translate {jocre}

Conversion of confidence levels between intervals and ellipses

Description

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.

Usage

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.

Value

A numeric value giving the calculated confidence level.

Author(s)

Philip Pallmann ([e-mail])

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.

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")