     Hello,

I ´m dealing with a  fishing dataset obtained from a research cruise two 
trawl gears were fishing in paralel (twin trawling) during each of the 
fishing realizations (hauls) carried out. The response variable is the 
proportion of catches in the test gear prop=test/(test+reference). 
therefore:

  # prop=0.5 can be interpreted as  both  gears having the  same fishing 
efficiency on a given fish species
  # prop<0.5 means therefore less catch efficiency in the test gear.

The dataset contains a total of 14 hauls balanced in two different test 
*gear_setup* (setup1 (7 hauls) setup2 (7hauls)). Caught fishes were 
counted and measured (*fish_length*)

The aim of the modeling approach was:

-To evaluate if fish length size or gear setup significantly affects the 
response *prpp* .

Proposed model and first approach:

A mixed modeling approach using glmer(). Haul as  random intercept. The 
best model of this random intercept approach was:

mod5<-glmer(prop~gear_setup*fish_length+(1|haul),family=binomial,data=X.red,nAGQ=1,weights=ntotal)

              Df    AIC    BIC  logLik deviance   Chisq Chi Df Pr(>Chisq)
mod5  4 2067.4  2083.6 -1029.7   2059.4  7.3644      0  < 2.2e-16 ***

Random effects:

  Groups Name        Variance Std.Dev.
  haul   (Intercept)      0.2131   0.4617
Number of obs: 428, groups: haul, 14

Fixed effects:
                          Estimate Std. Error z value Pr(>|z|)
(Intercept)    -3.55598    0.29711 -11.969  < 2e-16 ***
setup2           1.60421    0.42128   3.808  0.00014 ***
fish_length    0.08660    0.01005   8.613  < 2e-16 ***
setup2:l        -0.06390    0.01409  -4.534  5.8e-06 ***


Second  approach:

Digging into the experimental data I realized the convenience of 
including  *fish_length* as random slope. After this change, the 
diagnostic criteria (AIC, BIC)  improved a lot, compared to the first 
modeling approach but the winner model only  gave the intercept as 
significant fixed effect:

mod45<-glmer(prop~1+(fish_length|haul),family=binomial,data=X.red,nAGQ=1,weights=ntotal)

       AIC       BIC              logLik         deviance
1876.6   1892.9283 -934.3459 1868.6918

Random effects:
  Groups Name        Variance Std.Dev. Corr
  haul   (Intercept)   6.97522    2.6411
fish_length             0.01171   0.1082   -0.98
Number of obs: 428, groups: haul, 14

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  -1.4575     0.1292  -11.28   <2e-16 ***

As I understand this model output, Including the  *fish_length* as 
random slope mask any fixed effect included in the model, since  the 
functional form of *prop* conditioned to *fish_length*  varied a lot 
between hauls. The problem arise when estimating the  confidence 
intervals from this model;


   prop.mu       F_lci      F_uci      R_lci            R_uci
            0.18    0.15      0.23         0.001        0.97


where *prop.mu* is the expected *prop* estimated in mod45; *F_* denotes  
the CI estimated using the fixed effect uncertainity, and *R_* 
represents the confidence intervals adding the uncertainity produced by 
the betweenn haul variation (sigma_2= 6.97522) . The *R_ * band is  
unexpectely high ranging  from 0.001 to 0.97, crossing by far the 
reference value of p=0.5 (equal catches).

I interpret this results as follows:

- Altough during the experiment there was a  significant catch reduction 
in test gear (0.18[0.15-0.23 ]), this catch reduction is not significant 
if we raise the inference into  a "population of hauls" perpective 
(0.18[ 0.001-0.97]).

So the questions are:

1.- Is my interpretation correct?
2.- How can this be possible, when plotting the experimental *prop* 
against *fish_length* -plot(prop~fish_length ) -  for each haul 
separately , it shows *prop* to  be less than 0.5 for  ~95% of 
*fish_length* presented in the catches?

Thank you in advance.



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