2
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I have fitted a GLMM with the function glmer of lme4 package. My data consists of a repeated measures count variable, which I am trying to explain with a continuous variable (week) and some categorical variables (zone, treatment and plot). The plot variable I used as a random factor, since I cannot tell the influence of plot itself.

Here is a subset of my data set, which provides the same error messages as the whole set:

     plot date       total_no zone    treatment  week fzone
3    110 2019-03-28      137  pioneer   ambient    3  pioneer
4    110 2019-04-04      187  pioneer   ambient    4  pioneer
5    110 2019-04-11      200  pioneer   ambient    5  pioneer
6    110 2019-04-18      203  pioneer   ambient    6  pioneer
7    110 2019-04-25      177  pioneer   ambient    7  pioneer
8    110 2019-05-02      123  pioneer   ambient    8  pioneer
9    110 2019-05-09      122  pioneer   ambient    9  pioneer
10   110 2019-05-16      123  pioneer   ambient   10  pioneer
11   110 2019-05-24      123  pioneer   ambient   11  pioneer
23   111 2019-03-28      122  pioneer      +1.5    3  pioneer
24   111 2019-04-04      153  pioneer      +1.5    4  pioneer
25   111 2019-04-11      136  pioneer      +1.5    5  pioneer
26   111 2019-04-18      145  pioneer      +1.5    6  pioneer
27   111 2019-04-25      110  pioneer      +1.5    7  pioneer
28   111 2019-05-02       65  pioneer      +1.5    8  pioneer
29   111 2019-05-09       89  pioneer      +1.5    9  pioneer
30   111 2019-05-16       79  pioneer      +1.5   10  pioneer
31   111 2019-05-24       54  pioneer      +1.5   11  pioneer
43   112 2019-03-28       89  pioneer        +3    3  pioneer
44   112 2019-04-04      101  pioneer        +3    4  pioneer
45   112 2019-04-11      104  pioneer        +3    5  pioneer
46   112 2019-04-18       95  pioneer        +3    6  pioneer
47   112 2019-04-25      110  pioneer        +3    7  pioneer
48   112 2019-05-02       88  pioneer        +3    8  pioneer
49   112 2019-05-09       89  pioneer        +3    9  pioneer
50   112 2019-05-16       98  pioneer        +3   10  pioneer
51   112 2019-05-24       99  pioneer        +3   11  pioneer
63   120 2019-03-28       77  pioneer   ambient    3  pioneer
64   120 2019-04-04      104  pioneer   ambient    4  pioneer
65   120 2019-04-11      107  pioneer   ambient    5  pioneer
66   120 2019-04-18      131  pioneer   ambient    6  pioneer
67   120 2019-04-25      171  pioneer   ambient    7  pioneer
68   120 2019-05-02       89  pioneer   ambient    8  pioneer
69   120 2019-05-09       94  pioneer   ambient    9  pioneer
70   120 2019-05-16       66  pioneer   ambient   10  pioneer
71   120 2019-05-24       63  pioneer   ambient   11  pioneer
83   121 2019-03-28       23  pioneer      +1.5    3  pioneer
84   121 2019-04-04       47  pioneer      +1.5    4  pioneer
85   121 2019-04-11       63  pioneer      +1.5    5  pioneer
86   121 2019-04-18       52  pioneer      +1.5    6  pioneer
87   121 2019-04-25       54  pioneer      +1.5    7  pioneer
88   121 2019-05-02       46  pioneer      +1.5    8  pioneer
