[R-sig-ME] ICC on random slopes in mixed logistic regression

[Martin Leclerc]

Hi everyone,

I wanted to know if someone knows how to calculate repeatability on a  
random slope of a mixed logistic regression with a nested intercept. I  
want to evaluate the repeatability of the variable X. The function  
glmer in the lme4 package doesn?t give me an estimate of the residual  
variance and I am not sure if ICC is calculated the same way in mixed  
linear and logistic regressions (and with nested intercept). Here is  
what the model looks like:

reg = glmer ( Y ~ X + (X | ID / IDyear), family = binomial)

Where Y = dichotomous dependent variable, ID = factor of 34 levels,  
IDyear = factor of 93 levels.

The output is the following:

Random effects:

  Groups            Name         Variance     Std.Dev.    Corr
  IDyear : ID      (Intercept)   0.0056611    0.075241
                    X            0.0898307    0.299718    0.670

  ID               (Intercept)   0.0331178    0.181983
                    X            0.0699248    0.264433    0.564

Number of obs: 76740, groups: bearyear:bearID, 93; bearID, 34

Even though I am not familiar with other package, I have also tried  
with the glmmPQL function. Here is the model (Is it normal that this  
function is really much faster to converge? From 25 min. to 4 min.):

reg2 = glmmPQL ( Y ~ X, random = ~ X | ID / IDyear), family= binomial )

Here is the output:

Random effects:

Formula: ~ X | ID
  Structure: General positive-definite, Log-Cholesky parametrization

                   StdDev      Corr
(Intercept)       0.3067025    (Intr)
X                 1.4141289    -0.943


Formula: ~ X | IDyear  %in%  ID
  Structure: General positive-definite, Log-Cholesky parametrization

                    StdDev         Corr
(Intercept)        0.2676970    (Intr)
X                  1.6009115    -0.965
Residual           0.9964824


Is there a way to calculate an ICC on each random slopes and intercept  
or the ICC needs to be calculated at each level of my nested intercept  
(i.e. one ICC for ID and one ICC for IDyear). The way I see it, is  
that my random ID variance (intercept + slope) is my intergroup  
variance and my IDyear variance (intercept + slope) is my intragroup  
variance. Therefore, I would just evaluate the repeatability as:

random variance of ID / random variance of ID + random variance of IDyear

Thanks a lot for your comments and your help,

Martin
-----------------------------------------------------
Martin Leclerc, biol. M.Sc.,
Candidat Ph.D.
Labo de démographie évolutive et conservation

Département de biologie, Université de Sherbrooke
Sherbrooke, Québec, Canada, J1K 2R1
Tel: 1-(819)-821-8000 #63020
Sans frais: 1-800-267-8337
Fax: (819)-821-8049