[R-sig-ME] generalized mixed linear models, glmmPQL and GLMER give very different results that both do not fit the data well...

[David Duffy]

On Fri, 18 Mar 2011, Franssens, Samuel wrote:

> Hi,
>
> I have the following type of data: 86 subjects in three independent 
> groups (high power vs low power vs control). Each subject solves 8 
> reasoning problems of two kinds: conflict problems and noconflict 
> problems. I measure accuracy in solving the reasoning problems. To 
> summarize: binary response, 1 within subject var (TYPE), 1 between 
> subject var (POWER).
>
> I wanted to fit the following model: for problem i, person j:
> logodds ( Y_ij ) = b_0j + b_1j TYPE_ij
> with b_0j = b_00 + b_01 POWER_j + u_0j
> and b_1j = b_10 + b_11 POWER_j
>
> I think it makes sense, but I'm not sure.
> Here are the observed cell means:
>             conflict       noconflict
> control     0.6896552      0.9568966
> high        0.6935484      0.9677419
> low         0.8846154      0.9903846
>
> GLMER gives me:
> Formula: accuracy ~ f_power * f_type + (1 | subject)
>   Data: syllogisms
> Random effects:
> Groups  Name        Variance Std.Dev.
> subject (Intercept) 4.9968   2.2353
> Number of obs: 688, groups: subject, 86
>
> Fixed effects:
>                            Estimate Std. Error z value Pr(>|z|)
> (Intercept)                  1.50745    0.50507   2.985  0.00284 **
> f_powerhp                    0.13083    0.70719   0.185  0.85323
> f_powerlow                   2.04121    0.85308   2.393  0.01672 *
> f_typenoconflict             3.28715    0.64673   5.083 3.72e-07 ***
> f_powerhp:f_typenoconflict   0.21680    0.93165   0.233  0.81599
> f_powerlow:f_typenoconflict -0.01199    1.45807  -0.008  0.99344
> ---
>
> Strange thing is that when you convert the estimates to probabilities, 
> they are quite far off. For control, no conflict (intercept), the 
> estimation from glmer is 1.5 -> 81% and for glmmPQL is 1.14 -> 75%, 
> whereas the observed is: 68%.
>
> Am I doing something wrong?

You are forgetting that your model includes a random intercept for each 
subject.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v