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### How to estimate a multi-level multi-process event history model (binary and categorical responses)

Posted: Fri Apr 10, 2020 11:14 am
Hello,

I want to estimate a discrete-time multi-level multi-process event history model with 2 processes in which one process has a binary response and the other process has a categorical response. I believe it is possible to estimate such a model using MLwiN, but I am unsure how. I think my main issue is figuring out how to restructure the data before defining a multinomial logit model. Can you confirm that I can estimate such a model using multinomial logit? If so, how do I need to restructure the data before setting the model using mnom?

What I’ve done so far:

I think this is the way to proceed having worked through the discrete-time event history material on the CMM website (http://www.bristol.ac.uk/cmm/software/s ... s/eha.html) including the MLwiN exercises. However, the event history workshop exercises only consider a competing risk model as a single process model (ex4) or a multi-process model with two binary responses (ex5) separately. From slide 118 of the PowerPoint slides the link above and Steele et al. (2005) it seems that it is possible to estimate my model using MLwiN however I am unclear how to structure the data to accommodate both competing risks and multi-process.

I have tried to combine the ideas set out in ex4 and ex5 in the event history workshop exercises. However, I have not figured out what how to structure the categorical variable I need to input into mnom and whether I need to alter the covariates I wish to include.

From working through the exercises, it is my understanding that estimating a competing risk model, modelled as a multinomial logit model with random effects, is straightforward. The data is structured so that there is one row for each id-duration combination. To define a multinomial model the variable plugged into mnom is categorical, equaling 1 when event A occurs and equaling 2 when event B occurs. Consequently, in the model window two equations appear one for each possible event.

It appears that a multi-process model in which both processes have a binary response requires data restructuring before a multinomial model can be defined. It is my understanding that you have to restructure the data so that that are 2 rows for every id-duration combination, one for each process. A new variable is created and used to define a multinomial model (plugged into nmom) which is binary and equals to 1 in rows corresponding to the duration and the process in which an event occurs. Independent variables have to be created by interacting the process with the covariates. The model window then displays a single equation.

Following this, I have attempted to restructure the data so that there are multiple rows for each id-duration. For example, I have constructed one row per process for each id-duration, however, I am unsure whether the variable should be populated with a 1 or 2 when the binary response event occurs. I then considered creating two rows for the binary response within each id-duration combination so that one could be equal to 1 and the other equal to 2. However, I am then unsure of how to include covariates in the model.

Is trying to utilize a multinomial logit model a good way to proceed to estimate a discrete-time multi-level multi-process event history model? If so, how do I need to restructure my data to estimate such a model?

Many thanks,

Ashley

### Re: How to estimate a multi-level multi-process event history model (binary and categorical responses)

Posted: Fri May 15, 2020 8:32 am
Hi Ashley,
Thanks for your question. I am a bit rusty on these sorts of models and taking a quick look at the equations window in MLwiN when you try and fit multivariate response models you are restricted to responses being normal, binomial or Poisson. I don't know if this has changed since the slides you refer to were written but you are probably better off emailing Fiona Steele directly as she is these days at the LSE.
In fact looking at our user guide it clearly says on page 228 in chapter 14 'Negative binomial or multinomial response variables cannot be included in
multivariate response models, but can be used in univariate response models.' so clearly that is not currently an option
I know we have done some work on these models using the REALCOM and StatJR software packages when thinking about missing data and you may also want to look at the aML software.
Hope that helps.
Bill.

### Re: How to estimate a multi-level multi-process event history model (binary and categorical responses)

Posted: Mon Jun 08, 2020 8:24 am
Hi Bill,

Thanks for your response. I will reach out to Fiona Steele and look into the other programs you suggested.

All the best,

Ashley