This function implements an estimator that correctly handles left hand
side variables that are either numeric or plausible values, allows for survey
sampling weights and estimates variances using the jackknife replication method.
The Statistics vignette describes estimation of the reported statistics.
(Run vignette("statistics", package="EdSurvey") at the R prompt to see the vignette.)
Regardless of the variance estimation, the coefficients are estimated
using the sample weights according to the section titled
“estimation of weighted means when plausible values are not present.”
or the section titled
“estimation of weighted means when plausible values are present.”
depending on if there are assessment variables or variables with plausible values
in them.
How the standard errors of the coefficients are estimated depends on the
value of varMethod and the presence of plausible values (assessment variables),
But, once it is obtained the t statistic
is given by $$t=\frac{\hat{\beta}}{\sqrt{\mathrm{var}(\hat{\beta})}}$$ where
\( \hat{\beta} \) is the estimated coefficient and \(\mathrm{var}(\hat{\beta})\) is
its variance of that estimate. The p-value associated with the coefficient
is then calculated using the number of jackknife replicates as the degrees of freedom.
The coefficient of determination (R-squared value) is similarly estimated by finding
the average R-squared using the sample weights for each set of plausible values.
Variance estimation of coefficients
All variance estimation methods are shown in the “Statistics” vignette.
When varMethod is set to “jackknife” and the predicted
value does not have plausible values, the variance of the coefficients
is estimated according to the section,
“Estimation of standard errors of weighted means when
plausible values are not present, using the jackknife method.”
When plausible values are present and varMethod is “jackknife,” the
the variance of the coefficients is estimated according to the section
“Estimation of standard errors of weighted means when
plausible values are present, using the jackknife method.”
When plausible values are not present and varMethod is “Taylor,” the
the variance of the coefficients is estimated according to the section
“Estimation of standard errors of weighted means when plausible
values are not present, using the Taylor series method.”
When plausible values are present and varMethod is “Taylor,” the
the variance of the coefficients is estimated according to the section
“Estimation of standard errors of weighted means when plausible
values are present, using the Taylor series method.”