Error in repeat measures

Question

I am trying to run a linear mixed model with repetitive measures at 57 different time points. But I keep getting the error message:

Error in solve.default(estimates[dimE[1L] - (p:1), dimE[2L] - (p:1), drop = FALSE]) : 

System

is computationally singular: the number of inverse conditions = 7.7782e-18

What does it mean?

My code is this:

 model.dataset = data.frame(TimepointM=timepoint,SubjectM=sample,GeneM=gene) library("nlme") model = lme(score ~ TimepointM + GeneM,data=model.dataset,random = ~1|SubjectM) 

Here is the data:

 score = c(2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,6,7,2,-3,11,14,1,7,6,7,2,-3,11,14,1,7,6,2,-3,11,14,1,7,7,2,-3,11,14,1,7,6,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,6,2,-3,11,14,1,7,7,2,-3,11,14,1,7,6,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,6,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,6,7,2,-3,11,14,1,7,6,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7,2,-3,11,14,1,7) timepoint = c(1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,19,19,19,19,19,19,19,20,20,20,20,20,20,21,21,21,21,21,21,24,24,24,24,24,24,24,25,25,25,25,25,25,25,27,27,27,27,27,27,28,28,28,28,28,28,29,29,29,29,29,29,30,30,30,30,30,30,30,31,31,31,31,31,31,31,32,32,32,32,32,32,33,33,33,33,33,33,33,33,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,38,38,38,39,39,39,39,39,39,39,40,40,40,40,40,40,40,41,41,41,41,41,41,41,41,42,42,42,42,42,42,42,42,43,43,43,43,43,43,44,44,44,44,44,44,44,45,45,45,45,45,45,46,46,46,46,46,46,47,47,47,47,47,47,48,48,48,48,48,48,49,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,52,52,53,53,53,53,53,53,53,54,54,54,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,57,57,57,57) sample = c("S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S13T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S01T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0","S02T0","S03T0","S07T0","S09T0","S10T0","S12T0") gene =c(24.1215870,-18.8771658,-27.3747309,-41.5740199,26.1561877,-2.7836332,20.8322796,36.5745088,-24.1541743,-11.2362216,4.9042852,7.4230219,155.8663563,16.4465366,-11.7982286,-1.6102783,-35.9559091,27.7909495,-13.9181661,-29.6037658,-68.4297261,-45.0877920,-48.3157529,17.1649982,-26.9084544,19.7358439,-5.8991143,-24.1541743,-23.5960654,13.0780939,-2.7836332,18.6394081,-28.3157487,-49.9186269,-33.7086648,41.6864242,-30.6199654,36.1823804,-36.5745088,-49.9186269,-44.9448864,-4.9042852,-34.3314764,62.3465425,-42.7609951,-11.7982286,-32.2055657,-56.1811080,5.7216661,-17.6296771,4.3857431,-43.6534459,9.6616697,-44.9448864,18.7997599,-12.9902884,109.1064494,7.6750504,-43.6534459,-17.7130611,-25.8433097,5.7216661,-18.5575548,35.2750175,36.1823804,2.3596457,-25.7644526,-55.0574858,15.5302365,-19.4854325,73.3687689,63.1668918,20.8322796,16.5175201,-22.5438960,-28.0905540,15.5302365,7.4230219,39.5062602,107.4657509,36.1823804,-23.5964573,-45.0877920,-43.8212642,4.0869043,-40.8266205,26.3375068,13.1572292,-25.9561030,-40.2569571,-52.8102415,2.4521426,-49.1775202,246.1047731,36.1823804,11.7982286,-35.4261223,-26.9669318,-2.4521426,-38.0429873,38.5656349,9.8679219,16.5175201,8.0513914,-42.6976421,26.9735686,-26.9084544,4.3857431,12.9780515,-32.2055657,-33.7086648,9.8085704,-36.2800196,215.7518511,6.5786146,-9.4385829,-19.3233394,-40.4503978,17.1649982,-7.4230219,14.2536650,-23.5964573,-53.1391834,-52.8102415,22.0692834,-54.7447866,24.1215870,-44.8332688,-24.1541743,-42.6976421,26.9735686,-40.8266205,191.1413737,17.5429723,-70.7893718,-37.0364006,-39.3267756,-4.9042852,-0.9278777,93.5198138,-6.5786146,-24.7762801,-28.9850091,-39.3267756,22.0692834,-50.1053979,14.2536650,23.5964573,-20.9336177,-53.9338637,14.7128556,-39.8987428,4.3857431,-64.8902575,-59.5802966,-33.7086648,22.0692834,2.7836332,46.0503024,-35.3946859,-43.4775137,-53.9338637,30.2430921,-34.3314764,80.3942259,28.5073300,-87.3068919,-24.1541743,-62.9228410,13.0780939,-25.0526990,35.0859447,-24.7762801,-38.6466789,-58.4283523,31.0604729,0.0000000,24.4562563,1.0964358,-27.1359259,-75.6830794,-16.8543324,20.4345217,-11.1345329,74.1390629,18.2282447,-27.3044720,-45.2890768,-46.7707724,15.3258912,-27.9523169,-6.9763039,117.3099418,18.6394081,-21.2368115,-38.6466789,-34.8322870,22.0692834,-48.2496425,6.5786146,-64.8902575,-51.5289052,-80.9007955,23.7040451,-26.9084544,223.1349942,8.7714862,10.6184058,-127.2119846,-31.4614205,0.8173809,-16.7017993,9.8679219,-35.3946859,-54.7494617,-44.9448864,14.7128556,-18.5575548,97.5827836,-166.3550237,-95.0064189,-123.5984376,104.6247509,-121.5519839,33.9895089,-44.8332688,-40.2569571,-56.1811080,51.4949946,0.0000000,-16.9312544,95.9808615,6.5786146,-21.2368115,-9.6616697,-13.4834659,10.6259513,-25.9805767,116.4895926,-1.0964358,-16.5175201,-56.3597400,-44.9448864,13.8954747,-12.9902884,-5.6437515,71.3703842,25.2180227,-41.2938002,-53.1391834,-32.5850426,8.9911895,12.9902884,31.9812582,1.0964358,-70.7893718,-33.8158440,-38.2031534,-15.5302365,-25.0526990,153.4053085,36.1823804,-34.2148630,-41.8672354,-19.1015767,22.8866643,0.9278777,20.8322796,-29.4955716,-43.4775137,-69.6645739,33.5126155,-45.4660092,26.3144585,-33.0350402,24.1541743,-42.6976421,0.0000000,-28.7642099,38.3752520,-7.0789372,-22.5438960,-20.2251989,34.3299964,19.4854325,4.3857431,-61.3507889,-33.8158440,-64.0464631,39.2342816,-28.7642099,183.7582306,-4.3857431,-22.4166344,-28.9850091,-57.3047302,25.3388069,-26.9084544,35.0859447,7.0789372,-33.8158440,-43.8212642,-1.6347617,5.5672664,-35.0859447,-40.1139773,-14.4925046,-12.3598438,21.2519025,-14.8460438,119.7709896,30.7002016,-22.4166344,-46.6980703,-43.8212642,5.7216661,-10.2066551,203.4466124,116.2221917,-83.7674233,-109.4989234,-38.2031534,78.4685632,-56.6005421,21.9287154,-63.7104346,-56.3597400,-4.4944886,25.3388069,-73.3023414,29.6037658,-31.8552173,-46.6980703,-79.7771734,21.2519025,-18.5575548,16.4465366,-27.1359259,-43.4775137,-41.5740199,-11.4433321,-23.1969435,27.4108943,-84.9472461,-53.1391834,-40.4503978,22.8866643,16.7017993) 

