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
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.