Regression {s2dv}

Compute the regression of an array on another along one dimension.

Description

Compute the regression of the array 'datay' on the array 'datax' along the 'reg_dim' dimension by least square fitting (default) or self-defined model. The function provides the slope of the regression, the intercept, and the associated p-value and confidence interval. The filtered datay from the regression onto datax is also provided.
The p-value relies on the F distribution, and the confidence interval relies on the student-T distribution.

Usage

Regression(
  datay,
  datax,
  reg_dim = "sdate",
  formula = y ~ x,
  pval = TRUE,
  conf = TRUE,
  sign = FALSE,
  alpha = 0.05,
  na.action = na.omit,
  ncores = NULL
)

Arguments

datay

An numeric array as predictand including the dimension along which the regression is computed.

datax

An numeric array as predictor. The dimension should be identical as parameter 'datay'.

reg_dim

A character string indicating the dimension along which to compute the regression. The default value is 'sdate'.

formula

An object of class "formula" (see function link[stats]{lm}).

pval

A logical value indicating whether to retrieve the p-value or not. The default value is TRUE.

conf

A logical value indicating whether to retrieve the confidence intervals or not. The default value is TRUE.

sign

A logical value indicating whether to compute or not the statistical significance of the test The default value is FALSE.

alpha

A numeric of the significance level to be used in the statistical significance test. The default value is 0.05.

na.action

A function or an integer. A function (e.g., na.omit, na.exclude, na.fail, na.pass) indicates what should happen when the data contain NAs. A numeric indicates the maximum number of NA position (it counts as long as one of datay and datax is NA) allowed for compute regression. The default value is na.omit-

ncores

An integer indicating the number of cores to use for parallel computation. Default value is NULL.

Value

A list containing:

$regression

A numeric array with same dimensions as parameter 'datay' and 'datax' except the 'reg_dim' dimension, which is replaced by a 'stats' dimension containing the regression coefficients from the lowest order (i.e., intercept) to the highest degree. The length of the 'stats' dimension should be polydeg + 1.

$conf.lower

A numeric array with same dimensions as parameter 'daty' and 'datax' except the 'reg_dim' dimension, which is replaced by a 'stats' dimension containing the lower value of the siglev% confidence interval for all the regression coefficients with the same order as $regression. The length of 'stats' dimension should be polydeg + 1. Only present if conf = TRUE.

$conf.upper

A numeric array with same dimensions as parameter 'daty' and 'datax' except the 'reg_dim' dimension, which is replaced by a 'stats' dimension containing the upper value of the siglev% confidence interval for all the regression coefficients with the same order as $regression. The length of 'stats' dimension should be polydeg + 1. Only present if conf = TRUE.

$p.val

A numeric array with same dimensions as parameter 'daty' and 'datax' except the 'reg_dim' dimension, The array contains the p-value.

sign

A logical array of the statistical significance of the regression with the same dimensions as $regression. Only present if sign = TRUE.

$filtered

A numeric array with the same dimension as paramter 'datay' and 'datax', the filtered datay from the regression onto datax along the 'reg_dim' dimension.

Examples

# Load sample data as in Load() example:
example(Load)
datay <- sampleData$mod[, 1, , ]
names(dim(datay)) <- c('sdate', 'ftime')
datax <- sampleData$obs[, 1, , ]
names(dim(datax)) <- c('sdate', 'ftime')
res1 <- Regression(datay, datax, formula = y~poly(x, 2, raw = TRUE))
res2 <- Regression(datay, datax, alpha = 0.1)