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I'm investigating environmental effects (wind) on acoustic receiver detection probability for two types of transmitters using a binomial glmer. While my model analysis indicates that there's a significant effect between wind speed and transmitter type, graphical visualisation does not confirm this. If I'm correct, an interaction should demonstrate different regression slopes.

m1 <- glmer(cbind(df$Valid.detections, df$False.Detections) ~ Transmitter.depth + 
               Receiver.depth + Water.temperature + Wind.speed + Transmitter + 
               Distance + Habitat + Replicate + (1 | Day) + (Distance | SUR.ID) + Transmitter:Distance + Transmitter.depth:Habitat + 
               Receiver.depth:Habitat + Wind.speed:Transmitter, data=df, family=binomial(link=logit))

The model summary is as follows:

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: cbind(df$Valid.detections, df$False.Detections) ~ Transmitter.depth +  
    Receiver.depth + Water.temperature + Wind.speed + Transmitter +  
    Distance + Habitat + Replicate + (1 | Day) + (Distance |  
    SUR.ID) + Transmitter:Distance + Transmitter.depth:Habitat +      Receiver.depth:Habitat + Wind.speed:Transmitter
   Data: df

     AIC      BIC   logLik deviance df.resid 
  3941.9   4043.8  -1953.9   3907.9     2943 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-9.4911  0.0000  0.0000  0.5666  1.9143 

Random effects:
 Groups Name        Variance Std.Dev. Corr
 SUR.ID (Intercept)  0.33414 0.5781       
        Distance     0.09469 0.3077   1.00
 Day    (Intercept) 15.96629 3.9958       
Number of obs: 2960, groups:  SUR.ID, 20 Day, 6

Fixed effects:
                                Estimate Std. Error z value Pr(>|z|)    
(Intercept)                      3.20222    2.84984   1.124  0.26116    
Transmitter.depth               -0.35015    0.11794  -2.969  0.00299 ** 
Receiver.depth                  -0.57331    0.51919  -1.104  0.26949    
Water.temperature               -0.26595    0.11861  -2.242  0.02495 *  
Wind.speed                       1.31735    1.50457   0.876  0.38127    
TransmitterPT-04                -0.68854    0.08016  -8.590  < 2e-16 ***
Distance                        -0.39547    0.09228  -4.286 1.82e-05 ***
HabitatFinger                   -0.23746    3.57783  -0.066  0.94708    
Replicate2                      -0.21559    0.08009  -2.692  0.00710 ** 
TransmitterPT-04:Distance       -0.27874    0.08426  -3.308  0.00094 ***
Transmitter.depth:HabitatFinger  0.73965    0.28612   2.585  0.00973 ** 
Receiver.depth:HabitatFinger     3.02083    0.74546   4.052 5.07e-05 ***
Wind.speed:TransmitterPT-04     -0.15540    0.06572  -2.364  0.01806 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Trnsm. Rcvr.d Wtr.tm Wnd.sp TrPT-04 Distnc HbttFn Rplct2 TPT-04: Tr.:HF Rc.:HF
Trnsmttr.dp -0.024                                                                               
Recevr.dpth -0.120 -0.267                                                                        
Watr.tmprtr  0.019 -0.159  0.007                                                                 
Wind.speed   0.130  0.073 -0.974  0.040                                                          
TrnsmtPT-04 -0.015  0.027  0.020 -0.018 -0.024                                                   
Distance     0.022 -0.080  0.151 -0.052 -0.141 -0.164                                            
HabitatFngr -0.813  0.010  0.241 -0.025 -0.253  0.009   0.029                                    
Replicate2  -0.067  0.033  0.377 -0.293 -0.394  0.010   0.085  0.103                             
TrnsPT-04:D -0.006  0.043 -0.007 -0.050 -0.003  0.516  -0.373  0.004  0.006                      
Trnsmtt.:HF  0.017 -0.352  0.021  0.055  0.049  0.026  -0.142  0.031 -0.088  0.025               
Rcvr.dpt:HF  0.103  0.189 -0.830  0.051  0.817 -0.036  -0.143 -0.224 -0.385 -0.003  -0.229       
Wnd.:TPT-04 -0.002  0.026 -0.015  0.003 -0.009  0.176  -0.114 -0.002  0.016  0.306  -0.008  0.014

enter image description here

A side question: I noticed a strong negative correlation between the intercept and a dichotome categorical predictor. I wonder if this causes any problems for my data analysis. All the covariates are centered and scaled for numerical stability during modelling.

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    $\begingroup$ Interactions in nonlinear models are messier than in linear models. See Karaca-Mandic et al. (2012) for an overview. Basically the problem can be boiled down to all terms (not just interactions) have differing effects at different points on the original untransformed probability metric. This naturally makes life difficult for us sometimes. $\endgroup$
    – Affine
    Commented Jul 14, 2014 at 13:57
  • $\begingroup$ Hm. I will have a look at the paper. Thanks for your reply. $\endgroup$ Commented Jul 14, 2014 at 15:40
  • $\begingroup$ The p-values you're seeing in the table are (1) Wald tests [based on curvature] and (2) not corrected for finite-size effects. Guessing appropriate degrees of freedom is hard, but your number of groups is small, so I would definitely worry about this. If you have time, I would try confint(.,method="boot",which="beta_") to see how these CIs compare with the implicit Wald/Normal CIs you would get from the summary (or from confint(.,method="Wald")). (PS: good for you for sanity-checking your results graphically!) $\endgroup$
    – Ben Bolker
    Commented Jul 14, 2014 at 16:53
  • $\begingroup$ Hi Ben, I will def check the CI with bootstrapping methods. I will come back to your suggestion. Actually, I did stepwise backwards regression using the drop1(,test="Chi") test to test significance of parameter values. Although the coefficient value is different, it too is significant. $\endgroup$ Commented Jul 14, 2014 at 20:25
  • $\begingroup$ I tried to calculate bootstrap CIs, however, after 3 hours it was still computing. So I cancelled it, and then I saw an accumulation of warning messages "In optwrap(optimizer, par = start, fn = function(x) dd(mkpar(npar1, ... : convergence code 1 from bobyqa: bobyqa -- maximum number of function evaluations exceeded". This looks like the problem why it's taking so long. Can I do anything to get rid of this warning message? $\endgroup$ Commented Jul 15, 2014 at 12:48

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