在R中生成可行的离散数据采样分布

Question

I'm trying to simulate 2 X 2 data that would yield a relatively strong negative phi coefficients.

I'm using the library GenOrd as follows:

library(GenOrd)

# Specify sample size N
N <- 40

# Marginal distribution
marginal <- list(c(.5), c(.5))

# Matrix
Sigma <- matrix(c(1.0, -.71, -.71, 1.0), 2, 2, byrow=TRUE)

# Generate a sample of the categorical variables with specified parameters
m <- ordsample(N, marginal, Sigma)

However, I'm getting the following error whenever I input a correlation larger than -.70 .

Error in contord(list(marginal[[q]], marginal[[r]]), matrix(c(1, Sigma[q,  : 
Correlation matrix not valid!

I'm clearly specifying something untenable somewhere - but I don't know what it is.

Help appreciated.

Answer 1

I'll give a go at answering this as a coding question. The error points to where the packages spots the problem beginning: at your Sigma entry. Given your marginal distribution, having -.71 in your corr. matrix is out of bounds and the packages is warning you of this. You can see this by altering the signs in your Sigma:

Sigma <- matrix(c(1.0, .71, .71, 1.0), 2, 2, byrow=TRUE)
m <- ordsample(N, marginal, Sigma)
> m
       [,1] [,2]
  [1,]    1    1
  [2,]    1    2
  ....

As to WHY -.71 is not valid, you may want to direct that statistical question to Cross Validated for a succinct answer.

Answer 2

I'm not exactly sure "why", however, I found no problems simulating 2 X 2 data that would yield a relatively strong negative correlation using the generate.binary() function from the MultiOrd package.

For example, the following code will work for the complete range of correlation inputs. The documentation for the generate.binary() function indicates that the matrix specified is interpreted as a tetrachoric correlation matrix.

library(MultiOrd)

# Specify sample size N
N <- 40

# Marginal distribution for two variables as a vector for MultiOrd rather than a list
marginal <- c(.5, .5)

# Correlation (tetrachoric) matrix as target for simulated relationship between variables
Sigma <- matrix(c(1.0, -.71, -.71, 1.0), 2, 2, byrow=TRUE)

# Generate a sample of the categorical variables with specified parameters
m <- generate.binary(40, marginal, Sigma)