[Package car/data.ellipse]: confidence intervals off by factor sqrt(2)??? (PR#2584)

Full_Name: Volker Franz
Version: Version 1.6.2  (2003-01-10)
OS: Debian
Submission from: (NULL) (192.124.28.104)


Hi there,

it seems to me that data.ellipse of package "car" (Version 1.0-1)
produces confidence interval's which are too big. To see this, do:

library(car)
plot(c(-2,2),c(-2,2),pch=0)
data.ellipse(rnorm(10000),rnorm(10000),levels=0.68,plot.points=F)
abline(v=+1)
abline(v=-1)
abline(h=+1)
abline(h=-1)

To my knowledge, this should result in a circle with radius
1. However, the circle is larger. It seems that the problem is due to
an erroneous specification of the degrees of freedom and can be fixed
with the following patch:

======================================================================
--- Ellipse.R   Wed Feb 26 17:49:43 2003
+++ Ellipse.orig        Thu Sep 19 18:20:41 2002
@@ -34,7 +34,7 @@
         stop("x and y must be vectors of the same length")
     if (plot.points & !add) plot(x, y, xlab=xlab, ylab=ylab, col=col, 
pch=pch,
las=las, ...)
     if (plot.points & add) points(x, y, col=col, pch=pch, ...)
-    dfn<-1
+    dfn<-2
     dfd<-length(x)-1
     if (robust) {
         require(MASS)
======================================================================

Or --- am I totally on the wrong track here?

Best
Volker

"JF" == John Fox <jfox@mcmaster.ca> writes:

Hi John,

"JF" == John Fox <jfox@mcmaster.ca> writes:

    JF> Dear Volker, If the data ellipse (or, in this case, circle) is
    JF> scaled so that its shadows (projections) on the axes each
    JF> includes 68% of the data (that is of the marginal distribution
    JF> of each variable), then the ellipse will include less than 68%
    JF> of the data (i.e., of the joint distribution of the two
    JF> variables). Conversely, to include 68% of the data in the
    JF> ellipse, the shadows of the ellipse have to be larger.
    JF> Did I understand your point correctly?

I am not sure. I will try to rephrase my initial request:

Let X by a one--dimensional random variable (standard normal
distribution; mean=0; std=1). The 68% confidence intervall of X will
approximately be: [-1,1]. Now, if I combine X with a stochastically
independent second random variable Y, the marginal distribution of X
should not change. Therefore, the projections of the error ellipse on
the X--axis should still be: [-1,1].

Hi John,

"JF" == John Fox <jfox@mcmaster.ca> writes:

    JF> Dear Volker, If the data ellipse (or, in this case, circle) is
    JF> scaled so that its shadows (projections) on the axes each
    JF> includes 68% of the data (that is of the marginal distribution
    JF> of each variable), then the ellipse will include less than 68%
    JF> of the data (i.e., of the joint distribution of the two
    JF> variables). Conversely, to include 68% of the data in the
    JF> ellipse, the shadows of the ellipse have to be larger.
    JF> Did I understand your point correctly?

I am not sure. I will try to rephrase my initial request:

Let X by a one--dimensional random variable (standard normal
distribution; mean=0; std=1). The 68% confidence intervall of X will
approximately be: [-1,1]. Now, if I combine X with a stochastically
independent second random variable Y, the marginal distribution of X
should not change. Therefore, the projections of the error ellipse on
the X--axis should still be: [-1,1].

If I do this with the function data.ellipse:

   data.ellipse(rnorm(10000),rnorm(10000),levels=0.68,plot.points=F)

I get a projection on the X-axis which is larger than [-1,1]. In fact,
it is a little bit larger than [-sqrt(2),+sqrt(2)].

My interpretation is that this is due to the construction of the
radius in data.ellipse:

   dfn<-2
   radius <- sqrt ( dfn * qf(level, dfn, dfd ))

I would expect a dfn<-1 here (such that the radius would correspond to
the t-distribution).

Does this make sense?