89   121 2019-05-09       43  pioneer      +1.5    9  pioneer
90   121 2019-05-16       46  pioneer      +1.5   10  pioneer
91   121 2019-05-24       44  pioneer      +1.5   11  pioneer
103  122 2019-03-28       85  pioneer        +3    3  pioneer
104  122 2019-04-04      109  pioneer        +3    4  pioneer
105  122 2019-04-11      126  pioneer        +3    5  pioneer
106  122 2019-04-18      110  pioneer        +3    6  pioneer
107  122 2019-04-25      113  pioneer        +3    7  pioneer
108  122 2019-05-02       97  pioneer        +3    8  pioneer
109  122 2019-05-09       89  pioneer        +3    9  pioneer
110  122 2019-05-16       74  pioneer        +3   10  pioneer
111  122 2019-05-24       95  pioneer        +3   11  pioneer
123  130 2019-03-28       62  pioneer   ambient    3  pioneer
124  130 2019-04-04       64  pioneer   ambient    4  pioneer
125  130 2019-04-11       75  pioneer   ambient    5  pioneer
126  130 2019-04-18       58  pioneer   ambient    6  pioneer
127  130 2019-04-25       60  pioneer   ambient    7  pioneer
128  130 2019-05-02       47  pioneer   ambient    8  pioneer
129  130 2019-05-09       86  pioneer   ambient    9  pioneer
130  130 2019-05-16       72  pioneer   ambient   10  pioneer
131  130 2019-05-24       69  pioneer   ambient   11  pioneer
143  131 2019-03-28      233  pioneer      +1.5    3  pioneer
144  131 2019-04-04      277  pioneer      +1.5    4  pioneer
145  131 2019-04-11      303  pioneer      +1.5    5  pioneer
146  131 2019-04-18      281  pioneer      +1.5    6  pioneer
147  131 2019-04-25      216  pioneer      +1.5    7  pioneer
148  131 2019-05-02      202  pioneer      +1.5    8  pioneer
149  131 2019-05-09      197  pioneer      +1.5    9  pioneer
150  131 2019-05-16      144  pioneer      +1.5   10  pioneer
151  131 2019-05-24      167  pioneer      +1.5   11  pioneer
163  132 2019-03-28      170  pioneer        +3    3  pioneer
164  132 2019-04-04      211  pioneer        +3    4  pioneer
165  132 2019-04-11      323  pioneer        +3    5  pioneer
166  132 2019-04-18      298  pioneer        +3    6  pioneer
167  132 2019-04-25      297  pioneer        +3    7  pioneer
168  132 2019-05-02      212  pioneer        +3    8  pioneer
169  132 2019-05-09      202  pioneer        +3    9  pioneer
170  132 2019-05-16      204  pioneer        +3   10  pioneer
171  132 2019-05-24      215  pioneer        +3   11  pioneer
183  240 2019-03-28        9 lowmarsh   ambient    3 lowmarsh
184  240 2019-04-04       16 lowmarsh   ambient    4 lowmarsh
185  240 2019-04-11        8 lowmarsh   ambient    5 lowmarsh
186  240 2019-04-18        8 lowmarsh   ambient    6 lowmarsh
187  240 2019-04-25        8 lowmarsh   ambient    7 lowmarsh
188  240 2019-05-02        8 lowmarsh   ambient    8 lowmarsh
189  240 2019-05-09       11 lowmarsh   ambient    9 lowmarsh
190  240 2019-05-16       12 lowmarsh   ambient   10 lowmarsh
191  240 2019-05-24       11 lowmarsh   ambient   11 lowmarsh
203  241 2019-03-28        9 lowmarsh      +1.5    3 lowmarsh
204  241 2019-04-04       20 lowmarsh      +1.5    4 lowmarsh
