Distribution of Area Estimates

[Odd Jacobson]

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]

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]

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]

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]

Hi Chris,

Thanks for your help. Really appreciate it.

Best,

Odd