Answer 1

tl; dr I think your problem is that each person has exactly the same answer value (score) for each point in time (that is, perfect homogeneity within individuals), so the term random effects fully explains the data; for fixed effects there is nothing left. Are you sure you don't want to use gene as the response variable? (Discovered after starting modeling attempts, by building damned data, something that everyone should always do first ...)

 ## simplifying names etc. slightly dd <- data.frame(timepoint,sample,gene,score,) library("nlme") m0 <- lme(score ~ timepoint + gene, data=dd, random = ~1|sample) ## reproduces error 

As a first check, let's just see if there is anything in your model with a fixed effect, which is the only one:

 lm(score~timepoint+gene,dd) ## ## Call: ## lm(formula = score ~ timepoint + gene, data = dd) ## ## Coefficients: ## (Intercept) timepoint gene ## 5.414652 -0.004064 -0.024485 

No, it works great.

Try it in lme4 :

 library(lme4) m1 <- lmer(score ~ timepoint + gene + (1|sample), data=dd) ## Error in fn(x, ...) : Downdated VtV is not positive definite 

Try scaling and centering the data - sometimes it helps:

 ddsc <- transform(dd, timepoint=scale(timepoint), gene=scale(gene)) 

lme still fails:

 m0sc <- lme(score ~ timepoint + gene, data=ddsc, random = ~1|sample) 

lmer works - sort of!

 m1sc <- lmer(score ~ timepoint + gene + (1|sample), data=ddsc) ## Warning message: ## In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : ## Model is nearly unidentifiable: very large eigenvalue ## - Rescale variables? 

The results give coefficients for parameters that are vanishingly close to zero. (The residual variance is also vanishingly small.)

 ## m1sc ## Linear mixed model fit by REML ['lmerMod'] ## Formula: score ~ timepoint + gene + (1 | sample) ## Data: ddsc ## REML criterion at convergence: -9062.721 ## Random effects: ## Groups Name Std.Dev. ## sample (Intercept) 7.838e-01 ## Residual 3.344e-07 ## Number of obs: 348, groups: sample, 8 ## Fixed Effects: ## (Intercept) timepoint gene ## 5.714e+00 -4.194e-16 -1.032e-14 

At this point, I can only think of a few possibilities:

• there is something about experimental design, which means that random effects somehow (?) completely mix with one or both fixed effects
• is it simulated data that is artificially designed to be perfectly balanced ...?

 library(ggplot2); theme_set(theme_bw()) ggplot(dd,aes(timepoint,score,group=sample,colour=gene))+ geom_point(size=4)+ geom_line(colour="red",alpha=0.5) 

Yeah!

Answer 2

In order for R to solve the matrix, it must be computationally invertible. The error you return tells you that for computational purposes, your matrix is ​​singular, which means that it does not have the opposite.

Since this error is more related to the side of statistical theory, it is probably better suited for cross-validation. See this link for more details.

Check your data to make sure that you do not have absolutely correlated independent variables.