Hi Statalist,
I am running a multilevel model. In my dataset, I have children nested within districts. I am modeling the risk of a child being placed in state care institutions. I am confused between the random effects var(cons_) reported in the output and the ICC (intraclass correlation). I understand the ICC tells me the total proportion of the total variance in my outcome that is accounted for by clustering, that is, an ICC of .06 would mean that 6% of the risk of going into state care is explained by between-district differences.
My questions are:
- What is the difference between var(cons_) reported in the output and the ICC. For example, how does one interpret a var(cons_) of 0.14 in a null model (no predictors added)?
- I have seen papers report statistical significance associated with the random effects at the district level but I do not see a p-value reported, how do we determine whether the random effects are statistically significant?
Because of data restrictions I cannot share my data but I include an example code and output below where var(_cons) is what I am having difficulty interpreting and determining significance.
Example code/output:
I am running a multilevel model. In my dataset, I have children nested within districts. I am modeling the risk of a child being placed in state care institutions. I am confused between the random effects var(cons_) reported in the output and the ICC (intraclass correlation). I understand the ICC tells me the total proportion of the total variance in my outcome that is accounted for by clustering, that is, an ICC of .06 would mean that 6% of the risk of going into state care is explained by between-district differences.
My questions are:
- What is the difference between var(cons_) reported in the output and the ICC. For example, how does one interpret a var(cons_) of 0.14 in a null model (no predictors added)?
- I have seen papers report statistical significance associated with the random effects at the district level but I do not see a p-value reported, how do we determine whether the random effects are statistically significant?
Because of data restrictions I cannot share my data but I include an example code and output below where var(_cons) is what I am having difficulty interpreting and determining significance.
Example code/output:
Code:
meqrlogit state_care || district:, or
Refining starting values:
Iteration 0: log likelihood = -3296.207 (not concave)
Iteration 1: log likelihood = -3294.4865 (not concave)
Iteration 2: log likelihood = -3286.6989
Performing gradient-based optimization:
Iteration 0: log likelihood = -3286.6989
Iteration 1: log likelihood = -3286.4405
Iteration 2: log likelihood = -3286.3902
Iteration 3: log likelihood = -3286.3902
Mixed-effects logistic regression Number of obs = 9,611
Group variable: district Number of groups = 22
Obs per group:
min = 74
avg = 436.9
max = 636
Integration points = 7 Wald chi2(0) = .
Log likelihood = -3286.3902 Prob > chi2 = .
------------------------------------------------------------------------------
state_care | Odds Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 8.218159 .7437935 23.27 0.000 6.882332 9.813264
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
district: Identity |
var(_cons) | .1497317 .0558011 .0721262 .3108382
------------------------------------------------------------------------------
LR test vs. logistic model: chibar2(01) = 78.69 Prob >= chibar2 = 0.0000