205  241 2019-04-11       19 lowmarsh      +1.5    5 lowmarsh
206  241 2019-04-18       15 lowmarsh      +1.5    6 lowmarsh
207  241 2019-04-25       21 lowmarsh      +1.5    7 lowmarsh
208  241 2019-05-02       19 lowmarsh      +1.5    8 lowmarsh
209  241 2019-05-09       21 lowmarsh      +1.5    9 lowmarsh
210  241 2019-05-16       14 lowmarsh      +1.5   10 lowmarsh
211  241 2019-05-24       17 lowmarsh      +1.5   11 lowmarsh
223  242 2019-03-28       17 lowmarsh        +3    3 lowmarsh
224  242 2019-04-04       22 lowmarsh        +3    4 lowmarsh
225  242 2019-04-11       28 lowmarsh        +3    5 lowmarsh
226  242 2019-04-18       26 lowmarsh        +3    6 lowmarsh
227  242 2019-04-25       25 lowmarsh        +3    7 lowmarsh
228  242 2019-05-02       15 lowmarsh        +3    8 lowmarsh
229  242 2019-05-09       14 lowmarsh        +3    9 lowmarsh
230  242 2019-05-16       17 lowmarsh        +3   10 lowmarsh
231  242 2019-05-24       14 lowmarsh        +3   11 lowmarsh
243  250 2019-03-28       53 lowmarsh   ambient    3 lowmarsh
244  250 2019-04-04       55 lowmarsh   ambient    4 lowmarsh
245  250 2019-04-11       66 lowmarsh   ambient    5 lowmarsh
246  250 2019-04-18       64 lowmarsh   ambient    6 lowmarsh
247  250 2019-04-25       19 lowmarsh   ambient    7 lowmarsh
248  250 2019-05-02       11 lowmarsh   ambient    8 lowmarsh
249  250 2019-05-09       60 lowmarsh   ambient    9 lowmarsh
250  250 2019-05-16       66 lowmarsh   ambient   10 lowmarsh
251  250 2019-05-24       50 lowmarsh   ambient   11 lowmarsh
263  251 2019-03-28       11 lowmarsh      +1.5    3 lowmarsh
264  251 2019-04-04       20 lowmarsh      +1.5    4 lowmarsh
265  251 2019-04-11       21 lowmarsh      +1.5    5 lowmarsh
266  251 2019-04-18       13 lowmarsh      +1.5    6 lowmarsh
267  251 2019-04-25       12 lowmarsh      +1.5    7 lowmarsh
268  251 2019-05-02       62 lowmarsh      +1.5    8 lowmarsh
269  251 2019-05-09       11 lowmarsh      +1.5    9 lowmarsh
270  251 2019-05-16       12 lowmarsh      +1.5   10 lowmarsh
271  251 2019-05-24       13 lowmarsh      +1.5   11 lowmarsh
283  252 2019-03-28       18 lowmarsh        +3    3 lowmarsh
284  252 2019-04-04       29 lowmarsh        +3    4 lowmarsh
285  252 2019-04-11       50 lowmarsh        +3    5 lowmarsh
286  252 2019-04-18       43 lowmarsh        +3    6 lowmarsh
287  252 2019-04-25       47 lowmarsh        +3    7 lowmarsh
288  252 2019-05-02       12 lowmarsh        +3    8 lowmarsh
289  252 2019-05-09       15 lowmarsh        +3    9 lowmarsh
290  252 2019-05-16       20 lowmarsh        +3   10 lowmarsh
291  252 2019-05-24       29 lowmarsh        +3   11 lowmarsh
303  260 2019-03-28        6 lowmarsh   ambient    3 lowmarsh
304  260 2019-04-04       14 lowmarsh   ambient    4 lowmarsh
305  260 2019-04-11       15 lowmarsh   ambient    5 lowmarsh
306  260 2019-04-18       10 lowmarsh   ambient    6 lowmarsh
307  260 2019-04-25       10 lowmarsh   ambient    7 lowmarsh
308  260 2019-05-02       11 lowmarsh   ambient    8 lowmarsh
309  260 2019-05-09       11 lowmarsh   ambient    9 lowmarsh

