Warning message glmer

Question

I am looking at the interaction of 2 fixed variables and 1 random variable. Year has 19 levels and is numeric, beach is a factor and has 4 levels, method is a factor and has 3 levels. I am confused on the error messages below. NS1 is my nest success and it is weighted by the total number of eggs.

fit10<-glmer(NS1~0+beach+method+(1|year)+(1+beach*method|year),data=new1,weights=egg_total,family=binomial())

Warning messages:

1: In eval(expr, envir, enclos) : non-integer #successes in a binomial glm!

2: In commonArgs(par, fn, control, environment()) : maxfun < 10 * length(par)^2 is not recommended.

3: In optwrap(optimizer, devfun, start, rho$lower, control = control, : convergence code 1 from bobyqa: bobyqa -- maximum number of function evaluations exceeded

4: In (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, : failure to converge in 10000 evaluations

5: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : unable to evaluate scaled gradient

6: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 17 negative eigenvalues

EDIT: I have changed my code to:

    fit10<-glmer(NS1~0+beach+method+(1|year)+(1|beach/year)+  (1+method|year),data=new1,weights=crawls,family=binomial(),control=glmerControl(optimizer = "Nelder_Mead",optCtrl=list(maxfun=100000)))

which only gave me this warning message:

   Warning message:
    In eval(expr, envir, enclos) : non-integer #successes in a binomial glm!

A sample of my data looks like this:
 year     beach     method FC..         NS        NS1     egg_total   crawls
1   1997 Hillsboro   HTL only    7  12.500000 0.12500000         0      8
2   1997 Hillsboro   HTL only    4  33.333333 0.33333333        99      6
3   1997 Hillsboro   HTL only    3  57.142857 0.57142857         0      7
4   1997 Hillsboro   HTL only    2  33.333333 0.33333333         0      3
5   1997 Hillsboro   HTL only    0 100.000000 1.00000000       104      2
6   1997 Hillsboro   HTL only    0 100.000000 1.00000000         0      2
7   1997 Hillsboro   HTL only    0 100.000000 1.00000000       190      4
8   1997 Hillsboro   HTL only    1  66.666667 0.66666667         0      3
9   1997 Hillsboro   HTL only    0 100.000000 1.00000000       114      1
10  1997     P/FTL   HTL only    0 100.000000 1.00000000         0      1
11  1997     P/FTL   no clean    0 100.000000 1.00000000       140      1
12  1997     P/FTL   no clean    3  40.000000 0.40000000       277      5
13  1997     P/FTL HTL and SB    0 100.000000 1.00000000         0      1
14  1997       JUL   no clean    0 100.000000 1.00000000       153      2
15  1997       JUL   no clean    0 100.000000 1.00000000       113      2
16  1997       JUL   no clean    0 100.000000 1.00000000         0      1

NS1 is simple NS/100

This goes on for a total of 866 lines in excel

Answer 1

Repeating the model here for reference.

fit10<-  glmer(NS1~0+beach+method+(1|year)+ 
    (1+beach*method|year),
    data=new1,
    weights=egg_total,family=binomial())

The (1+beach*method|year) term seems optimistic; this is estimating the among-year variation in the interaction between beach and method, which represents a 12x12 variance-covariance matrix (=n*(n+1)/2 = 78 parameters). Unless you have at least 1000 observations, you probably shouldn't try this. Also, the (1|year) (intercept variation) and (1+beach*method|year) terms are redundant, because the latter estimates the among-year variation in intercept, beach effect, method effect, and their interaction ... It might be more realistic to try (1|beach/year) + (1+method|year) which fits intercept variation among beaches, years, beach:year interactions, and variation in method effects among years - a total of 1+1+(3*4/2)=8 variance-covariance parameters, which might still be too much depending on your data.

1: In eval(expr, envir, enclos) : non-integer #successes in a binomial glm!

To figure out what's going on here, as @aosmith comments above, y <- NS1*egg_total must be close to an integer (see binomial()$initialize for the test, which is (any(abs(y - round(y)) > 0.001)). If NS1 is supposed to be a proportion of eggs surviving, then this should work unless you made some kind of typo/rounding error somewhere.

This is something you want to figure out in order to make sure that the model actually makes sense; it's also possible that lme4 will behave badly with non-integer response variables for a distribution that's supposed to be integral.

2: In commonArgs(par, fn, control, environment()) : maxfun < 10 * length(par)^2 is not recommended.

This happens when your model has lots of parameters. You can increase maxfun by using control=glmerControl(optCtrl=list(maxfun=1e6)), but the real

3: In optwrap(optimizer, devfun, start, rho$lower, control = control, : convergence code 1 from bobyqa: bobyqa -- maximum number of function evaluations exceeded

This means the function didn't finish optimizing (see previous comment)

4: In (function (fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, : failure to converge in 10000 evaluations

Ditto.

5: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : unable to evaluate scaled gradient
6: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 17 negative eigenvalues

Not worth worrying about these too much before your model is minimally working.

Answer 2

The level left out is your reference level. Each parameter for the shown levels in your model summary should be added/subtracted from your reference level(the one left out). The reference level is parameter is estimated in the intercept term.