LMMstar (version 1.1.0)

partialCor: Partial Correlation

Description

Estimate the partial correlation based on equation 19 of Lloyd et al 2008 (partialCor.lmm) or explicitely modeling the correlation via a linear mixed model (partialCor.list, partialCor.formula). The first option is numerically more efficient and exact with a single observation per cluster. With multiple repetitions, what is being estimated with the first option may not be clear and the second option is therefore preferrable.

Usage

partialCor(object, ...)
# S3 method for list
partialCor(
  object,
  data,
  repetition = NULL,
  structure = NULL,
  by = NULL,
  effects = NULL,
  rhs = NULL,
  method = "none",
  df = NULL,
  transform.rho = NULL,
  name.short = c(TRUE, FALSE),
  ...
)
# S3 method for formula
partialCor(object, repetition, ...)
# S3 method for lmm
partialCor(object, level = 0.95, R2 = FALSE, se = TRUE, df = TRUE, ...)

Value

A data.frame with the estimate partial correlation (rho), standard error, degree of freedom, confidence interval, and p-value (test of no correlation). When structure="CS" or structure="HCS" is used with repeated measurements, a second correlation coefficient (r) is output where the between subject variance has been removed (similar to Bland et al. 1995).

Arguments

object

a formula with in the left hand side the variables for which the correlation should be computed and on the right hand side the adjustment set. Can also be a list of formula for outcome-specific adjustment set.

...

arguments passed to confint for partialCor.list and partialCor.formula. Not used for partialCor.lmm.

data

[data.frame] dataset containing the variables.

repetition

[formula] Specify the structure of the data: the time/repetition variable and the grouping variable, e.g. ~ time|id.

structure

[character] Specify the residual variance-covariance structure. Without repetitions, either "UN" or "CS". With repetitions, one of "UN", "PEARSON", "HLAG", "LAG", "HCS", "CS".

by

[character] variable used to stratified the correlation on.

effects

[character or matrix] type of contrast to be used for comparing the correlation parameters. One of "Dunnett", "Tukey", "Sequen", or a contrast matrix.

rhs

[numeric vector] right hand side for the comparison of correlation parameters.

method

[character] adjustment for multiple comparisons (e.g. "single-step").

df

[logical] Should a Student's t-distribution be used to model the distribution of the coefficient. Otherwise a normal distribution is used.

transform.rho

[character] scale on which perform statistical inference (e.g. "atanh")

name.short

[logical vector of length 2] use short names for the output coefficients (omit the name of the by variable, omit name of the correlation parameter)

level

[numeric,0-1] the confidence level of the confidence intervals.

R2

[logical] Should the R2 (coefficient of determination) be computed?

se

[logical] Should the uncertainty about the partial correlation be evaluated? Only relevant for partialCor.lmm.

Details

Fit a mixed model to estimate the partial correlation with the following variance-covariance pattern:

• no repetition: unstructure or compound symmetry structure for M observations, M being the number of variables on the left hand side (i.e. outcomes).

• repetition: structure for M*T observations where M being the number of variables (typically 2) and T the number of repetitions. Can be

  • "UN": unstructured (except the off-diagonal containing the correlation parameter which is constant).

  • "PEARSON": same as unstructured except it only uses a single variance parameter per variable, i.e. it assumes constant variance over repetitions.

  • "HLAG": toeplitz by block with variable and repetition specific variance.

  • "LAG": toeplitz by block, i.e. correlation depending on the gap between repetitions and specific to each variable. It assumes constant variance over repetitions.

  • "HCS": heteroschedastic compound symmetry by block, i.e. variable specific correlation constant over repetitions. A specific parameter is used for the off-diagonal crossing the variables at the same repetition (which is the marginal correlation parameter).

  • "CS": compound symmetry by block. It assumes constant variance and correlation over repetitions.

References

Bland J M, Altman D G. Statistics notes: Calculating correlation coefficients with repeated observations: Part 1—correlation within subjects BMJ 1995; 310 :446 doi:10.1136/bmj.310.6977.446 Edwards, L.J., Muller, K.E., Wolfinger, R.D., Qaqish, B.F. and Schabenberger, O. (2008), An R2 statistic for fixed effects in the linear mixed model. Statist. Med., 27: 6137-6157. https://doi.org/10.1002/sim.3429

Examples

#### no repetition ####

## example from ppcor::pcor 
y.data <- data.frame(
  hl=c(7,15,19,15,21,22,57,15,20,18),
  disp=c(0.000,0.964,0.000,0.000,0.921,0.000,0.000,1.006,0.000,1.011),
  deg=c(9,2,3,4,1,3,1,3,6,1),
  BC=c(1.78e-02,1.05e-06,1.37e-05,7.18e-03,0.00e+00,0.00e+00,0.00e+00
,  4.48e-03,2.10e-06,0.00e+00)
)
## ppcor::pcor(y.data)

## partial correlation based on a formula
partialCor(c(hl,disp)~BC+deg, data = y.data)
partialCor(hl + disp~BC+deg, data = y.data)
## partial correlation based on a list
partialCor(list(hl~BC+deg,disp~BC+deg), data = y.data)
## via an existing model
e.lm <- lmm(hl~disp+BC+deg, data = y.data)
partialCor(e.lm)

## using a different set of covariates for outcome
partialCor(list(hl~BC+deg, disp~BC), data = y.data)

## statified correlation (using another dataset)
data(gastricbypassW, package = "LMMstar")
gastricbypassW$weight.bin <- gastricbypassW$weight1>=120
partialCor(glucagonAUC1+glucagonAUC2~1, data = gastricbypassW, by = "weight.bin")

## compared correlation between groups
partialCor(glucagonAUC1+glucagonAUC2~1, data = gastricbypassW, by = "weight.bin",
           effects = "Dunnett") 

#### with repetitions ####
if (FALSE) {
data(gastricbypassL, package = "LMMstar")
## via a mixed model
eUN.lmm <- lmm(weight ~ glucagonAUC+time, repetition =~time|id,
               data = gastricbypassL, structure = "UN")
partialCor(eUN.lmm)

## mean: variable and timepoint specific mean parameter (8)
## variance: variable and timepoint specific variance parameter (8)
## correlation: correlation parameter specific for each variable and time lag (10)
e.cor <- partialCor(weight+glucagonAUC~time, repetition =~time|id,
                    data = gastricbypassL, structure = "LAG")
e.cor
coef(attr(e.cor,"lmm"), effects = "correlation")
if(require(ggplot2)){
autoplot(e.cor)
}

## same except for the mean structure: variable specific mean parameter (2)
e.cor2 <- partialCor(weight+glucagonAUC~time, repetition =~time|id,
                    data = gastricbypassL, structure = "LAG")

## mean: variable and timepoint specific mean parameter (8)
## variance: variable specific variance parameter (2)
## correlation: correlation parameter specific for each variable and some time lag (4)
e.cor3 <- partialCor(weight+glucagonAUC~time, repetition =~time|id,
                     data = gastricbypassL, structure = "CS")
e.cor3
coef(attr(e.cor3,"lmm"), effects = "correlation")
if(require(ggplot2)){
autoplot(e.cor3)
}

}