topic Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite. in Statistical Procedures

Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Sun, 06 Oct 2019 22:30:02 GMT

Can I ignore this warning? If not, any suggestions on what to check.

I get this error message with a ZINB model but not with a ZIP model with the same terms.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 11:02:05 GMT

A search of the Internet for "negative of hessian not positive definite" returns a number of discussions on this issue.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

Ksharp — Mon, 07 Oct 2019 11:25:10 GMT

@Rick_SAS wrote a blog about it . In general, your model is not specified correctly or your initial value is not good.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

Ksharp — Mon, 07 Oct 2019 11:33:27 GMT

https://blogs.sas.com/content/iml/2019/04/03/g-matrix-is-not-positive-definite.html

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 12:11:15 GMT

@Ksharp wrote:

@Rick_SAS wrote a blog about it . In general, your model is not specified correctly or your initial value is not good.

In addition, I think there are other causes, such as the model is overspecified, or not enough data, and probably a few others.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Mon, 07 Oct 2019 16:34:09 GMT

There was one variable in my zinb model that came out with a missing Wald Chi-Square. I reran with that variable removed and the error went away, but I have still have missing Chi-Square values in my Type 3 table. Is this also a sign of misspecification?

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 17:13:09 GMT

Please show us the output.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Mon, 07 Oct 2019 17:55:41 GMT

I dropped variable F from my zero model and the warning went away, but my type 3 tables look like this:

LR Statistics For Type 3 Analysis
Source	DF	Chi-Square	Pr > ChiSq
a	5	4184.93	<.0001
b	1	3.38	0.0662
c	1	833.46	<.0001
d	1	.	.
e	1	1303.81	<.0001
f	1	.	.
g	1	1156.32	<.0001
h	1	110.49	<.0001
i	1	35.01	<.0001
j	4	.	.
k	2	284.19	<.0001
l	3	577.5	<.0001
m	1	.	.
n	1	.	.
o	1	592.15	<.0001
p	1	521.37	<.0001
q	1	1572.42	<.0001
r	1	877.94	<.0001

LR Statistics For Type 3 Analysis of Zero
Inflation Model
Source	DF	Chi-Square	Pr > ChiSq
a	5	105.13	<.0001
b	1	57.31	<.0001
c	1	101.84	<.0001
d	1	8.43	0.0037
e	1	47.75	<.0001
g	1	2.99	0.0839
h	1	0.19	0.6623
i	1	1.5	0.2212
j	4	295.27	<.0001
k	2	.	.
l	3	.	.
m	1	.	.
n	1	15.08	0.0001
o	1	15.55	<.0001
p	1	0.09	0.7666
q	1	27.7	<.0001
r	1	15.6	<.0001

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 18:07:14 GMT

Please read message 3 in this thread: https://communities.sas.com/t5/Statistical-Procedures/Interpreting-Multivariate-Linear-Regression-with-Categorical/m-p/591230#M28913

Although that discussion was about logistic regression, the concept applies to all modeling in SAS with a CLASS variable(s).

In addition, you probably can't estimate all of the factors in your model, as they are not independent of one another, if you know an estimate of one coefficient, you can determine the estimate of other coefficients.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Mon, 07 Oct 2019 19:33:55 GMT

But these aren’t levels of a categorical variable, they are each separate categorical variables. This isn’t a parameter estimates table like in the link, it is a type 3 table.

Would the lack of independence show up in VIF/TOL type statistics?

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 20:01:08 GMT

Suppose you have temperature (Celsius) and temperature (Fahrenheit) and temperature (Kelvin) as three variables, and you want to put them all in the model. These are not independent, these are completely dependent, if you know one, you know the others exactly, and after putting one of these in the model, there's no additional information to be gained by putting the others in the model. That's the situation you are in, that is why some of the variables cannot be estimated by your model.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Mon, 07 Oct 2019 20:41:30 GMT

I would think that would show up as high correlation or high VIF, but I don't see any correlations above .25 and all VIFs are below 2. Also why does this show up in the ZINB model but not the ZIP model?

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

PaigeMiller — Mon, 07 Oct 2019 22:41:53 GMT

This can also happen if one variable is a linear combination of other variables. Such as

x4 = 0.25*x1 - 2.75*x2 + 61*x3

and if this is the case, you still can't estimate the effect of x4, even though the correlation might not indicate a problem. Or it may be something specific to ZINB, but I don't know enough about ZINB to be sure.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

Rick_SAS — Thu, 10 Oct 2019 17:36:50 GMT

Please show your PROC GENMOD statements.

Re: Genmod ZINB model - WARNING: Negative of Hessian not positive definite.

telligent — Fri, 11 Oct 2019 01:50:25 GMT

proc genmod data = temp

class bene_id a b c d

e f g h i j

k l m n o p q r;

model &outcome. = a b c d

e f g h i j

k l m n o p q r / dist = zinb link = log offset=logofsomething type3;

zeromodel a b c d

e f g h i j

k l m n o p q r;

run;

removing f from the zeromodel removes the error but leaves me with blanks in my type 3 table.