Hi all,

I am trying to see whether I should include a random effects in my models.
I am trying to predict child mortality based on a buch of covariates. There
are covariates at the maternal level (education of the mother, income of
the mother, whether she lives in a rural area or not); at the child level
(sex, year of birth, birth order) and at the country level ( I just have
one country but those are time varying)

The random effects will be for mothers. The problem is that in my sample
mothers don't have a lot of children: mean 2, median: 2.4

So I run two models and compared them using AIC and BIC. There are a couple
of weird things though. First, the estimates are the same, even though the
the sd's are not. Secondly, I am not sure whether I can compare AIC and BIC
across both packages.

Thus my question is: what would be a sensible way to decide the inclusion
of not of a random effect? Thanks a bunch.

> summary(n.kids)
             CASEID          ncase
         1 31  2:    1   Min.   : 1.000
         1 41  1:    1   1st Qu.: 1.000
         1 51  2:    1   Median : 2.000
         1 61  1:    1   Mean   : 2.395
         1101  2:    1   3rd Qu.: 3.000
         2 11  6:    1   Max.   :18.000


> summary(glm.1)

Call:
glm(formula = mortality.under.2 ~ maternal_age + I(maternal_age^2) +
    birth_year + I(birth_year^2) + residence + sex + wealth,
    family = binomial(link = "logit"), data = colombia2)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-0.5945  -0.3130  -0.2667  -0.2271   2.9626

Coefficients:
                         Estimate Std. Error z value Pr(>|z|)
(Intercept)             8.576e+03  3.008e+03   2.851  0.00435 **
maternal_age           -2.292e-01  7.790e-02  -2.943  0.00325 **
I(maternal_age^2)       4.295e-03  1.700e-03   2.527  0.01151 *
birth_year             -8.598e+00  3.031e+00  -2.837  0.00456 **
I(birth_year^2)         2.155e-03  7.636e-04   2.822  0.00477 **
residenceUrban          1.476e-01  7.645e-02   1.930  0.05361 .
sexMale                 3.219e-01  5.482e-02   5.871 4.32e-09 ***
wealthSecond quintile  -2.374e-01  8.042e-02  -2.952  0.00316 **
wealthMiddle quintile  -5.922e-01  9.651e-02  -6.137 8.43e-10 ***
wealthFourth quintile  -8.237e-01  1.073e-01  -7.677 1.63e-14 ***
wealthHighest quintile -9.350e-01  1.160e-01  -8.060 7.61e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 12082  on 35953  degrees of freedom
Residual deviance: 11798  on 35943  degrees of freedom
AIC: 11820

Number of Fisher Scoring iterations: 6



> summary(glmer.11)
Generalized linear mixed model fit by the adaptive Gaussian Hermite
approximation
Formula: mortality.under.2 ~ maternal_age + I(maternal_age^2) + birth_year
+      I(birth_year^2) + +residence + sex + wealth + (1 | CASEID)
   Data: colombia2
   AIC   BIC logLik deviance
 17448 17550  -8712    17424
Random effects:
 Groups Name        Variance Std.Dev.
 CASEID (Intercept) 1.1133   1.0552
Number of obs: 35954, groups: CASEID, 15011

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)
(Intercept)             8.576e+03  4.017e+03   2.135   0.0328 *
maternal_age           -2.292e-01  1.023e-01  -2.240   0.0251 *
I(maternal_age^2)       4.295e-03  2.231e-03   1.925   0.0543 .
birth_year             -8.598e+00  4.048e+00  -2.124   0.0337 *
I(birth_year^2)         2.155e-03  1.020e-03   2.113   0.0346 *
residenceUrban          1.476e-01  1.044e-01   1.414   0.1575
sexMale                 3.219e-01  7.207e-02   4.467 7.95e-06 ***
wealthSecond quintile  -2.374e-01  1.096e-01  -2.166   0.0303 *
wealthMiddle quintile  -5.922e-01  1.318e-01  -4.495 6.95e-06 ***
wealthFourth quintile  -8.237e-01  1.466e-01  -5.617 1.95e-08 ***
wealthHighest quintile -9.350e-01  1.578e-01  -5.925 3.13e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


> AIC(glmer.11,glm.1)
         df      AIC
glmer.11 12 17447.64
glm.1    11 11819.75
> BIC(glmer.11,glm.1)
         df      BIC
glmer.11 12 17549.52
glm.1    11 11913.14

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