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I conducted a multilevel binomial regression (glmer) and I obtain quite wide confidence intervals for my odds ratio. What could be causing such large 95% CI and what can be done to provide more precise CI? Is it right to assume that odds ratio can be interpreted in the same way for a multilevel logistic regression as for a normal logistic regression?

formal_c <- glmer(formal~type_opld_binary2+gender_binary2+pfeat2+(1 | opleader), data=political_data, family=binomial(link="logit"), control = glmerControl(optimizer = "bobyqa"), nAGQ=1)
summary(formal_c)

ORformal_c <- exp(fixef(formal_c))

CIformal_c<-exp(confint(formal_c, parm= "beta_", method="Wald"))

ORformal_c.CIformal_c <- rbind (cbind(ORformal_c, CIformal_c))
ORformal_c.CIformal_c

I tried a bootstrapping method below but no difference was found...

CIformal_c<-exp(confint.merMod(formal_c, method="boot"))

Here is the output:

Formula: 
formal ~ type_opld_binary2 + gender_binary2 + pfeat2 + (1 | opleader)
   Data: political_data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
   312.0    334.7   -150.0    300.0      322 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.8863 -0.3788 -0.1705  0.4527  3.4420 

Random effects:
 Groups   Name        Variance Std.Dev.
 opleader (Intercept) 2.865    1.693   
Number of obs: 328, groups:  opleader, 48

Fixed effects:
                            Estimate Std. Error z value Pr(>|z|)
(Intercept)                  0.92427    0.66839   1.383 0.166714
type_opld_binary2athlete    -3.47398    0.93910  -3.699 0.000216
type_opld_binary2influencer -3.67788    0.84842  -4.335 1.46e-05
gender_binary2female         1.50796    0.68908   2.188 0.028642
pfeat2story                  0.09136    0.45331   0.202 0.840274
(Intercept)                    
type_opld_binary2athlete    ***
type_opld_binary2influencer ***
gender_binary2female        *  
pfeat2story                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
               (Intr) typ_pld_bnry2t typ_pld_bnry2n gndr_2
typ_pld_bnry2t -0.474                                     
typ_pld_bnry2n -0.480  0.525                              
gndr_bnry2f    -0.398 -0.185         -0.103               
pfeat2story    -0.351  0.036         -0.144         -0.091

                            ORformal_c       2.5 %     97.5 %
(Intercept)                 2.52003814 0.679946015  9.3398477
type_opld_binary2athlete    0.03099351 0.004919372  0.1952683
type_opld_binary2influencer 0.02527639 0.004792244  0.1333187
gender_binary2female        4.51749331 1.170456269 17.4357183
pfeat2story                 1.09566606 0.450625842  2.6640375

Any advice would be appreciated, I'm quite new in those analyses. Thanks!!

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  • $\begingroup$ It would be nice to have the data you used to fit the model, or a small sample of it with which one can reproduce the results. $\endgroup$
    – mastropi
    Commented Oct 12, 2022 at 9:06
  • $\begingroup$ @mastropi thanks for your comment! I shared my data on OSF at this link osf.io/as6rj/?view_only=142b7297f6bf422699a1a99bf5d75652 [document is in .sav format], thanks!! $\endgroup$
    – AnaG
    Commented Oct 13, 2022 at 12:47
  • $\begingroup$ I took a quick look at the data and I see it has ~ 100 records. There isn't much that can be done to shorten the confidence intervals (CI), other than trying to predict the outcome better (which however might lead to overfitting, so do it carefully). If you want to understand why the CIs are too large, I suggest taking a look at the frequency distribution in each category being analyzed by the odds ratio (e.g. type_opld_binary2 = "athlete", type_opld_binary2 = "influencer", etc.) and analyzing the distribution of your target variable at each category. $\endgroup$
    – mastropi
    Commented Oct 14, 2022 at 14:00

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