DoFCorrection: Degrees of Freedom

Description

Calculates the degrees of freedom for a statistic (or of a contrast between two statistics) based on the jackknife and imputation variance estimates.

Usage

DoFCorrection(
  varEstA,
  varEstB = varEstA,
  varA,
  varB = varA,
  method = c("WS", "JR")
)

Value

numeric; the estimated degrees of freedom

Arguments

varEstA: the varEstInput object returned from certain functions, such as lm.sdf when returnVarEstInputs=TRUE). The variable varA must be on this dataset. See Examples.
varEstB: similar to the varEstA argument. If left blank, both are assumed to come from varEstA. When set, the degrees of freedom are for a contrast between varA and varB, and the varB values are taken from varEstB.
varA: a character that names the statistic in the varEstA argument for which the degrees of freedom calculation is required.
varB: a character that names the statistic in the varEstB argument for which a covariance is required. When varB is specified, returns the degrees of freedom for the contrast between varA and varB.
method: a character that is either WS for the Welch-Satterthwaite formula or JR for the Johnson-Rust correction to the Welch-Satterthwaite formula

Author

Paul Bailey

Details

This calculation happens under the notion that statistics have little variance within strata, and some strata will contribute fewer than a full degree of freedom.

The functions are not vectorized, so both varA and varB must contain exactly one variable name.

The method used to compute the degrees of freedom is in the vignette titled Statistical Methods Used in EdSurvey section “Estimation of Degrees of Freedom.”

References

Johnson, E. G., & Rust, K. F. (1992). Population inferences and variance estimation for NAEP data. Journal of Educational Statistics, 17, 175--190.

Examples

Run this code

if (FALSE) {
sdf <- readNAEP(system.file("extdata/data", "M36NT2PM.dat", package="NAEPprimer"))
lm1 <- lm.sdf(composite ~ dsex + b017451, sdf, returnVarEstInputs=TRUE)
summary(lm1)
# this output agrees with summary of lm1 coefficient for dsex
DoFCorrection(lm1$varEstInputs,
              varA="dsexFemale",
              method="JR")
# second example, a covariance term requires more work
# first, estimate the covariance between two regression coefficients
# note that the variable names are parallel to what they are called in lm1 output
covFEveryDay <- varEstToCov(lm1$varEstInputs,
                            varA="dsexFemale",
                            varB="b017451Every day",
                            jkSumMultiplier=EdSurvey:::getAttributes(sdf, "jkSumMultiplier"))
# second, find the difference and the SE of the difference
se <- lm1$coefmat["dsexFemale","se"] + lm1$coefmat["b017451Every day","se"] +
      -2*covFEveryDay
# third, calculate the t-statistic
tv <- (coef(lm1)["dsexFemale"] - coef(lm1)["b017451Every day"])/se
# fourth, calculate the p-value, which requires the estimated degrees of freedom
dofFEveryDay <- DoFCorrection(lm1$varEstInputs,
                              varA="dsexFemale",
                              varB="b017451Every day",
                              method="JR")
# finally, the p-value
2*(1-pt(abs(tv), df=dofFEveryDay))
}

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