2
$\begingroup$

I have paired cobalt concentrations in bird blood and feathers. Blood levels give me an idea of how recent the cobalt exposure was (<30days), feather give the 6 month accumulated total. Previous investigators defined the relationship between blood and feathers by combining populations of birds whose cobalt exposure is low-constant, med-constant, and high-constant (all within bounds of cobalt levels of healthy normal birds). They used OLS blood~feathers to define the "normal" physiological cobalt relationship and then plotted individual blood and feather levels obtained from birds that had recently arrived at a contaminated site. These birds had much higher blood values but much lower feather values than predicted by the OLS (outside the OLS prediction interval). Since there is a difference in the sampling and analytical error for each of these tissues (feather errors are more than 4x the blood errors) I considered using Demming or total least squares RMA regression. In order to identify individual birds whose paired blood and feather values are outside the model I would have liked to rely on the prediction intervals. Would a better, or equally adequate alternative be using quantile regression and use the t 0.75 and t 0.25 lines as an approximation of the prediction interval?

Here's an example using Deming regression in GraphPad Prism:blue dots (constant exposure) are used to generate the regression line, the difference in error measurements between x and y are clear, the red individuals are superimposed for comparison against the constant exposure. I'd like to set a boundary around the regression line that predicts where any future constant exposures will exist (prediction interval) but takes into the consideration the error around X and Y measurements. enter image description here

$\endgroup$
2
  • $\begingroup$ I don't quite understand what you are trying to do. What are the dependent and independent variables and what is the goal of the analysis? $\endgroup$
    – Peter Flom
    May 18 '16 at 12:48
  • $\begingroup$ Under constant exposure, the relationship between blood and feathers is linear. It's really just a ratio of the concentrations, described best by a linear regression. If exposed to a sudden pulse, we expect a deviation from that ratio. I'd like to identify those individuals graphically, as points that deviate from the linear regression line. If the blood and feather levels of that individual are in a position outside the linear regression prediction interval then I would be confident in saying that the exposure was truly outside the norm. Does that clarify? $\endgroup$
    – user95572
    May 18 '16 at 13:01
0
$\begingroup$

Given the comment, I think what you want to do is probably look at the outliers and high leverage points from a linear regression. That would identify the points you mention.

If you are also interested in modeling this, and whether it is related to the presence of a pulse, then the dependent variable becomes some measure of distance from the regression line and the independent variable would be presence/absence of a pulse.

$\endgroup$
2
  • $\begingroup$ Can high leverage be calculated on new data points that are not used in the linear regression? I thought that Cook's D (very new to this) identified influential points that are being used in the regression. $\endgroup$
    – user95572
    May 18 '16 at 14:10
  • $\begingroup$ If they are new points, you can still calculate various distances from the regression line. It may not be as automated but there is no reason it can't be done. The formulas for the various distances are available. $\endgroup$
    – Peter Flom
    May 18 '16 at 14:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.