Description Usage Arguments Details Value Author(s) References See Also Examples
This function fits a multivariate linear regression model based on identity, spatial sign or spatial rank scores. Both inner and outer standardization are possible.
1 2 3 
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 left part of the formula (the response) must be a n x p matrix with at least two columns. 
scores 
score to be used. Can be either 
stand 
can be 
maxiter 
maximum number of iterations. Used only for 
eps 
convergence tolerance. Used only for 
eps.S 
lower limit for the residual norms. Used only for 
x 
logical. Indicating whether the design matrix 'x' returned from the model matrix should be stored. Default is 
y 
logical. Indicating whether the response matrix 'y' should be stored. Default is 
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 'mv.l1lm' is called. 
subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
na.action 
a function which indicates what should happen when the data contain 'NA's. 
The theory behind this function is described in detail in Chapter 13 of the MNM book.
For regular multivariate L2regression the function lm
might be more efficient and offers more methods. Note however that
the results given by lm
and mv.l1lm
may differ slightly due to different divisors of the covariance matrix.
The algorithms for the sign and rank scores are still in an early phase and therefore any feedback is very welcome. For example if p+1 residuals are 0, then the algorithms may not return correct values. Note also that the computations for rank scores might be slow.
Rank regression does not provide an estimate for the intercept parameter is not considered a parameter, a HodgesLehmann estimator of the residuals is then an estimate when an interecept term is in the formula.
For the one sample case however the function cannot be used for rank scores. We recommend that the regression function should not be used for the one or two sample case. There are
distinct functions designed for that purpose. Note furthermore that in the two sample case the covariance matrix returned from the regression function differs
slightly from the one returned by the function mv.2sample.est
since there matrix A is computed in a different way.
In general it is recommended to use the data
argument and specify there the data frame that contains the variables and matrices. For having a matrix Y in a data frame
for example the following methods work:
MyData < data.frame(I(Y),...)
or
MyData < data.frame(...)
MyData$Y < Y
Otherwise also the function cbind
can be used on the left side of the formula to combine numeric vectors on the fly.
mv.l1ml
returns an object of 'class' mvl1lm
.
The functions summary
is the best choice to view the results. The
generic accessor functions coefficients
, fitted
, residuals
and vcov
extract various useful features of
the value returned by mv.l1ml
.
An object of class mv.l1ml
is a list wich contains different information depending on the scores and standardization used.
To see its content use the function str
.
Klaus Nordhausen
Oja, H. (2010), Multivariate Nonparametric Methods with R, Springer.
Nordhausen, K. and Oja, H. (2011), Multivariate L1 Methods: The Package MNM, Journal of Statistical Software, 43, 128.
lm
, mv.1sample.est
, mv.1sample.test
, mv.2sample.est
, mv.Csample.test
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72  # creating simple data
X < cbind(rep(1,100),rmvnorm(100,c(0,0,0)) )
B < matrix(c(4,1,1,0.5,3,2,2,2),ncol=4, byrow=TRUE)
Y < X %*% t(B)+ rmvnorm(100,c(0,0), diag(0.2,2))
DAT < data.frame(x1=X[,2],x2=X[,3], x3=X[,4], Y=I(Y))
# true B
t(B)
# example using identity scores
test1 < mv.l1lm(Y ~ x1 + x2 + x3, data=DAT)
print(test1)
summary(test1)
coef(test1)
vcov(test1)
head(fitted(test1))
head(residuals(test1))
# example using outer sign scores
test2 < mv.l1lm(Y ~ x1 + x2 + x3, scores= "s", data=DAT)
print(test2)
summary(test2)
coef(test2)
vcov(test2)
head(fitted(test2))
head(residuals(test2))
# example using inner sign scores
test3 < mv.l1lm(Y ~ x1 + x2 + x3, scores= "s", stand="i",
data=DAT)
print(test3)
summary(test3)
coef(test3)
vcov(test3)
head(fitted(test3))
head(residuals(test3))
# example using outer rank scores
test4 < mv.l1lm(Y ~ x1 + x2 + x3, scores= "r", stand="o",
data=DAT)
print(test4)
summary(test4)
coef(test4)
vcov(test4)
head(fitted(test4))
head(residuals(test4))
# example using inner rank scores
test5 < mv.l1lm(Y ~ x1 + x2 + x3, scores= "r", stand="i",
data=DAT)
print(test5)
summary(test5)
coef(test5)
vcov(test5)
head(fitted(test5))
head(residuals(test5))
# prediction
newData < data.frame(x1=c(1,2),x2=c(0.5,0.7), x3=c(1,1))
newData
predict(test1,newData)
predict(test2,newData)
predict(test3,newData)
predict(test4,newData)
predict(test5,newData)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.