Interpreting independent categorical variable in a generalized linear mixed model (GLMM)

Question

I use a generalized linear mixed model (GLMM) with quasi-Poisson regression and fit the model with multivariate normal random effects, using Penalized Quasi-Likelihood, i.e. glmmPQL. The output is as follows:

Income variable has 3 categories, low income, lower middle income, upper middle income. In the output, low income appears to be refence category but I dont know how should ı interpret and report this.

Thank you so much in advance.

 Linear mixed-effects model fit by maximum likelihood
 Data: my_scaled_data 
 AIC BIC logLik
 NA  NA     NA

 Random effects:
 Formula: ~1 | country
    (Intercept) Residual
 StdDev:    1.191246 7.062197

 Variance function:
 Structure: fixed weights
 Formula: ~invwt 
 Fixed effects:  protests ~ stringency + cpi + income 
                              Value Std.Error  DF   t-value p-value
(Intercept)                3.993691 0.3732307 428 10.700329  0.0000
stringency                 0.152788 0.0322449 428  4.738373  0.0000
cpi                       -0.509498 0.3093523 428 -1.646984  0.1003
incomelower middle income -0.028550 0.2156300 428 -0.132403  0.8947
incomeupper middle income -0.528267 0.2520429 428 -2.095941  0.0367
 Correlation: 
                          (Intr) strngn cpi    incmlmi
stringency                -0.005                      
cpi                        0.065 -0.311               
incomelower middle income -0.302 -0.089  0.056        
incomeupper middle income -0.244 -0.060 -0.004  0.539 

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-1.6874331 -0.4638920 -0.1344516  0.2557120 10.2539363 

Number of Observations: 444
Number of Groups: 12

I’m voting to close this question because it should be asked on [stats.se]. — Peter O., Nov 21 '21 at 09:51

score 0 · Accepted Answer · answered Jan 21 '22 at 18:39

Income variable has 3 categories, low income, lower middle income, upper middle income. In the output, low income appears to be reference category but I don't know how should I interpret and report this.

This is the normal way to handle categorical regressors. Each estimate is interpreted as a contrast with the reference level. So the linear predictor is 0.028550 lower for incomelower middle income compared to the reference level, and the linear predictor is 0.528267 lower for incomeupper middle income compared to the reference level.

Interpreting independent categorical variable in a generalized linear mixed model (GLMM)

1 Answers1