[R] Nested mixed effectts question

[Caroline]

Hi,

I am helping a friend with an analysis for a study where she sampled wrack biomass in 15 different sites across three years. At each site, she sampled from three different transects. She is trying to estimate the effect of year*site on biomass while accounting for the nested nature (site/transcet) and repeated measure study design. 

wrack.biomass ~ year * site + (1 | site/trans)

However she gets the following warning messages:
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
   Hessian is numerically singular: parameters are not uniquely determined

And her model output is: 

> summary(wrackbio)
Linear mixed model fit by REML 
t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: (actual.mean.biomass.m2.50.m.transect) ~ year * site + (1 | site/trans)
   Data: wrack_resp_allyrs_transname

REML criterion at convergence: 691

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.3292 -0.2624 -0.0270  0.1681  3.8024 

Random effects:
 Groups     Name        Variance Std.Dev.
 trans:site (Intercept)  0.0000  0.0000  
 site       (Intercept)  0.5531  0.7437  
 Residual               94.6453  9.7286  
Number of obs: 132, groups:  trans:site, 44; site, 15

Fixed effects:
                    Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)        9.692e+00  5.666e+00  1.119e-04   1.711    0.999    
year2016           1.256e+01  7.943e+00  8.700e+01   1.582    0.117    
year2017           2.395e+00  7.943e+00  8.700e+01   0.302    0.764    
siteCL             5.672e+01  8.013e+00  1.119e-04   7.079    0.999    
siteDO            -4.315e+00  8.013e+00  1.119e-04  -0.539    0.999    
siteFL             7.872e+00  8.013e+00  1.119e-04   0.982    0.999    
siteFS            -7.619e+00  8.013e+00  1.119e-04  -0.951    0.999    
siteGH             4.369e+00  8.013e+00  1.119e-04   0.545    0.999    
siteLB            -3.747e+00  8.013e+00  1.119e-04  -0.468    0.999    
siteLBP           -5.298e+00  8.943e+00  1.736e-04  -0.592    0.999    
siteNB            -2.953e+00  8.013e+00  1.119e-04  -0.369    1.000    
siteNS             1.005e+00  8.013e+00  1.119e-04   0.125    1.000    
sitePC            -5.238e+00  8.013e+00  1.119e-04  -0.654    0.999    
siteSB            -7.649e+00  8.013e+00  1.119e-04  -0.955    0.999    
siteSILT          -4.734e+00  8.013e+00  1.119e-04  -0.591    0.999    
siteSL            -7.890e+00  8.013e+00  1.119e-04  -0.985    0.999    
siteUD            -8.230e+00  8.013e+00  1.119e-04  -1.027    0.999    
year2016:siteCL   -6.359e+01  1.123e+01  8.700e+01  -5.660 1.91e-07 ***
year2017:siteCL   -5.210e+01  1.123e+01  8.700e+01  -4.638 1.23e-05 ***
year2016:siteDO   -1.550e+01  1.123e+01  8.700e+01  -1.380    0.171    
year2017:siteDO   -3.022e+00  1.123e+01  8.700e+01  -0.269    0.789    
year2016:siteFL   -7.522e+00  1.123e+01  8.700e+01  -0.670    0.505    
year2017:siteFL   -1.167e+01  1.123e+01  8.700e+01  -1.039    0.302    
year2016:siteFS   -1.391e+01  1.123e+01  8.700e+01  -1.238    0.219    
year2017:siteFS   -2.170e+00  1.123e+01  8.700e+01  -0.193    0.847    
year2016:siteGH   -9.135e+00  1.123e+01  8.700e+01  -0.813    0.418    
year2017:siteGH   -4.031e+00  1.123e+01  8.700e+01  -0.359    0.721    
year2016:siteLB   -8.668e+00  1.123e+01  8.700e+01  -0.772    0.442    
year2017:siteLB   -1.530e+00  1.123e+01  8.700e+01  -0.136    0.892    
year2016:siteLBP  -5.336e+00  1.256e+01  8.700e+01  -0.425    0.672    
year2017:siteLBP  -1.826e+00  1.256e+01  8.700e+01  -0.145    0.885    
year2016:siteNB   -7.999e+00  1.123e+01  8.700e+01  -0.712    0.478    
year2017:siteNB   -5.645e+00  1.123e+01  8.700e+01  -0.502    0.617    
year2016:siteNS   -8.871e+00  1.123e+01  8.700e+01  -0.790    0.432    
year2017:siteNS   -3.443e+00  1.123e+01  8.700e+01  -0.306    0.760    
year2016:sitePC   -1.603e+01  1.123e+01  8.700e+01  -1.427    0.157    
year2017:sitePC   -2.955e+00  1.123e+01  8.700e+01  -0.263    0.793    
year2016:siteSB   -1.316e+01  1.123e+01  8.700e+01  -1.171    0.245    
year2017:siteSB   -3.220e+00  1.123e+01  8.700e+01  -0.287    0.775    
year2016:siteSILT -1.616e+01  1.123e+01  8.700e+01  -1.438    0.154    
year2017:siteSILT -2.497e-01  1.123e+01  8.700e+01  -0.022    0.982    
year2016:siteSL   -1.004e+01  1.123e+01  8.700e+01  -0.894    0.374    
year2017:siteSL    1.123e+00  1.123e+01  8.700e+01   0.100    0.921    
year2016:siteUD   -1.345e+01  1.123e+01  8.700e+01  -1.197    0.235    
year2017:siteUD    3.810e+00  1.123e+01  8.700e+01   0.339    0.735    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 45 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

convergence code: 0
unable to evaluate scaled gradient
 Hessian is numerically singular: parameters are not uniquely determined

Is the model unable to converge because her dataset is too small to include an interaction term or is stemming from issues of model structure?

Thanks! 

Caroline








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