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Is it peculiar for variance estimate to be negative despite placing positive constraint in optimization ? Here is an example case that I just encountered. I have marked the random effect estimate with *. Model was run in R with sommer::mmer() function.

Also, with big AIC/BIC values and with so many variance-covariance parameters to estimate, is the model really badly formulated ? Please note that total observations = 72.

summary(bean_compound_symmetry)
===========================================================================================
                         Multivariate Linear Mixed Model fit by REML                         
**************************************  sommer 4.1  ************************************** 
===========================================================================================
        logLik       AIC       BIC Method Converge
Value 21.21391 -36.42783 -29.63979     NR     TRUE
===========================================================================================
Variance-Covariance components:
                                                           VarComp VarCompSE  Zratio Constraint
u:g.seed_yield_per_ha-seed_yield_per_ha                   -0.01081*  0.02174 -0.4974   Positive
1:g.seed_yield_per_ha-seed_yield_per_ha                    0.00000   0.03645  0.0000   Positive
2:g.seed_yield_per_ha-seed_yield_per_ha                    0.18755   0.13733  1.3657   Positive
3:g.seed_yield_per_ha-seed_yield_per_ha                    0.01471   0.04508  0.3263   Positive
4:g.seed_yield_per_ha-seed_yield_per_ha                    0.00000   0.03645  0.0000   Positive
Bhatte:year.seed_yield_per_ha-seed_yield_per_ha            0.00000   0.05513  0.0000   Positive
Chaumae:year.seed_yield_per_ha-seed_yield_per_ha           0.87331   0.78049  1.1189   Positive
Dhankute Chirrke:year.seed_yield_per_ha-seed_yield_per_ha  0.34065   0.33230  1.0251   Positive
Trishuli:year.seed_yield_per_ha-seed_yield_per_ha          2.07321   1.73773  1.1931   Positive
White OP:year.seed_yield_per_ha-seed_yield_per_ha          0.00000   0.05513  0.0000   Positive
WP Con Bean:year.seed_yield_per_ha-seed_yield_per_ha       0.04779   0.07970  0.5996   Positive
u:units.seed_yield_per_ha-seed_yield_per_ha                0.13937   0.03264  4.2700   Positive
===========================================================================================
Fixed effects:
              Trait      Effect Estimate Std.Error t.value
1 seed_yield_per_ha (Intercept) 0.732327    0.1057 6.92928
2 seed_yield_per_ha year2017/18 0.003516    0.1647 0.02135
3 seed_yield_per_ha year2018/19 1.100930    0.1647 6.68456
===========================================================================================
Groups and observations:
                      seed_yield_per_ha
u:g                                   6
1:g                                   6
2:g                                   6
3:g                                   6
4:g                                   6
Bhatte:year                           3
Chaumae:year                          3
Dhankute Chirrke:year                 3
Trishuli:year                         3
White OP:year                         3
WP Con Bean:year                      3
===========================================================================================
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A few things stand out here.

  • you seem to be fitting a lot of random effects, and with only 72 observations, it seems very likely that the random structure is overfitted.

  • some of them have only 3 observations. This is not really a sensible thing to do. I would advise fitting them as fixed effects for those

  • some of the variance components are estimate to have zero variance, which could either reflect an overfitted, singular model, or actually very veriation in those components.

  • the presence of the negative estimate for one variance component also suggests that there are serious problems with this model.

I would definitely simplify the random structure a lot.

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  • $\begingroup$ On a related note, my design has genotype (6 levels) effects nested in blocks (4 levels) with the latter nested within years (3 levels). I expect genotypes within the same block to be correlated. Likewise, correlated genotypes effects are expected for a given year. Now, how do you suggest I specify a model with given information ? Should it be all fixed, or should certain terms only be fixed with other random ? $\endgroup$
    – dd_rookie
    Commented Oct 20, 2020 at 14:38
  • $\begingroup$ That sounds like genotype and block are crossed, not nested (unless each genotype belongs to one and only 1 level of block). Anyway it's an interesting question that deserves it's own post :) $\endgroup$
    – Robert Long
    Commented Oct 20, 2020 at 15:53
  • $\begingroup$ Actually, you're right about genotypes being crossed with block. Thank you. $\endgroup$
    – dd_rookie
    Commented Oct 21, 2020 at 2:44

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