conditional_Spearman: Conditional Partial Spearman's Rank Correlation
In PResiduals: Probability-Scale Residuals and Residual Correlations
View source: R/conditional_Spearman.R
conditional_Spearman R Documentation
Conditional Partial Spearman's Rank Correlation
Description
conditional_Spearman computes the partial Spearman's rank
correlation between variable X and variable Y adjusting for
variable Z conditional on Zc. X and Y can be any
orderable variables, including continuous and discrete
variables. Covariate Z can be multidimensional. X, Y,
and Z are specified by the argument ‘formula’. Zc is a
one-dimensional covariate, specified by the argument
‘conditional.by’. The basic approach involves fitting a specified
model of X on Z, a specified model of Y on Z,
obtaining the probability-scale residuals, Xres and Yres, from
both models, and then modeling their Pearson's correlation conditional on
Zc. Different methods are provided to model the Pearson's
correlation between the two sets of probability-scale residuals. See
details in ‘conditional.method’. As in ‘partial.Spearman’, by
default conditional_Spearman uses cumulative link models for both
continous and discrete ordinal variables X and Y to preserve
the rank-based nature of Spearman's correlation. For some specific types
of variables, options of fitting parametric models are also available. See
details in ‘fit.x’ and ‘fit.y’.
Usage
conditional_Spearman(
formula,
conditional.by,
data,
conditional.method = c("lm", "kernel", "stratification"),
conditional.formula = paste("~", conditional.by, sep = ""),
kernel.function = c("normal", "gaussian", "triweight", "quartic", "biweight",
"epanechnikov", "uniform", "triangle"),
kernel.bandwidth = "silverman",
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’.
conditional.by
the name of the variable on which the partial
Spearman's correlation is conditional. See ‘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 conditional_Spearman is called.
conditional.method
the method to be used for modeling conditional
correlation between probability-scale residuals. The default option is
‘lm’, which fits linear regression models for
XresYres on Zc, Xres^2 on Zc, and
Yres^2 on Zc, and then uses the fitted values to compute
the Pearson's correlation between Xres and Yres
conditional on Zc. Other options include ‘kernel’, which
computes correlation between Xres and Yres conditional on
Zc using a kernel weighted method, and ‘stratification’,
which computes the correlation between Xres and Yres
seperately for each value of Zc.
conditional.formula
the formula to be used when
‘conditional.method’ is specified as ‘lm’.
kernel.function
the kernel function to be used when
‘conditional.method’ is specified as ‘kernel’. Defaults to
‘normal’. Other options are ‘triweight’, ‘quartic’,
‘biweight’, ‘epanechnikov’, ‘uniform’, and
‘triangle’.
kernel.bandwidth
the kernel bandwidth to be used when
‘conditional.method’ is specified as ‘kernel’. The default
value is calculated using Silverman' rule. Users can also specify a
positive numeric value.
fit.x, fit.y
the fitting functions used for the model of X or
Y on Z. The default function is ‘orm’, which fits
cumulative link models for continuous or discrete ordinal
variables. Other options include ‘lm’ (fit linear regression
models and obtain the probability-scale residuals by assuming
normality), ‘lm.emp’ (fit linear regression and obtain the
probability-scale residuals by empirical ranking), ‘poisson’ (fit
Poisson models for count variables), ‘nb’ (fit negative binomial
models for count variables), and ‘logistic’ (fit 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’, ‘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 conditional on Zc, ‘formula’ is
specified as X | Y ~ Z and ‘conditional.by’
is specified as Zc. This indicates that models of X ~
Z and Y ~ Z will be fit, and the correlation
between the probability-scale residuals from these two models will be
modeled conditional on Zc.
Value
object of ‘conditional_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.conditional_Spearman,print.conditional_Spearman
Examples
data(PResidData)
library(rms)
#### fitting cumulative link models for both Y and W
result <- conditional_Spearman(c|y~ x + w, conditional.by="w",
conditional.method="lm", conditional.formula="~rcs(w)",
fit.x="poisson",fit.y="orm",
data=PResidData, fisher=TRUE)
plot(result)
PResiduals documentation built on Dec. 16, 2025, 1:07 a.m.
