Title: | Detection of Outliers in Circular-Circular Regression |
---|---|
Description: | Detection of outliers in circular-circular regression models, modifying its and estimating of models parameters. |
Authors: | Azade Ghazanfarihesari, Majid Sarmad- Ferdowsi University Of Mashhad |
Maintainer: | Azade Ghazanfarihesari <[email protected]> |
License: | GPL (>= 2) |
Version: | 3.2.3 |
Built: | 2024-12-14 06:34:56 UTC |
Source: | CRAN |
The data used in here, obtained by using Monte-Carlo simulation method.
data("DMCE")
data("DMCE")
A simulation study is carried out to find the percentile (cut-off) point of DMCE by using Monte-
Carlo methods. Fifteen different sample sizes are used, namely n = 10, . . . , 150. For each
sample size n, a set of random circular errors is generated from the von Mises distribution with
mean direction 0 and various values of concentration parameter k = 1, 2, . . . , 100. Samples
of von Mises distribution VM(/4, 10) with corresponding size n are generated to represent the
values of X variable. The parameters of model
(mod 2
)
(i=1,2,...,n) are fixed at
=0 and
=1. Observed values
of the response variable y are calculated based on model
(mod 2
)
(i=1,2,...,n) and subsequently the fitted values Y
are obtained. We then compute the value of the MCE statistic for full data set. Sequentially, we
exclude the ith observation from the generated sample, where i = 1, . . . , n. We refit the reduced
data using model
(mod 2
) (i=1,2,...,n)
and then calculate the values of MCe. Then, we obtain the value of DMCE.
The process is carried out 2000 times for each combination of sample size n and concentration
parameter k.
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detecting of outliers in simple circular regression models using the mean circular error statistics.
This function calculates the absolute values of the difference between the values of MCE and MCe statistic. Then, it draws the scatter plot of them and estimates the concentration parameter of k. Given the sample size and the estimated value of K, cut-off point from the table DMCE in the significance level of 0.05 or 0.1 will be found. Outliers are locatedon the top of teh line corresponding to the cut-off point.
DMCEE(x, y, b)
DMCEE(x, y, b)
x |
independent variable on model |
y |
the response variable on model |
b |
the level of significance (0.05 or 0.1) |
The ith observation is identified as an outlier if the absolute values of the difference between the values of MCE and MCe statistic exceeds a pre-specified cut-off point.
Azade Ghazanfarihesari, Majid Sarmad
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection of outliers in simple circular regression models using the mean circular error statistics
circular, CircStats
data(wind2) DMCEE(wind2[,1], wind2[,2], .9)
data(wind2) DMCEE(wind2[,1], wind2[,2], .9)
This function is used to identify outliers in circular data sets. and with do the procedure Huberized on this outliers, the results improve. Huberizing the outliers will improve the results. circular and sd.circular are mean and standard deviation of circular data.
Huberized(t)
Huberized(t)
t |
circular data set which contains suspected outliers. |
In this method, we progressively transform the original data by a process called winsorisation. Assume that we have initial estimates called m,s. (These coulde evaluated as mean and standard deviation.) If a value falls above
m+(1.5*s) then we change it to
.
Likewise if a value falls below m-(1.5*s) then we change it to
. We then
calculate an improved estimate of mean as m1=mean.circular(
), and of the standard deviation as s1=1.134*(sd.circular(
)).(The factor 1.134 is derived
from the normal distribution, given a value 1.5 for the multiplier most often used in the winsorisation process.) (see the first reference)
Two plot and four number
a list containing the following values:
plot1 |
plot data set when exist outlier. |
plot2 |
plot data set after modified outlier. |
m |
mean.circular when exist outlier. |
m1 |
mean.circular after modified outlier. |
s |
sd.circular when exist outlier. |
s1 |
sd.circular after modified outlier. |
Azade Ghazanfarihesari, Majid Sarmad
Analytical Methods Committe, Robust statistics: a method coping with outliers, Royal Society of Chemistry 2001, amc technical brief.
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detecting of outliers in simple circular regression models using the mean circular error statistics.
circular, CircStats
data(wind) Huberized(wind)
data(wind) Huberized(wind)
Removal of the ith observation from the data set calculate mean circular error for reduced data set
MCe(u)
MCe(u)
u |
cosine the difference between the observed value of the response variable y and fitted values Y on model |
This function after removal of the ith observation from the data set.
Number, that is mean circular error after removal of the ith observation from the data set.
Azade Ghazanfarihesari, Majid Sarmad
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection of outliers in simple circular regression models using the mean circular error statistics
circular, CircStats
# Generate a data set dependent of circular variables. library(CircStats) x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) # Fit a circular-circular regression model. circ.lm <- circ.reg(x, y, order = 1) Y <- circ.lm$fitted MCe(cos(y - Y))
# Generate a data set dependent of circular variables. library(CircStats) x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) # Fit a circular-circular regression model. circ.lm <- circ.reg(x, y, order = 1) Y <- circ.lm$fitted MCe(cos(y - Y))
Mean circular error
MCE(y,Y,n)
MCE(y,Y,n)
y |
observed values of the response variable are calculated based on model
having a VonMises distribution with circular mean 0 and concentration parameter k. |
Y |
the estimeted value of y under model |
n |
the sample size |
This function may be considered as a type of arithmetic mean which is not robust to the existence of outlier.thus it can be used to detect the possible outliers in the circular regression.
Number, that is mean circular error.
Azade Ghazanfarihesari, Majid Sarmad
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection of outliers in simple circular regression models using the mean circular error statistics.
circular, CircStats
#Generate a data set dependent of circular variables. library(CircStats) n <- 50 x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) # Fit a circular-circular regression model. circ.lm <- circ.reg(x, y, order = 1) Y <- circ.lm$fitted MCE(y, Y, n)
#Generate a data set dependent of circular variables. library(CircStats) n <- 50 x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) # Fit a circular-circular regression model. circ.lm <- circ.reg(x, y, order = 1) Y <- circ.lm$fitted MCE(y, Y, n)
This function calculated the maximum-likelihood estimates parameters
Predict(x, y)
Predict(x, y)
x |
independent variable on model |
y |
the response variable on model |
This function uses of iterative methods for the parameter estimates in circular-circular regression model and The user can default values The desired change.
Number
a list containing the following values:
alpha1 |
estimate of |
beta1 |
estimate of |
.
Azade Ghazanfarihesari, Majid Sarmad
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection of outliers in simple circular regression models using the mean circular error statistics
circular,CircStats
# Generate a data set dependent of circular variables. library(CircStats) x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) Predict(x, y)
# Generate a data set dependent of circular variables. library(CircStats) x <- rvm(n = 50, 0, 2) y <- rvm(n = 50, pi/4, 5) Predict(x, y)
The data used in here, obtained after doing some calculations on the data to be recorded of Holderness coastline(the Humberside coast of the North sea, UK).
data("wind")
data("wind")
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection of outliers in simple circular regression models using the mean circular error statistics.
The data used in here, recorded over a period of 22.7 days along the Holderness coastline(the Humberside coast of the North sea, UK) by using two different instruments: a high frequency (HF) radar system and an anchored wave buoy.
data("wind2")
data("wind2")
A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detecting of outliers in simple circular regression models using the mean circular error statistics.