Calcite | Level 5

## simulation multivariate continuous and ordered categorical data

hi all

i need your help to simulate multivariate continuous and ordered categorical data (10 variables :5 continuous normal and 5 ordered categorical data).

8 REPLIES 8

## Re: simulation multivariate continuous and ordered categorical data

It might be easier to simulate 10 MVN variables and then apply cutpoints to create the ordinal categorical data.

Steve Denham

Calcite | Level 5

Thanks alot

## Re: simulation multivariate continuous and ordered categorical data

See the following discussion on how to put values into labeled bins:

https://communities.sas.com/message/193351#193351

Steve Denham

SAS Super FREQ

## Re: simulation multivariate continuous and ordered categorical data

It's great that you are so interested in this topic.  From your comments, I am guessing that you are a student doing a project or thesis.  I am a former university professor myself, so I'd like to encourage you to work hard to figure out some of these issues yourself. By wrestling with the problems, real learning takes place, which leads to a greater understanding of the math and enables you to generalize your knowledge to the next level.

I have shown you how to generate  normal variables, binary variables, and ordinal variables that have a given mean and correlation structure. Read and reread chapter 9 of my book, which discusses "cut points" like Steve mentions.  Also read Appendix B: Generating Multivariate Ordinal Variables, which is available on the book's Web page.  If you are studying at the graduate level, you should also read the relevant references in those chapters.

Calcite | Level 5

## Re: simulation multivariate continuous and ordered categorical data

Thank you dr. Rich actually I am interesting in sas especially simulation data in sas.iml and I am phd student .applied statistics in my thesis I must simulate 6models  with all combinations of data so I am so happy to meet you in sas community and I will read ch9as you said thank you for your encouraging.

Regards

Calcite | Level 5

## Re: simulation multivariate continuous and ordered categorical data

hi

if i want to simulate mixture models like (normal+ordered categorical, normal+dichotomous, ordered categorical +dichotomous) i must depend on mvnormal to create the previos models by using cut point or there is another method. thanks in advance

SAS Super FREQ

## Re: simulation multivariate continuous and ordered categorical data

Mixture models are described in Simulating Data with SAS pp 119-121 and pp140-141.

## Re: simulation multivariate continuous and ordered categorical data

Thanoon,

I believe you are confusing mixture models, in which a single variable comes from one of a finite number of distributions (finite mixture model) or contaminated mixture models, with data ensembles having a variety of variables of different distributions, but with known (or possibly unknown, but still estimable) covariances between the variables.  In the first case, which is not what I think you are trying to accomplish, the code is given in Simulating Data with SAS.  However, for the data ensembles, where the variables come from different distributions but have some sort of underlying covariance, you will need to search out conjoint distributions.  If, however, you can reasonably presuppose that the ordinal variables (or dichotomous variables, in the extreme case) are merely aggregated representations of underlying continuous distributions, then there is a wholly different approach.  And it is not well researched having lots of gaps in theory, thus making it a very suitable topic for dissertation research.

Steve Denham

From The DO Loop