In superdesolator/NORTARA: An implementation of NORTA approach with bounding RA algorithm

Who does need the package?

The package implements the NORTA approach with bounding RA algorithm for simultaneous generation of random vectors with specified marginals and correlations. The marginals can be arbitrary(continuous or discrete), So if you want to generate a data set with specified mariginals and correlations to do some research, the package is a good choice.

Where can i learn more about the details about the algorithm?

The package is an implementation of NORTA approach with bounding RA algorithm introduced by the following paper: Huifen Chen, (2001) Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations. INFORMS Journal on Computing 13(4):312-331. See more details in the above paper.

Is the package completely implement the above algorithm?

NO, the package does some slightly changes according to the paper, e.g. the initial sample size be set to 60 not 40, and the random seeds choice go to the third choice not the first choice which introduced by Appendix in the above paper. But the practice results of the package showes it work well in a lot of situations.

How can i use the package?

You can see examples in by ?functionname after library(nortaRA). Here is a workflow for you to use the package. Suppose you want to generate a sample size of 10000, from 4 marginals:

• t with df = 5
• normal with mean = 0, sd = 1
• poisson with lambda = 3

• weibull with shape = 1, scale = 1

• Give your marginals(The inverse CDF functions):

   #exists in basic packages: you can use their names directly or by a new name
   qt
   qnorm
   b <- qpois
   #or from other packages  : Here you must give it a new name
   #you can replace the package::functionname on your needs.
   f <- stats::qweibull
   invcdfnames <- c("qt","qnorm","qpois","f")
  #or invcdfnames <- c("qt","qnorm","b","f") but never
  #invcdfnames <- c("qt","qnorm","qpois","stats::qweibull")

1. Give the marginals' arguments:

  #always you can use the following way, the inner lists' names should match the
  #above functions' arguments names.  
  paramslists <- list(
             m1 = list(df = 5 ),
             m2 = list(mean = 0, sd = 1),
             m3 = list(lambda = 3),
             m4 = list(shape = 1, scale = 1)                 
             )
  #if you are lazy,e.g. qnorm using the default values, then you can use the following way:
 paramslists2 <- list(
             m1 = list(df = 5 ),             
             m3 = list(lambda = 3),
             m4 = list(shape = 1, scale = 1)                 
             )
 defaultindex <- c(2)

3.Give the other arguments for bounding RA algorithm:

 #If you are familiar with the bounding RA algorithm, you can set the functions' arguments
 #on your needs. e.g. let m1 = 80, sigma0 = 0.001 will be ok if you know the smaller 
 #sigma0  the more time will be costed. But if you don't familiar with it, you'd better  
 #use the default values

4.Give the target correlation matrix

cor_matrix <- matrix(c(1.0,-0.4,0.1,-0.2,-0.4,
                       1.0,0.8,0.6,0.1,0.8,1.0,
                       0.5, -0.2,0.6,0.5,1.0
                       ),4,4)

5.Generate the wanted samples:

  f <- stats::qweibull
  invcdfnames <- c("qt","qnorm","qpois","f")
  paramslists <- list(
             m1 = list(df = 5 ),
             m2 = list(mean = 0, sd = 1),
             m3 = list(lambda = 3),
             m4 = list(shape = 1, scale = 1)                 
             )
  cor_matrix <- matrix(c(1.0,-0.4,0.1,-0.2,-0.4,
                       1.0,0.8,0.6,0.1,0.8,1.0,
                       0.5, -0.2,0.6,0.5,1.0
                       ),4,4) 
  cor_matrix
  res <- nortaRA::gennortaRA(10000,cor_matrix,invcdfnames,paramslists)
  head(res,5)
  cor(res)
  paramslists2 <- list(
             m1 = list(df = 5 ),             
             m3 = list(lambda = 3),
             m4 = list(shape = 1, scale = 1)                 
             )
  defaultindex <- c(2)
  res2 <- nortaRA::gennortaRA(10000,cor_matrix,invcdfnames,paramslists2,defaultindex)
  head(res2,5)
  cor(res2)

what should i also be careful?

• You should not use the gennortaRA to generate multivariate normal virables there are a lot of packages can do it. That's mean, you can't ask the gennortaRA to generate samples when you put invcdfnames = c("qnorm","qnorm","qnorm",..)
• The other important thing is that your input target correlation matrix should be valid. The gennortaRA function will call checking cor_matrix functions for you. If you want to check yourself, you can use check_input_cormat function.
• Sometimes, there will be a warning message telling you a nearest positive definite matrix is used, it gives from function BoundingRA, in these cases, the cor(res) may not be very close to the target input correlation matrix.

How can i contact the author if i have problems in using the package?

You can send your email to [e-mail]

superdesolator/NORTARA documentation built on May 30, 2019, 8:40 p.m.