Multivariate Poisson regression with covariance structure

[sabelo]

Hi, 

I am trying to fit a multivariate Poisson model to my data, my response is categorized into four level, I am dealing with accidents and i need to know how to use the glm procedures for the multivariate poisson regression

[PGStats]

The response in Poisson regression as the name suggests follows a Poisson distribution, which has all non-negative integer as support and a variance equal to the mean. It is most useful to model count data.

Proc GLM is for normally distributed responses. Poisson regression is available with proc genmod, proc glimmix, proc countreg (requires SAS/ETS), among others.

[sabelo]

I am trying to do what is done in the attached article, they have estimate their Poisson regression model us GLM procedures, and they have estimate their parameters using maximum likelihood estimation via EM algorithm.

http://download.springer.com/static/pdf/77/art%253A10.1007%252Fs11222-005-4069-4.pdf?originUrl=http%...

[sabelo]

Proc glimmix allows me to put only one variable as my response, but my response has four levels, I want to state my model as follows:

model uninjured slightlyInjured seriouslyInjured Fatalities= independent variables.

But proc glm allows me to do that, just that I donyt know how to specify the distribution since it gives me errors, and how to apply the method of maximum likelihood via the em algorithm to estimate the Poisson parameters. 

[Ksharp]

It looks like you have longititude data . You need MIXED Model . proc mixed , proc glimmix .....

[Rick_SAS]

---

@sabelo wrote:

Proc glimmix allows me to put only one variable as my response, but my response has four levels, I want to state my model as follows:

model uninjured slightlyInjured seriouslyInjured Fatalities= independent variables.

---

Create a response variable named InjuryStatus that has the value 0 (=uninjured), 1 (=slightly injured), 2 (=seriously), or 3 (=fatality).

Then use PROC GENMOD or PROC GLIMMIX and specify

model InjuryStatus = indepvar1 indepvar2... / dist=poisson;

You might need to specify an offset variable.  I highly recommend reading the Getting Started example in the PROC GENMOD documentation, which explains the structure of the data and how to specify the model and interpret the results.

[sabelo]

Thanks again, how do I create the variable, because the responses are on their own colums( separately) on excel, i.e the observations for fatality are on their own colum and the observation for serious injuries are on their own coulum;

fatalities    serious

0                 8 

1                 5

2                 5

5                 2

.

.

.

How do I create the response variable in a situation like this.

[Ksharp]

If your response variable has four levels that lead to discrete model, you can't use Poisson model on it.
Try Logistic Model .

[sabelo]

I want to apply the EM alogorithm for multivatriate Poisson, see the article on the link, I want to do something similar, these results in the article.

http://www.tandfonline.com/doi/abs/10.1080/0266476022000018510

Thanks again

[Ksharp · Accepted solution]

I searched EM Algorithm at Stat documentation, and found this :


IRT Procedure

MAXMITER= Specifies the maximum number of iterations in the maximization
step of the EM algorithm

[Ksharp]

Maybe you should take a look at Example 43.2: Log-Linear Model for Count Data
in documentation of PROC GEE .
It used a strata Poisson Model Like @Rick said by using offset= to identify these four levels :


proc gee data = Seizure;
class ID Visit;
model Count = X1 Trt X1 * Trt / dist=poisson link=log offset= Ltime;
repeated subject = ID / within = Visit type=unstr covb corrw;
run;