Nested mixed effectts question

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Nested mixed effectts question

CK98
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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Re: Nested mixed effectts question

Phillip Alday-2
(once again with the list)

Hi Caroline,

This question is probably better suited to r-sig-mixed-models
(https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models). Some things
are hard to tell without better understanding your design (I am not an
ecologist/relevant type of biologist), but I'll give it a go.

I suspect that your model is over-parameterized. It's very rare to see a
factor occur both as a fixed effect and as a grouping variable (the
stuff behind the | ) in the random effects.

If you don't care about particular sites but rather only the general
pattern across sites, then I would start with the model:

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

This treats site as a known source of variance, but not one that you
care about estimating particular effects for. You can still extract
predictions for them, i.e. the BLUPs, via coef(wrackbio), but their
theoretical interpretation is a bit different than the other option below.

If you do care about particular sites, I would use the model

# if your transects are uniquely labeled across sites
wrack.biomass ~ year * site + (1 | trans)
# if the transect labels are only unique within sites
wrack.biomass ~ year * site + (1 | sites:trans)

This will give you fixed effects as in your model, but models the
transects as a source of repetition and hence variance due to that
grouping. The choice of exact specification depends on the labeling in
your dataset; the sites:trans just guarantees unique labelling. The
random effect in this case would estimate the average variance across
all sites due to transects.

Best,
Phillip




On 16/01/19 12:00, [hidden email] wrote:
> Send R-help mailing list submissions to

> Today's Topics:
>
>    6. 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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Re: Nested mixed effectts question

CK98
Great! Your suggestions made perfect sense and worked well. Thank you so much.

> On Jan 18, 2019, at 3:33 AM, Phillip Alday <[hidden email]> wrote:
>
> (once again with the list)
>
> Hi Caroline,
>
> This question is probably better suited to r-sig-mixed-models
> (https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models). Some things
> are hard to tell without better understanding your design (I am not an
> ecologist/relevant type of biologist), but I'll give it a go.
>
> I suspect that your model is over-parameterized. It's very rare to see a
> factor occur both as a fixed effect and as a grouping variable (the
> stuff behind the | ) in the random effects.
>
> If you don't care about particular sites but rather only the general
> pattern across sites, then I would start with the model:
>
> wrack.biomass ~ year  + (1 + year | site/trans)
>
> This treats site as a known source of variance, but not one that you
> care about estimating particular effects for. You can still extract
> predictions for them, i.e. the BLUPs, via coef(wrackbio), but their
> theoretical interpretation is a bit different than the other option below.
>
> If you do care about particular sites, I would use the model
>
> # if your transects are uniquely labeled across sites
> wrack.biomass ~ year * site + (1 | trans)
> # if the transect labels are only unique within sites
> wrack.biomass ~ year * site + (1 | sites:trans)
>
> This will give you fixed effects as in your model, but models the
> transects as a source of repetition and hence variance due to that
> grouping. The choice of exact specification depends on the labeling in
> your dataset; the sites:trans just guarantees unique labelling. The
> random effect in this case would estimate the average variance across
> all sites due to transects.
>
> Best,
> Phillip
>
>
>
>
> On 16/01/19 12:00, [hidden email] wrote:
>> Send R-help mailing list submissions to
>
>> Today's Topics:
>>
>>   6. 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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