I have some hierarchical data (roughly 23 observations per individual, 20 individuals per region, and 17 regions in total), and use linear mixed models (LMM) to adjust for the dependencies that come due to the hierarchical nature of the data. I thus run the following model in R:
lmer(Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 + X12 + (1 | region) + (1 + X1 + X2 + X3 + X4 | region:ID), data=MyData)
When I estimated my model with four random slopes and a random intercept, using the command I got the following correlations among my random effects:
Random effects:
Groups Name Variance Std.Dev. Corr
region:ID (Intercept) 79.53741 8.9184
X1 0.30512 0.5524 0.48
X2 0.06766 0.2601 -0.50 -0.68
X3 0.14973 0.3870 -0.57 0.00 -0.40
X4 0.52897 0.7273 -0.79 -0.28 -0.09 0.95
region (Intercept) 4.93030 2.2204
Residual 16.88022 4.1086
Number of obs: 9091, groups: region:ID, 383; region, 17
Noting that the correlation between the random effects of $X_4$ and $X_3$ is high, I tried also ran the model while forcing independence on the random slopes. That is I ran:
lmer(Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 + X12 + (1 | region) + (1 + X1 + X2 + X3 + X4 || region:ID), data=MyData)
However, once I did this, the random effects structure was changed so that variance of the random effects for $X_1$ and $X_2$ suddenly was zero.
Random effects:
Groups Name Variance Std.Dev.
region.ID X1 0.2246 0.4739
region.ID X2 0.0000 0.0000
region.ID X3 0.0000 0.0000
region.ID X4 0.3236 0.5689
region.ID (Intercept) 11.4392 3.3822
region (Intercept) 9.3745 3.0618
Residual 18.1717 4.2628
Number of obs: 9091, groups: region:ID, 383; region, 17
My question is thus, why can the exclusion correlation parameters lead to non-zero variances becoming zero?
Edit:
$X_1,X_2,X_3$ and $X_4$ are all continuous. However, they are measured on the region level. So for a given year (it's longitudinal data) each individual within the same region has the same value of those variables. So they vary between regions and between years, but not within a region-year.
X1 + X2 + X3 + X4categorical or continuous? – amoeba Nov 05 '18 at 10:58(X | region)included in the model then it does not make any sense to include(X | region:ID)into the model. – amoeba Nov 05 '18 at 16:38(1 | region)... Then maybe it's okay, but I would still suggest to do(1 + X1 + X2 + X3 + X4 | region) + (1 | region:ID)and then see whether changing|to||will have the same drastic effect. This model makes more sense to me. – amoeba Nov 05 '18 at 16:43