Calculate marginal correlations with response, from a funeigen object

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Description

A function for internal use. Its main job is to be called by MarginalCor, and do the technical work for calculating estimated marginal correlations. It uses R. A. Fisher's classic r-to-z transform to create confidence intervals for the correlations. This process is explained in easy-to-follow detail by David Shen and Zaizai Lu in a technical report.

Usage

1
marginal.cor.funeigen(object, id, response, alpha = 0.05)

Arguments

object

An object of type funeigen.

id

The vector of subject id's. These tell which responses in response correspond to which curves in object.

response

The vector of responses

alpha

The alpha level for confidence intervals (one minus the two-sided coverage)

Value

Returns a data.frame with four columns. The first, time, is the time index of the rows. That is, it is a grid of points t along the time axis and these points correspond to the rows. The next three are the lower bound, best estimate, and upper bound, of the correlation between the smoothed value of the covariate x(t) and the response y at each of the time points t. We refer to the correlation function estimated here as marginal because it ignores any other functional covariates (rather than trying to adjust or control for them).

Note

The confidence intervals are simply based on Fisher's r-to-z transform and do not take into account the uncertainty in estimating the smoothed value of x(t).

References

Shen, D., and Lu, Z. (2006). Computation of correlation coefficient and its confidence interval in SAS (r). SUGI 31 (March 26-29, 2006), paper 170-31. Available online at http://www2.sas.com/proceedings/sugi31/170-31.pdf.