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I used the GLMMadmb function to asses the effect of three fixed factors (and two interactions) and two random factors on the abundance af a specie; my data had a negative binomial distribution. My fixed factors are: size (categorical with 5 levels), size (continous), height (continous) and my random factors: week and patch.

First I ran the model with all interactions and then I removed the non-significant

negbin= glmmadmb(abundance~size + neighbour +height + size*neighbour+ size*height +(1|week) + (1|patch),data=nedyus, family= "nbinom1")

Call: glmmadmb(formula = abundance ~ size + neighbour + height + size * 
neighbour + size * height + (1 | week) + (1 | patch), data = nedyus, 
family = "nbinom1")
AIC: 2684.1 

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)        3.07872    0.65738    4.68  2.8e-06 ***
sizeV             -1.46324    0.88029   -1.66  0.09647 .  
sizeIII           -2.86801    0.72962   -3.93  8.5e-05 ***
sizeII            -3.07838    0.79007   -3.90  9.8e-05 ***
sizeI             -3.99529    0.92210   -4.33  1.5e-05 ***
neighbour         -0.03386    0.01267   -2.67  0.00751 ** 
height            -0.02401    0.00628   -3.83  0.00013 ***
sizeV:neighbour    0.02705    0.02483    1.09  0.27601    
sizeIII:neighbour  0.01241    0.01560    0.80  0.42604    
sizeII:neighbour   0.03231    0.01416    2.28  0.02248 *  
sizeI:neighbour    0.02929    0.01474    1.99  0.04685 *  
sizeV:height       0.01405    0.00739    1.90  0.05726 .  
sizeIII:height     0.02655    0.00686    3.87  0.00011 ***
sizeII:height      0.01858    0.00788    2.36  0.01838 *  
sizeI:height       0.02679    0.00909    2.95  0.00321 ** 

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Number of observations: total=976, week=8, patch=122 
Random effect variance(s):
Group=week
        Variance StdDev
Intercept)  0.01442 0.1201
Group=patch
        Variance StdDev
(Intercept)   0.4469 0.6685

Negative binomial dispersion parameter: 1.676 (std. err.: 0.10951)

Log-likelihood: -1324.03 
Warning message:
In .local(x, sigma, ...) :
  'sigma' and 'rdig' arguments are present for compatibility only: ignored

I want to report this results in my work, but instead of the AIC value iwould also like to have an R-squared value to know how well does the model fit, is there a way to get it?

Any additional observation you can share with me about my model is more than welcome, thank you.

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    $\begingroup$ The AIC has nice qualities insofar as it is seen as a proxy for the Kullback-Liebler metric in information theory. The biggest problem with AIC is that it's unbounded. R2's are undefined for any model that doesn't employ OLS estimation. The literature is replete with various proxies for it such as the pseudo-R2 used in discrete choice modeling (McFadden, D., 1974 Conditional logit analysis of qualitative choice behavior). Assuming you have split your data into test and control (holdout), one proxy is to square the holdout correlation between predicted and actual values. $\endgroup$
    – user78229
    Commented Jul 31, 2017 at 11:33

1 Answer 1

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First, running the model and removing all that were not significant is not a great method of variable selection. But your table includes ones that are not significant, so it's not clear what you did exactly.

Second, there is no exact equivalent of $R^2$ for models other than linear regression. In particular, for negative binomial regression. For some ideas on substitutes, see Cameron and Windmeijer. You have the additional complexity of having a multilevel model, I don't know of any work on this particular problem. It's probably possible to generalize what Cameron and Windmeijer did, but I don't know if it's been done.

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    $\begingroup$ As my 'size' variable is categorical, I cannot remove the interaction if at least at one level the interaction is significant (I, II, III and V are being compared with IV). I will check the paper, thank you! $\endgroup$
    – Biaani
    Commented Jul 31, 2017 at 11:36
  • $\begingroup$ Actually, it depends on how much emphasis the size interaction has on your model, ecologically speaking. Check Zuur's book Mixed Effects Models and Extensions in Ecology with R on this. As to the paper provided by @Peter Flom, unfortunately one without an institutional connection can't view it. DO you know of any open access papers on the same subject? $\endgroup$
    – Eric Lino
    Commented Jul 28, 2018 at 22:07

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