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I am performing a linear mixed-effect model.

library(readr)
library(nlme)
data = read_csv('data/data.csv') #131 observations, 22 variables
head(data)

states   year  green…¹   it  preCAPE     prePr   preRH  preTEMP  preVPD preWS
  <chr>  <dbl> <dbl>    <dbl>   <dbl>    <dbl>   <dbl>   <dbl>   <dbl>  <dbl>
1 AK     2011   4.61     49.6   0.056   -20.3   -1.74    -7.22   0.015  0.59 
2 AK     2013  19.1      26.4   13.8     6.38    1.39     3.54  -0.018 -3.17
3 AK     2003   0.605    23.0  -3.37    -4.12   -1.31    -9.16   0.052  7.51 
4 NJ     2007  10.9      14.5   7.22    -5.28   -1.55    -4.87   0.044  1.61 
5 WY     2004   2.74     14.5  -0.533   -20.8   -0.01    -5.09   0.016  1.54 
6 AK     2001  -4.39     13.2  -9.65     52.3   -0.71     6.80  -0.061  7.89 


lmm <- lme(greenup ~ preCAPE+prePr+preRH+preTEMP+preWS, data = data, random = ~1+preCAPE+prePr+preRH+preTEMP+preWS|states, method = 'ML', control = lmeControl(opt = "optim", msMaxIter=1000, maxIter = 1000, msMaxEval = 1000))

I get this error

Error in solve.default(pdMatrix(a, factor = TRUE)) : 
  system is computationally singular: reciprocal condition number = 3.08241e-44

I have used 5 variables in the linear mixed effect model for 131 observations. If I include the variable preVPD, I have 6 variables for 131 observations and everything works out well.

lmm <- lme(greenup ~ preCAPE+prePr+preRH+preTEMP+preVPD+preWS, data = data, random = ~1+preCAPE+prePr+preRH+preTEMP+preVPD+preWS|states, method = 'ML', control = lmeControl(opt = "optim", msMaxIter=1000, maxIter = 1000, msMaxEval = 1000))

These are the correlations between variables

> cor(postSM.early$preVPD, postSM.early$preCAPE)
[1] 0.2326779
> cor(postSM.early$preVPD, postSM.early$prePr)
[1] -0.1834306
> cor(postSM.early$preVPD, postSM.early$preRH)
[1] -0.6796942
> cor(postSM.early$preVPD, postSM.early$preTEMP)
[1] 0.8591199
> cor(postSM.early$preVPD, postSM.early$preWS)
[1] -0.144461
> cor(postSM.early$preCAPE, postSM.early$prePr)
[1] 0.5014529
> cor(postSM.early$preCAPE, postSM.early$preRH)
[1] -0.1001166
> cor(postSM.early$preCAPE, postSM.early$preTEMP)
[1] 0.2592998
> cor(postSM.early$preCAPE, postSM.early$preWS)
[1] 0.3096927
> cor(postSM.early$prePr, postSM.early$preRH)
[1] 0.4004015
> cor(postSM.early$prePr, postSM.early$preTEMP)
[1] 0.008052118
> cor(postSM.early$prePr, postSM.early$preWS)
[1] 0.5471488
> cor(postSM.early$preRH, postSM.early$preTEMP)
[1] -0.3157974
> cor(postSM.early$preRH, postSM.early$preWS)
[1] 0.08955221
> cor(postSM.early$preTEMP, postSM.early$preWS)
[1] -0.07545749

I have looked at this but it does not help. How can I fix this?

Edit: Here is a link to the data.

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  • 1
    $\begingroup$ your model is presumably extremely complicated, with a lot of r.e. $\endgroup$
    – utobi
    Commented Nov 13, 2022 at 12:21
  • $\begingroup$ also, can you tell something about the data? $\endgroup$
    – utobi
    Commented Nov 13, 2022 at 12:22
  • $\begingroup$ I have added some data information. Data is generally standardized to the mean. Should I standardize it even further e.g. with the range? I do not understand the complexity of the model may influence. Model 1 excl. VPD gives me an error but model 2 incl. VPD as a parameter does not give me an error? Is model 2 not more complex? $\endgroup$
    – Thomas
    Commented Nov 13, 2022 at 13:28
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    $\begingroup$ That is certainly unusual. Perhaps if you can share the data, ideally with dput() someone might be able to track down the issue. For what it is worth I do not think this is a programming issue, there is a statistical question hiding here. $\endgroup$
    – mdewey
    Commented Nov 13, 2022 at 16:46
  • 2
    $\begingroup$ I cannot post an answer while this is closed and I am not sure I have tracked down the exact cause but the bottom line as @utobi suggested is that you are trying to fit a complex pattern of random effects (re). If you delete either PR or WS from the random effect formula the model converges. However in the one case the re are negligible and virtually uncorrelated in the other the re are larger but highly correlated. Why adding a sixth term helps is anybody's guess. Incidentally I have used here the variable names from the data you posted not the ones in your question here. $\endgroup$
    – mdewey
    Commented Nov 14, 2022 at 13:47

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