Negative Binomial Coefficient Interpretation?

Question

I've fitted a negative binomial model with language (Tamil and French) as the IV and number of prolongations (count) as DV and number of words in each language as an offset (random effect). The question I'm trying to answer: on average, are there more occurrences of prolongations in one language than the other? My output shows a negative coeff for just 'Language' without specifying which one - so I don't know how to interpret these results.

Call:
glm.nb(formula = Prolongations ~ Language + offset(log(Words)), 
    data = Poisdf, init.theta = 2.963920129, link = log)
Deviance Residuals: 
    Min       1Q   Median       3Q      Max

-2.4382  -0.7270  -0.1176   0.3917   1.6092
Coefficients:
            Estimate Std. Error z value            Pr(>|z|)

(Intercept)  -2.6700     0.1994 -13.390 <0.0000000000000002 ***
Language     -0.6290     0.3103  -2.027              0.0426 *

Signif. codes:  0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for Negative Binomial(2.9639) family taken to be 1)
Null deviance: 23.049  on 17  degrees of freedom

Residual deviance: 19.014  on 16  degrees of freedom
AIC: 130.77
Number of Fisher Scoring iterations: 1
          Theta:  2.96 
      Std. Err.:  1.22 


2 x log-likelihood:  -124.769

How do I interpret this 'Language' Coeff? I can't really say that "for every 1 unit increase in IV, there is a .63 unit decrease (decrease because of the - sign or should -/+ signs be disregarded here?) in number of prolongations"? The last part (DV) makes sense but it doesn't really make sense to speak of a "1 unit increase" in languages when it is a categorical variable with 2 options (Tamil or French).

EDIT: In my data, Tamil = 0 and French = 1. Could this imply that for French, there is a (exp(.63) = .53*100 = 53) 53% decrease in number of prolongations?

An offset is not a random effect: How to formulate the offset of a GLM. The number of French/Tamil words hardly seem like random quantities either. — dipetkov, Jun 24 '22 at 20:56
What do you mean? I haven't set language as a random effect... — MaVeee2021, Jun 24 '22 at 21:02
The model in your question has no random effects, so it's unclear at least to me what you mean with "number of words in each language as an offset (random effect)". — dipetkov, Jun 24 '22 at 21:04
I shouldn't have called the offset a random effect. My bad. I was working on a mixed model at the same time and am confusing my vocabulary between the two -.- — MaVeee2021, Jun 24 '22 at 21:07

score 0 · Answer 1 · answered Jun 24 '22 at 16:51

0

Yes, that is correct. In French, the mean number of propagations is .53 of the mean in Tamil, or 47% less.

This comes from the link function in NB regression:

$$\ln(\mu)=\beta_0+\beta_1x$$

answered Jun 24 '22 at 16:51

Thanks! But do you mean "53% less"? The "47%" part is confusing me...where did you get that from? – MaVeee2021 Jun 24 '22 at 17:19
@MaVeee2021 that’s standard percentages. If something is 53% of something else, it’s 47% less than it, I think – Jun 24 '22 at 18:32
OH lol I get it now, thanks! – MaVeee2021 Jun 24 '22 at 18:50

Negative Binomial Coefficient Interpretation?

1 Answers1