I implemented this model

glmm.a<-glmer(total_no~week*treatment*fzone+(1|plot), data=subset,
              family=poisson
)
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.00689502 (tol = 0.002, component 1)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?

I got these warning messages above, which I researched can be solved in come cases by using different optimizers, so I did this:

glmm.1<-glmer(total_no~week*treatment+fzone+(1|plot), data=subset,
              family=poisson,   control=glmerControl(optimizer=c("bobyqa","Nelder_Mead"),optCtrl=list(maxfun=100000))
)

I still get the same warnings. Then I simplified the model, because one interaction had no significance at all (is this allowed, when such warning messages occur, or do I have to have a model to begin with, which has no warnings?)

glmm.1<-glmer(total_no~week*treatment+fzone+(1|plot), data=subset,
              family=poisson,
control=glmerControl(optimizer=c("bobyqa","Nelder_Mead"),optCtrl=list(maxfun=100000))
              )

The model outputs look like this:

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: poisson  ( log )
Formula: total_no ~ week * treatment * fzone + (1 | plot)
   Data: subset
Control: 
glmerControl(optimizer = c("bobyqa", "Nelder_Mead"), optCtrl = list(maxfun = 1e+05))

     AIC      BIC   logLik deviance df.resid 
  3312.7   3388.7  -1637.3   3274.7      386 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.9475 -1.0915 -0.0573  0.9091 12.2790 

Random effects:
 Groups Name        Variance Std.Dev.
 plot   (Intercept) 0.2371   0.4869  
Number of obs: 405, groups:  plot, 27

Fixed effects:
                                     Estimate Std. Error z value
(Intercept)                          1.553798   0.331032   4.694
week                                -0.052487   0.015483  -3.390
treatment+3                         -0.120870   0.452937  -0.267
treatmentambient                     0.375292   0.428522   0.876
fzonelowmarsh                        1.829767   0.443244   4.128
fzonepioneer                         3.614629   0.435442   8.301
week:treatment+3                    -0.002754   0.023291  -0.118
week:treatmentambient               -0.038247   0.021971  -1.741
week:fzonelowmarsh                  -0.051666   0.018045  -2.863
week:fzonepioneer                   -0.028577   0.015761  -1.813
treatment+3:fzonelowmarsh            0.358579   0.613986   0.584
treatmentambient:fzonelowmarsh      -0.423375   0.595685  -0.711
treatment+3:fzonepioneer             0.270593   0.604163   0.448
treatmentambient:fzonepioneer       -0.492087   0.586297  -0.839
week:treatment+3:fzonelowmarsh       0.007062   0.026282   0.269
week:treatmentambient:fzonelowmarsh  0.075966   0.024696   3.076
week:treatment+3:fzonepioneer        0.016768   0.023624   0.710
week:treatmentambient:fzonepioneer   0.055656   0.022369   2.488
                                    Pr(>|z|)    
(Intercept)                         2.68e-06 ***
week                                0.000699 ***
treatment+3                         0.789579    
treatmentambient                    0.381149    
fzonelowmarsh                       3.66e-05 ***
fzonepioneer                         < 2e-16 ***
week:treatment+3                    0.905880    
week:treatmentambient               0.081716 .  
week:fzonelowmarsh                  0.004194 ** 
week:fzonepioneer                   0.069808 .  
treatment+3:fzonelowmarsh           0.559208    
treatmentambient:fzonelowmarsh      0.477248    
treatment+3:fzonepioneer            0.654239    
treatmentambient:fzonepioneer       0.401293    
week:treatment+3:fzonelowmarsh      0.788157    
week:treatmentambient:fzonelowmarsh 0.002098 ** 
week:treatment+3:fzonepioneer       0.477846    
week:treatmentambient:fzonepioneer  0.012844 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 18 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

optimizer (Nelder_Mead) convergence code: 0 (OK)
Model failed to converge with max|grad| = 0.00689502 (tol = 0.002, component 1)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?
> summary(glmm.1)
Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: poisson  ( log )
Formula: total_no ~ week * treatment + fzone + (1 | plot)
   Data: subset
Control: 
glmerControl(optimizer = c("bobyqa", "Nelder_Mead"), optCtrl = list(maxfun = 1e+05))

     AIC      BIC   logLik deviance df.resid 
  3323.6   3359.6  -1652.8   3305.6      396 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-7.2154 -1.0578 -0.0778  0.9660 12.3568 

