Please help!

I have recently been criticized for using pairwise comparisons to explain all three levels of a factor within a negative binomial GLM rather than all levels at once. I was told that it is "long-winded" and "uneccessary". I was under the impression that in GLMs one cannot bulk all levels of a factor together to obtain a test statistic and corresponding p-value.

Obviously if a factor is "insignificant" at any level then carrying out a post-hoc analysis is pointless. My levels all have there own p-values therefore I discussed these values from the below global model. I was told to do an ANOVA instead which I don't believe is suitable for overdispersed, zero-inflated data.

p-value for all levels of a factor anyone?

(Below, lower field layer 0, upper field layer 1 and change1 is in intercept)

```
Deviance Residuals:
Min 1Q Median 3Q Max
-2.4284 -0.7956 -0.3862 0.4045 2.4233
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.3410884 1.8219786 2.383 0.01719 *
Height 0.0373584 0.0119929 3.115 0.00184 **
Width -0.0007891 0.0008246 -0.957 0.33859
MeanMin -0.1731877 0.1404434 -1.233 0.21752
as.factor(Site_Treat)2 -0.4080256 0.2480438 -1.645 0.09998 .
as.factor(Change)2 -0.4940398 0.1755487 -2.814 0.00489 **
as.factor(Change)3 -0.1613766 0.1763677 -0.915 0.36019
as.factor(Lower_Field_Layer)1 0.4873488 0.2931585 1.662 0.09643 .
as.factor(Lower_Field_Layer)2 -0.3292409 0.3717863 -0.886 0.37585
as.factor(Upper_Field_Layer)2 -0.0081040 0.3257734 -0.025 0.98015
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for Negative Binomial(4.7795) family taken to be 1)
Null deviance: 96.392 on 46 degrees of freedom
Residual deviance: 47.968 on 37 degrees of freedom
AIC: 403.94
```

Best wishes,

Platypezid

## Best Answer

You could fit the model with and without the categorical variable and do a likelihood ratio test to determine it's overall significance.