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View source: R/conditional_Spearman.R
| conditional_Spearman | R Documentation |
Conditional Partial Spearman's Rank Correlation
Description
conditional_Spearman computes the partial Spearman's rank
correlation between variable X and variable Y adjusting for
variable Z conditional on Zc. X and Y can be any
orderable variables, including continuous and discrete
variables. Covariate Z can be multidimensional. X, Y,
and Z are specified by the argument ‘formula’. Zc is a
one-dimensional covariate, specified by the argument
‘conditional.by’. The basic approach involves fitting a specified
model of X on Z, a specified model of Y on Z,
obtaining the probability-scale residuals, Xres and Yres, from
both models, and then modeling their Pearson's correlation conditional on
Zc. Different methods are provided to model the Pearson's
correlation between the two sets of probability-scale residuals. See
details in ‘conditional.method’. As in ‘partial.Spearman’, by
default conditional_Spearman uses cumulative link models for both
continous and discrete ordinal variables X and Y to preserve
the rank-based nature of Spearman's correlation. For some specific types
of variables, options of fitting parametric models are also available. See
details in ‘fit.x’ and ‘fit.y’.
Usage
conditional_Spearman(
formula,
conditional.by,
data,
conditional.method = c("lm", "kernel", "stratification"),
conditional.formula = paste("~", conditional.by, sep = ""),
kernel.function = c("normal", "gaussian", "triweight", "quartic", "biweight",
"epanechnikov", "uniform", "triangle"),
kernel.bandwidth = "silverman",
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 |
conditional.by |
the name of the variable on which the partial Spearman's correlation is conditional. See ‘Details’. |
data |
an optional data frame, list or environment (or object
coercible by |
conditional.method |
the method to be used for modeling conditional correlation between probability-scale residuals. The default option is ‘lm’, which fits linear regression models for XresYres on Zc, Xres^2 on Zc, and Yres^2 on Zc, and then uses the fitted values to compute the Pearson's correlation between Xres and Yres conditional on Zc. Other options include ‘kernel’, which computes correlation between Xres and Yres conditional on Zc using a kernel weighted method, and ‘stratification’, which computes the correlation between Xres and Yres seperately for each value of Zc. |
conditional.formula |
the formula to be used when ‘conditional.method’ is specified as ‘lm’. |
kernel.function |
the kernel function to be used when ‘conditional.method’ is specified as ‘kernel’. Defaults to ‘normal’. Other options are ‘triweight’, ‘quartic’, ‘biweight’, ‘epanechnikov’, ‘uniform’, and ‘triangle’. |
kernel.bandwidth |
the kernel bandwidth to be used when ‘conditional.method’ is specified as ‘kernel’. The default value is calculated using Silverman' rule. Users can also specify a positive numeric value. |
fit.x, fit.y |
the fitting functions used for the model of X or Y on Z. The default function is ‘orm’, which fits cumulative link models for continuous or discrete ordinal variables. Other options include ‘lm’ (fit linear regression models and obtain the probability-scale residuals by assuming normality), ‘lm.emp’ (fit linear regression and obtain the probability-scale residuals by empirical ranking), ‘poisson’ (fit Poisson models for count variables), ‘nb’ (fit negative binomial models for count variables), and ‘logistic’ (fit 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’, ‘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 |
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 conditional on Zc, ‘formula’ is
specified as X | Y ~ Z and ‘conditional.by’
is specified as Zc. This indicates that models of X ~
Z and Y ~ Z will be fit, and the correlation
between the probability-scale residuals from these two models will be
modeled conditional on Zc.
Value
object of ‘conditional_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.conditional_Spearman,print.conditional_Spearman
Examples
data(PResidData)
library(rms)
#### fitting cumulative link models for both Y and W
result <- conditional_Spearman(c|y~ x + w, conditional.by="w",
conditional.method="lm", conditional.formula="~rcs(w)",
fit.x="poisson",fit.y="orm",
data=PResidData, fisher=TRUE)
plot(result)
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