hi Chris,

Thanks so much for the quick response. Also, sorry for the vagueness in my questions. My stats brain is currently in development.

1) Yes you are correct, I was wondering about the posterior distribution of the area. Is there a way that I can extract this from the akde object?

2) I think we are on a similar page, but maybe I will rephrase my question slightly: Can I calculate a single standard deviation instead of CIs for the variance? Would I get this from the log transformed variance?

All the best,
Odd

Christen Fleming

unread,
Mar 18, 2022, 1:24:20 PMMar 18
to ctmm R user group
Hi Odd,

The two parameters that you need are in the summary() of the UD object - the point estimate and DOF[area]. The gamma relationship is

MEAN = POINT.EST = shape*rate
VAR = POINT.EST^2/DOF = shape*rate^2

and with some algebra (that you are free to check), I get

rate = POINT.EST/DOF
shape = DOF

which you can then plug into base R functions like dgamma().

The standard deviation would be given by sqrt() of the variance above.

If I now understand your previous question, throughout ctmm, I try to use CI formulas that are closest to the true sampling distribution. So for area estimates, I use gamma CIs, which are exact for the IID isotropic case and respect the lower bound of zero area.

Best,
Chris

Odd Jacobson

unread,
Mar 19, 2022, 4:48:30 PMMar 19
to ctmm R user group
Hi Chris,

Thanks for your help. Really appreciate it.

Best,
Odd

Reply all
Reply to author
Forward
0 new messages