Random effects:
 Groups Name        Variance Std.Dev.
 plot   (Intercept) 0.25     0.5     
Number of obs: 405, groups:  plot, 27

Fixed effects:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)            1.704335   0.225066   7.573 3.66e-14 ***
week                  -0.082407   0.002762 -29.831  < 2e-16 ***
treatment+3           -0.006115   0.235784  -0.026  0.97931    
treatmentambient       0.006505   0.234298   0.028  0.97785    
fzonelowmarsh          1.591394   0.243523   6.535 6.37e-11 ***
fzonepioneer           3.493139   0.242456  14.407  < 2e-16 ***
week:treatment+3       0.012080   0.003708   3.258  0.00112 ** 
week:treatmentambient  0.017372   0.003845   4.519 6.23e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) week   trtm+3 trtmnt fznlwm fznpnr wk:t+3
week        -0.107                                          
treatment+3 -0.550  0.102                                   
tretmntmbnt -0.563  0.103  0.605                            
fzonelwmrsh -0.562  0.000 -0.010  0.004                     
fzonepioner -0.565  0.000 -0.009  0.005  0.523              
wk:trtmnt+3  0.080 -0.745 -0.141 -0.076  0.000  0.000       
wk:trtmntmb  0.077 -0.719 -0.079 -0.141  0.000  0.000  0.535
optimizer (Nelder_Mead) convergence code: 0 (OK)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?

and without optimizers

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: poisson  ( log )
Formula: total_no ~ week * treatment * fzone + (1 | plot)
   Data: subset

     AIC      BIC   logLik deviance df.resid 
  3312.7   3388.7  -1637.3   3274.7      386 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.9475 -1.0915 -0.0573  0.9091 12.2790 

Random effects:
 Groups Name        Variance Std.Dev.
 plot   (Intercept) 0.2371   0.4869  
Number of obs: 405, groups:  plot, 27

Fixed effects:
                                     Estimate Std. Error z value
(Intercept)                          1.553798   0.331032   4.694
week                                -0.052487   0.015483  -3.390
treatment+3                         -0.120870   0.452937  -0.267
treatmentambient                     0.375292   0.428522   0.876
fzonelowmarsh                        1.829767   0.443244   4.128
fzonepioneer                         3.614629   0.435442   8.301
week:treatment+3                    -0.002754   0.023291  -0.118
week:treatmentambient               -0.038247   0.021971  -1.741
week:fzonelowmarsh                  -0.051666   0.018045  -2.863
week:fzonepioneer                   -0.028577   0.015761  -1.813
treatment+3:fzonelowmarsh            0.358579   0.613986   0.584
treatmentambient:fzonelowmarsh      -0.423375   0.595685  -0.711
treatment+3:fzonepioneer             0.270593   0.604163   0.448
treatmentambient:fzonepioneer       -0.492087   0.586297  -0.839
week:treatment+3:fzonelowmarsh       0.007062   0.026282   0.269
week:treatmentambient:fzonelowmarsh  0.075966   0.024696   3.076
week:treatment+3:fzonepioneer        0.016768   0.023624   0.710
week:treatmentambient:fzonepioneer   0.055656   0.022369   2.488
                                    Pr(>|z|)    
(Intercept)                         2.68e-06 ***
week                                0.000699 ***
treatment+3                         0.789579    
treatmentambient                    0.381149    
fzonelowmarsh                       3.66e-05 ***
fzonepioneer                         < 2e-16 ***
week:treatment+3                    0.905880    
week:treatmentambient               0.081716 .  
week:fzonelowmarsh                  0.004194 ** 
week:fzonepioneer                   0.069808 .  
treatment+3:fzonelowmarsh           0.559208    
treatmentambient:fzonelowmarsh      0.477248    
treatment+3:fzonepioneer            0.654239    
treatmentambient:fzonepioneer       0.401293    
week:treatment+3:fzonelowmarsh      0.788157    
week:treatmentambient:fzonelowmarsh 0.002098 ** 
week:treatment+3:fzonepioneer       0.477846    
week:treatmentambient:fzonepioneer  0.012844 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 18 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

optimizer (Nelder_Mead) convergence code: 0 (OK)
Model failed to converge with max|grad| = 0.00689502 (tol = 0.002, component 1)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?

