partial_Spearman {PResiduals}

Partial Spearman's Rank Correlation

Description

partial_Spearman computes the partial Spearman's rank correlation between variable X and variable Y adjusting for other variables, Z. The basic approach involves fitting a specified model of X on Z, a specified model of Y on Z, obtaining the probability-scale residuals from both models, and then calculating their Pearson's correlation. X and Y can be any orderable variables, including continuous or discrete variables. By default, partial_Spearman uses cumulative probability models (also referred as cumulative link models in literature) for both X on Z and Y on Z to preserve the rank-based nature of Spearman's correlation, since the model fit of cumulative probability models only depends on the order information of variables. However, for some specific types of variables, options of fitting parametric models are also available. See details in fit.x and fit.y

Usage

partial_Spearman(
  formula,
  data,
  fit.x = "orm",
  fit.y = "orm",
  link.x = c("logit", "probit", "cloglog", "loglog", "cauchit", "logistic"),
  link.y = c("logit", "probit", "cloglog", "loglog", "cauchit", "logistic"),
  subset,
  na.action = getOption("na.action"),
  fisher = TRUE,
  conf.int = 0.95
)

Arguments

formula

an object of class Formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which partial_Spearman is called.

fit.x, fit.y

the fitting functions used for the models of X or Y on Z. The default function is ‘⁠orm⁠’, which fits cumulative probability models for continuous or discrete ordinal variables. Other options include ‘⁠lm⁠’, which fits linear regression models and obtains the probability-scale residuals by assuming normality; ‘⁠lm.emp⁠’, which fits linear regression models and obtains the probability-scale residuals by empirical ranking; ‘⁠poisson⁠’, which fits Poisson models for count variables; ‘⁠nb⁠’, which fits negative binomial models for count variables; and ‘⁠logistic⁠’, which fits logistic regression models for binary variables.

link.x, link.y

the link family to be used for the ordinal model of X on Z. Defaults to ‘⁠logit⁠’. Other options are ‘⁠probit⁠’, ‘⁠cloglog⁠’, ‘⁠loglog⁠’, ‘⁠cauchit⁠’ and ‘⁠logistic⁠’ (equivalent with ‘⁠logit⁠’). Used only when ‘⁠fit.x⁠’ is ‘⁠orm⁠’.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

action to take when NA present in data.

fisher

logical indicating whether to apply fisher transformation to compute confidence intervals and p-values for the correlation.

conf.int

numeric specifying confidence interval coverage.

Details

To compute the partial Spearman's rank correlation between X and Y adjusting for Z, ‘⁠formula⁠’ is specified as X | Y ~ Z. This indicates that models of X ~ Z and Y ~ Z will be fit.

Value

object of ‘⁠partial_Spearman⁠’ class.

References

Li C and Shepherd BE (2012) A new residual for ordinal outcomes. Biometrika. 99: 473–480.

Shepherd BE, Li C, Liu Q (2016) Probability-scale residuals for continuous, discrete, and censored data. The Canadian Jouranl of Statistics. 44:463–476.

Liu Q, Shepherd BE, Wanga V, Li C (2018) Covariate-Adjusted Spearman's Rank Correlation with Probability-Scale Residuals. Biometrics. 74:595–605.

See Also

print.partial_Spearman

Examples

data(PResidData)
#### fitting cumulative probability models for both Y and W
partial_Spearman(c|w ~ z,data=PResidData)
#### fitting a cumulative probability model for W and a poisson model for c
partial_Spearman(c|w~z, fit.x="poisson",data=PResidData)
partial_Spearman(c|w~z, fit.x="poisson", fit.y="lm.emp", data=PResidData )