title: How to Interpret binomial GLMM results
body: <p>I have a large dataset (24765 obs)
  I am trying to look at how does cleaning method effect emergence success(ES).
  I have several factors: beach(4 levels), cleaning method(3 levels) -->fixed
  I also have a few random variables: Zone (128 levels),Year(18 years) and Index(24765)
  This is an ORLE model to account for overdispersion. </p>
  
  <p>My best fit model based on AIC scores is:</p>
  
  <pre><code>    mod8a&lt;-glmer(ES.test~beach+method+(1|Year)+(1|index),data=y5,weights=egg.total,family=binomial)
  </code></pre>
  
  <p>The summary showed:</p>
  
  <pre><code>    summary(mod8a)#AIC=216732.9, same affect at every beach
    Generalized linear mixed model fit by maximum likelihood (LaplaceApproximation) ['glmerMod']
   Family: binomial  ( logit )
  Formula: ES.test ~ beach + method + (1 | Year) + (1 | index)
     Data: y5
  Weights: egg.total
  
        AIC       BIC    logLik  deviance  df.resid 
   214834.2  214891.0 -107410.1  214820.2     24758 
  
  Scaled residuals: 
       Min       1Q   Median       3Q      Max 
  -1.92900 -0.09344  0.00957  0.14682  1.62327 
  
  Random effects:
   Groups Name        Variance Std.Dev.
   index  (Intercept) 1.6541   1.286   
   Year   (Intercept) 0.6512   0.807   
  Number of obs: 24765, groups:  index, 24765; Year, 19
  
  Fixed effects:
                 Estimate Std. Error z value Pr(&gt;|z|)    
  (Intercept)     0.65518    0.18646   3.514 0.000442 ***
  beachHillsboro -0.06770    0.02143  -3.159 0.001583 ** 
  beachHO/HA      0.31927    0.03716   8.591  &lt; 2e-16 ***
  methodHTL only  0.18106    0.02526   7.169 7.58e-13 ***
  methodno clean  0.05989    0.03170   1.889 0.058853 .  
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
  Correlation of Fixed Effects:
              (Intr) bchHll bHO/HA mtHTLo
  beachHllsbr -0.002                     
  beachHO/HA  -0.054  0.047              
  mthdHTLonly -0.107 -0.242  0.355       
  methodnclen -0.084 -0.060  0.265  0.628
  </code></pre>
  
  <p>What is my "intercept" (as seen above)? I am missing levels of fixed factors, is that because R could not compute it?</p>
  
  <p>I tested for Overdispersion:</p>
  
  <pre><code>overdisp_fun &lt;- function(mod8a) {
  +   ## number of variance parameters in 
  +   ##   an n-by-n variance-covariance matrix
  +   vpars &lt;- function(m) {
  +     nrow(m)*(nrow(m)+1)/2
  +   }
  +   
  +   model8a.df &lt;- sum(sapply(VarCorr(mod8a),vpars))+length(fixef(mod8a))
  +   rdf &lt;- nrow(model.frame(mod8a))-model8a.df
  +   rp &lt;- residuals(mod8a,type="pearson")
  +   Pearson.chisq &lt;- sum(rp^2)
  +   prat &lt;- Pearson.chisq/rdf
  +   pval &lt;- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)
  +   c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval) 
  + }
  &gt; overdisp_fun(mod8a)
         chisq        ratio          rdf            p 
  2.064765e+03 8.339790e-02 2.475800e+04 1.000000e+00 
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/NarPe.png" rel="nofollow noreferrer">This shows the plot of mod8a</a>
  I would like to know why I am getting such a curve and what it means</p>
  
  <p>Lastly I did a multicomparion analysis using multcomp</p>
  
  <pre><code>ls1&lt;- glht(mod8a, mcp(beach = "Tukey"))$linfct
  ls2 &lt;- glht(mod8a, mcp(method= "Tukey"))$linfct
  summary(glht(mod8a, linfct = rbind(ls1, ls2)))
  </code></pre>
  
  <p>Simultaneous Tests for General Linear Hypotheses</p>
  
  <pre><code>Fit: glmer(formula = ES.test ~ beach + method + (1 | Year) + (1 | 
      index), data = y5, family = binomial, weights = egg.total)
  
  Linear Hypotheses:
                              Estimate Std. Error z value Pr(&gt;|z|)    
  Hillsboro - FTL/P == 0     -0.06770    0.02143  -3.159  0.00821 ** 
  HO/HA - FTL/P == 0          0.31927    0.03716   8.591  &lt; 0.001 ***
  HO/HA - Hillsboro == 0      0.38696    0.04201   9.211  &lt; 0.001 ***
  HTL only - HTL and SB == 0  0.18106    0.02526   7.169  &lt; 0.001 ***
  no clean - HTL and SB == 0  0.05989    0.03170   1.889  0.24469    
  no clean - HTL only == 0   -0.12117    0.02524  -4.800  &lt; 0.001 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  (Adjusted p values reported -- single-step method)
  </code></pre>
  
  <p>At this point help with interpreting for analysis would help and be greatly appreciated. (Especially with that sigmoid curve for my residuals) </p>