NNS.reg: NNS Regression

Description Usage Arguments Value Note Author(s) References Examples

Description

Generates a nonlinear regression based on partial moment quadrant means.

Usage

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NNS.reg(
  x,
  y,
  factor.2.dummy = TRUE,
  order = NULL,
  stn = 0.95,
  dim.red.method = NULL,
  tau = NULL,
  type = NULL,
  point.est = NULL,
  location = "top",
  return.values = TRUE,
  plot = TRUE,
  plot.regions = FALSE,
  residual.plot = TRUE,
  std.errors = FALSE,
  confidence.interval = NULL,
  threshold = 0,
  n.best = NULL,
  noise.reduction = "off",
  dist = "L2",
  ncores = NULL,
  point.only = FALSE,
  multivariate.call = FALSE
)

Arguments

x

a vector, matrix or data frame of variables of numeric or factor data types.

y

a numeric or factor vector with compatible dimensions to x.

factor.2.dummy

logical; TRUE (default) Automatically augments variable matrix with numerical dummy variables based on the levels of factors.

order

integer; Controls the number of partial moment quadrant means. Users are encouraged to try different (order = ...) integer settings with (noise.reduction = "off"). (order = "max") will force a limit condition perfect fit.

stn

numeric [0, 1]; Signal to noise parameter, sets the threshold of (NNS.dep) which reduces ("order") when (order = NULL). Defaults to 0.95 to ensure high dependence for higher ("order") and endpoint determination.

dim.red.method

options: ("cor", "NNS.dep", "NNS.caus", "all", numeric vector, NULL) method for determining synthetic X* coefficients. Selection of a method automatically engages the dimension reduction regression. The default is NULL for full multivariate regression. (dim.red.method = "NNS.dep") uses NNS.dep for nonlinear dependence weights, while (dim.red.method = "NNS.caus") uses NNS.caus for causal weights. (dim.red.method = "cor") uses standard linear correlation for weights. (dim.red.method = "all") averages all methods for further feature engineering. Alternatively, user can specify a numeric vector of coefficients.

tau

options("ts", NULL); NULL(default) To be used in conjunction with (dim.red.method = "NNS.caus") or (dim.red.method = "all"). If the regression is using time-series data, set (tau = "ts") for more accurate causal analysis.

type

NULL (default). To perform a classification, set to (type = "CLASS"). Like a logistic regression, it is not necessary for target variable of two classes e.g. [0, 1].

point.est

a numeric or factor vector with compatible dimensions to x. Returns the fitted value y.hat for any value of x.

location

Sets the legend location within the plot, per the x and y co-ordinates used in base graphics legend.

return.values

logical; TRUE (default), set to FALSE in order to only display a regression plot and call values as needed.

plot

logical; TRUE (default) To plot regression.

plot.regions

logical; FALSE (default). Generates 3d regions associated with each regression point for multivariate regressions. Note, adds significant time to routine.

residual.plot

logical; TRUE (default) To plot y.hat and Y.

std.errors

logical; FALSE (default) To provide standard errors of each linear segment in the "Fitted.xy" output.

confidence.interval

numeric [0, 1]; NULL (default) Plots the associated confidence interval with the estimate and reports the standard error for each individual segment.

threshold

numeric [0, 1]; (threshold = 0) (default) Sets the threshold for dimension reduction of independent variables when (dim.red.method) is not NULL.

n.best

integer; NULL (default) Sets the number of nearest regression points to use in weighting for multivariate regression at sqrt(# of regressors). (n.best = "all") will select and weight all generated regression points. Analogous to k in a k Nearest Neighbors algorithm. Different values of n.best are tested using cross-validation in NNS.stack.

noise.reduction

the method of determining regression points options: ("mean", "median", "mode", "off"); In low signal:noise situations,(noise.reduction = "mean") uses means for NNS.dep restricted partitions, (noise.reduction = "median") uses medians instead of means for NNS.dep restricted partitions, while (noise.reduction = "mode") uses modes instead of means for NNS.dep restricted partitions. (noise.reduction = "off") uses an overall central tendency measure for partitions.

dist

options:("L1", "L2", "DTW", "FACTOR") the method of distance calculation; Selects the distance calculation used. dist = "L2" (default) selects the Euclidean distance and (dist = "L1") seclects the Manhattan distance; (dist = "DTW") selects the dynamic time warping distance; (dist = "FACTOR") uses a frequency.

ncores

integer; value specifying the number of cores to be used in the parallelized procedure. If NULL (default), the number of cores to be used is equal to the number of cores of the machine - 1.

point.only

Internal argument for abbreviated output.

multivariate.call

Internal argument for multivariate regressions.

Value

UNIVARIATE REGRESSION RETURNS THE FOLLOWING VALUES:

MULTIVARIATE REGRESSION RETURNS THE FOLLOWING VALUES:

Note

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp

Vinod, H. and Viole, F. (2017) "Nonparametric Regression Using Clusters" https://link.springer.com/article/10.1007/s10614-017-9713-5

Vinod, H. and Viole, F. (2018) "Clustering and Curve Fitting by Line Segments" https://www.preprints.org/manuscript/201801.0090/v1

Examples

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## Not run: 
set.seed(123)
x <- rnorm(100) ; y <- rnorm(100)
NNS.reg(x, y)

## Manual {order} selection
NNS.reg(x, y, order = 2)

## Maximum {order} selection
NNS.reg(x, y, order = "max")

## x-only paritioning (Univariate only)
NNS.reg(x, y, type = "XONLY")

## For Multiple Regression:
x <- cbind(rnorm(100), rnorm(100), rnorm(100)) ; y <- rnorm(100)
NNS.reg(x, y, point.est = c(.25, .5, .75))

## For Multiple Regression based on Synthetic X* (Dimension Reduction):
x <- cbind(rnorm(100), rnorm(100), rnorm(100)) ; y <- rnorm(100)
NNS.reg(x, y, point.est = c(.25, .5, .75), dim.red.method = "cor")

## IRIS dataset examples:
# Dimension Reduction:
NNS.reg(iris[,1:4], iris[,5], dim.red.method = "cor", order = 5)

# Dimension Reduction using causal weights:
NNS.reg(iris[,1:4], iris[,5], dim.red.method = "NNS.caus", order = 5)

# Multiple Regression:
NNS.reg(iris[,1:4], iris[,5], order = 2, noise.reduction = "off")

# Classification:
NNS.reg(iris[,1:4], iris[,5], point.est = iris[1:10, 1:4], type = "CLASS")$Point.est

## To call fitted values:
x <- rnorm(100) ; y <- rnorm(100)
NNS.reg(x, y)$Fitted

## To call partial derivative (univariate regression only):
NNS.reg(x, y)$derivative
## End(Not run)

NNS documentation built on June 26, 2021, 1:07 a.m.