added text in `constructors.md` to say NaN correlation is printed as a dot, fixes #819
fixes #819
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I think we might try to explain that result a little better while we are making this correction. The output looks like
julia> m1 = fit(MixedModel, @formula(reaction ~ 1 + days + (1|subj) + (days|subj)), MixedModels.dataset(:sleepstudy); contrasts=Dict(:days => DummyCoding()))
Minimizing 3068 Time: 0:00:00 ( 0.14 ms/it)
Linear mixed model fit by maximum likelihood
reaction ~ 1 + days + (1 | subj) + (days | subj)
logLik -2 logLik AIC AICc BIC
-819.1592 1638.3185 1752.3185 1806.5152 1934.3170
Variance components:
Column Variance Std.Dev. Corr.
subj (Intercept) 882.08342 29.69989
days: 1 403.87992 20.09676 .
days: 2 785.87492 28.03346 . +0.76
days: 3 1160.51146 34.06628 . +0.74 +0.89
days: 4 1375.06073 37.08181 . +0.58 +0.67 +0.93
days: 5 2177.61478 46.66492 . +0.44 +0.42 +0.72 +0.85
days: 6 3730.64143 61.07898 . +0.27 +0.48 +0.70 +0.78 +0.76
days: 7 1688.60255 41.09261 . +0.16 +0.41 +0.55 +0.59 +0.64 +0.72
days: 8 3029.32800 55.03933 . +0.25 +0.32 +0.59 +0.71 +0.91 +0.73 +0.75
days: 9 2999.41317 54.76690 . +0.24 +0.11 +0.41 +0.57 +0.78 +0.38 +0.53 +0.86
Residual 54.66356 7.39348
Number of obs: 180; levels of grouping factors: 18
Fixed-effects parameters:
───────────────────────────────────────────────────
Coef. Std. Error z Pr(>|z|)
───────────────────────────────────────────────────
(Intercept) 256.652 7.21398 35.58 <1e-99
days: 1 7.84395 5.33962 1.47 0.1418
days: 2 8.71009 7.05219 1.24 0.2168
days: 3 26.3402 8.3992 3.14 0.0017
days: 4 31.9976 9.08108 3.52 0.0004
days: 5 51.8667 11.2717 4.60 <1e-05
days: 6 55.5265 14.6059 3.80 0.0001
days: 7 62.0988 9.99425 6.21 <1e-09
days: 8 79.9777 13.2049 6.06 <1e-08
days: 9 94.1994 13.1418 7.17 <1e-12
───────────────────────────────────────────────────
and the dots are in the correlations of the random effects of days: 1 with other days: x random effects and the "variance component" is not estimated as zero. This is an over-specified model (more random effects than observations) so I am not even sure what these numbers mean.
Perhaps we could find a better example to illustrate the point we are trying to make. If someone (@palday ?) could tell me what the point of the discussion is, I can take a stab at illustrating it.
I agree it's a bad example. If I recall correctly, the idea was to show the interaction of the amalgamate behavior with categorical predictors
BTW, I was incorrect about an over-specified model because the days: 0 random effects are dropped. However, I'm still not sure what the model means.