# report negative biomial models (glmer.nb) in APA-Format: log-link?

So far I fitted my generalised mixed model with a negative binomial distribution (glmer.nb) and I like to report the results now. The output looks like this:

        AIC      BIC   logLik deviance df.resid
230.4    244.7   -106.2    212.4       27

Scaled residuals:
Min       1Q   Median       3Q      Max
-2.06055 -0.45755  0.03022  0.61356  1.31444

Random effects:
Groups    Name        Variance  Std.Dev.
A      (Intercept) 8.294e-03 9.107e-02
B      (Intercept) 3.161e-11 5.622e-06
C      (Intercept) 2.216e-02 1.489e-01
Number of obs: 36, groups:  A, 3; B, 2; C, 2

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  3.1112799  0.1597927  19.471  < 2e-16 ***
Sta2_6       0.2555441  0.0865718   2.952  0.00316 **
Sta3_5       0.3852168  0.0838978   4.591  4.4e-06 ***
Wi          -0.1068887  0.0504595  -2.118  0.03415 *
Bew         -0.0003687  0.0009392  -0.393  0.69459
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


so there are a few arising questions:

• most important: is it appropriate to report the results as written above in the log-link format or do I have to convert the Estimates and Std. Errors by exp()?
• it is correct to read the Intercept e.g. for the fixed factor "Wi" like - exp(0.1068887) ?
• Is there an currently working option to convert the summary for a glmer.nb model like above to a table in the APA-Format?

Kind regards and thank you a lot for helping, Julia

## 1 Answer

most important: is it appropriate to report the results as written above in the log-link format or do I have to convert the Estimates and Std. Errors by exp()?

Whether it is appropriate or not depends on your audience. Some people may be happy with the estimates being on the log count scale, but for other it may be better to exponentiate them so that they are on the count scale. Generally I would suggest the latter.

it is correct to read the Intercept e.g. for the fixed factor "Wi" like - exp(0.1068887) ?

this question doesn't make sense. the intercept is 3.1. The estimate for Wi is -0.11. If you want this estimate to be on the count scale you would do exp(-0.11) not -exp(0.11). For the intercept it is exp(3.11)

is there an currently working option to convert the summary for a glmer.nb model like above to a table in the APA-Format?

Why do you want to do that ? I doubt anyone is interested in z values and (hopefully) p values. The APA table format is quite standard so you can just paste the values into a template. Also, I would think that 2 decimal places is more than adequate - a log count of 0.01 is equivalent to 0.07 on the count scale. I would suggest reporting just the point estimate and confidence interval for each parameter.

Finally, according to your output you have 3 groups that you are fitting random intercepts for, of size 3, 2 and 2. Fitting random intercepts for these is wrong. You can't expect the software to reliably estimate a variance for a variable that has only 2 or 3 observations. These should be fixed effects.

• Thank you a lot for your answert. Oct 23 '20 at 20:10
• So I am correct in interpreting the Intercept for Sta2_6 (factorial Variable) as exp(3.11)+exp(0.2555441) = 23.71? Oct 23 '20 at 20:13
• It''s not the Intercept for Sta2_6". Why do you want to add them ? The estimate for Sta2_6 is 0.26 so the count of the outcome is expected to change by exp(0.26) for every one unit change in Sta2_6, leaving the other variables unchanged. The intercept is the estimated log count of the outcome when all the variables are zero. Oct 24 '20 at 16:53
• Does this answer your question ? If so, please consider marking it as the accepted answer, or if not please let us know why so that it can be improved. Nov 12 '20 at 20:07