 summary(glmm.1)
Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: poisson  ( log )
Formula: total_no ~ week * treatment + fzone + (1 | plot)
   Data: subset

     AIC      BIC   logLik deviance df.resid 
  3323.6   3359.6  -1652.8   3305.6      396 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-7.2154 -1.0578 -0.0778  0.9660 12.3568 

Random effects:
 Groups Name        Variance Std.Dev.
 plot   (Intercept) 0.25     0.5     
Number of obs: 405, groups:  plot, 27

Fixed effects:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)            1.704335   0.225066   7.573 3.66e-14 ***
week                  -0.082407   0.002762 -29.831  < 2e-16 ***
treatment+3           -0.006115   0.235784  -0.026  0.97931    
treatmentambient       0.006505   0.234298   0.028  0.97785    
fzonelowmarsh          1.591394   0.243523   6.535 6.37e-11 ***
fzonepioneer           3.493139   0.242456  14.407  < 2e-16 ***
week:treatment+3       0.012080   0.003708   3.258  0.00112 ** 
week:treatmentambient  0.017372   0.003845   4.519 6.23e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) week   trtm+3 trtmnt fznlwm fznpnr wk:t+3
week        -0.107                                          
treatment+3 -0.550  0.102                                   
tretmntmbnt -0.563  0.103  0.605                            
fzonelwmrsh -0.562  0.000 -0.010  0.004                     
fzonepioner -0.565  0.000 -0.009  0.005  0.523              
wk:trtmnt+3  0.080 -0.745 -0.141 -0.076  0.000  0.000       
wk:trtmntmb  0.077 -0.719 -0.079 -0.141  0.000  0.000  0.535
optimizer (Nelder_Mead) convergence code: 0 (OK)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?

For the minimal adequate model (the glmm.1 with optimizers)there is still the warning message with the very large eigenvalue. Here is what I did not solve by checking for similar questions:

  1. How do I know, if this warning is telling me of a misfitted model or if I can safely ignore this? I think this warning has to do with the random effect, but I don´t know how exactly.

  2. Is there a solution to this, which does not include scaling? I tried to rescale the only continuous variable (week) with no different result. I did not scale my response variable yet, but I don´t know if this would make a difference. I also thought about explicitly tell R to handle all factors as such, so this is also not the issue (I read this in another answer).

  3. if this was the model I can use for my data, how would I do a post hoc analysis? I researched that for a GLMM there are the options of the emmeans() and multcomp() packages.

  4. Would you agree with that or is a post hoc analysis unnessecary in this case?

If I did not provide you with all the information you need, please tell me and I will edit. Thank you in advance, any help is appreciated!!

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  • 2
    $\begingroup$ The column headings in the data listing are not aligned with the data, making it hard to associate them. But I think if you put in (week - 7) in place of week, it will considerably improve the conditioning of this model, and maybe you won't get those warning messages. $\endgroup$
    – Russ Lenth
    May 18 at 13:45
  • $\begingroup$ @RussLenth Thank you for your answer! Can you explain, why this might help? Is this just a data transformation or what will it do? Thanks $\endgroup$
    – Matonga
    May 19 at 7:47
  • 2
    $\begingroup$ It changes week = 3, 4, ..., 11 to week - 7 = -4, -3, ..., 4. Regression calculations involve adding up the squares of things and subtracting the square of the sum of the same numbers. If the sum is already zero, that makes it more accurate than taking the difference of two large numbers yielding a small one. $\endgroup$
    – Russ Lenth
    May 19 at 12:56

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