translate function

Conversion of confidence levels between intervals and ellipses

Translates the confidence level of a joint 100(1 -- alpha)% confidence ellipse into that of the corresponding marginal confidence interval when projecting the ellipse's boundary onto the axes. Also does the "inverse operation" i.e., calculates the confidence level of a joint confidence ellipse so that its perpendicular shadows onto the axes are 100(1 -- alpha)% confidence intervals.

translate(level=0.95, ddf, direction)

Arguments

• level: A numeric value giving the confidence level.
• ddf: An integer specifying the denominator degrees of freedom. Setting this to 0 enforces an asymptotic computation.
• direction: A character string indicating what is to be computed. Choose either ci2cr or cr2ci (see details).

Details

Setting direction="ci2cr" calculates the confidence level of a confidence interval generating ellipse (CIGE) whose perpendicular shadows onto the axes are 100(1 -- alpha)% confidence intervals with a marginal confidence level (1 -- alpha) as specified in level; see p. 205 of Fox (2008).

On the other hand, setting direction="cr2ci" computes the marginal confidence level of the intervals obtained by projecting a joint 100(1 -- alpha)% confidence ellipse with (1 -- alpha) as specified in level; see p. 254 of Monette (1990). These marginal intervals can be viewed as including a Scheffe penalty (Scheffe 1953).

For ddf=0 the F-distribution used for calculating the confidence levels is replaced with an asymptotic chi-square distribution.

Returns

A numeric value giving the calculated confidence level.

References

John Fox (2008) Applied Linear Regression and Generalized Linear Models. Second Edition. SAGE, Thousand Oaks, CA.

Georges Monette (1990). Geometry of multiple regression and interactive 3-D graphics. In: John Fox & J. Scott Long (eds.) Modern Methods of Data Analysis. SAGE, Newbury Park, CA.

Henry Scheffe (1953) A method for judging all contrasts in the analysis of variance. Biometrika, 40(1--2), 87--104.

Author(s)

Philip Pallmann (p.pallmann@lancaster.ac.uk )

Examples

# Get CIGE level
translate(0.95, ddf=1, "ci2cr")
translate(0.95, ddf=9999, "ci2cr")
translate(0.95, ddf=0, "ci2cr")

# Get Scheffe CI level
translate(0.95, ddf=1, "cr2ci")
translate(0.95, ddf=9999, "cr2ci")
translate(0.95, ddf=0, "cr2ci")