Im writing my thesis, which a monte-carlo study aimed at generating datasets for comparing the performance of various regression models (Neural networks amongst others). And since neural networks can fit some very complicated distributions, i am simulating breakpoints in the data (currently by different local means, and different distribution families).

But my question is then; is it possible to simulate a dataset with two different correlation matrices? (eg. different local relationships with the Y-term)

For at timeseries, I assume it would be suitable/ok, but does it make sense for an experimental setup, with no relation to time series?

Here's an illustration of the idea:

    #defining the two correlation matrices for the cholesky transformation:
    R1 <- matrix(c(   1, 0.2, 0.3,
                    0.2,   1,   0,
                    0.3,   0,   1),byrow = TRUE, nrow = 3, ncol = 3)

    R2 <- matrix(c(   1,   0.3, 0.4,
                      0.3,   1,   0,
                      0.4,   0,   1),byrow = TRUE, nrow = 3, ncol = 3)

    #part one of the dataset
    U = t(chol(R1))
    nvars = dim(U)[1]
    numobs = 5000
    random.normal = matrix(rnorm(nvars*numobs,100,5), 
                           nrow=nvars, ncol=numobs);  
    X = U %*% random.normal
    X1 = as.data.frame(t(X))

    #part two of the dataset
    U = t(chol(R2))                                   #different corr. matrix
    nvars = dim(U)[1]
    numobs = 5000
    random.normal = matrix(rnorm(nvars*numobs,200,5), #different local mean
                           nrow=nvars, ncol=numobs);  
    X = U %*% random.normal
    X2 = as.data.frame(t(X))

    #Combining the two datasets 
    Xfinal <- rbind(X1,X2)

    #looking at the correlation afterwards:

#          V1        V2        V3
#V1 1.0000000 0.9941870 0.9946056
#V2 0.9941870 1.0000000 0.9936319
#V3 0.9946056 0.9936319 1.0000000

#look at the distributions for first column:

enter image description here

Ideally I would want different relationships around the two local means. Am I breaking some statistical assumptions in this way?

Snce the goal is to predict the first column of the dataset, I would be able to validate the performance of the algorithm of choise, which is the overall goal of my thesis.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.