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:
summary(glmer(accuracy~f_power*f_type + (1|subject),
family=binomial,data=syllogisms))
Generalized linear mixed model fit by the Laplace approximation
Formula: accuracy ~ f_power * f_type + (1 | subject)
Data: syllogisms
AIC BIC logLik deviance
406 437.7 -196 392
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
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) f_pwrh f_pwrl f_typn f_pwrh:_
f_powerhp -0.714
f_powerlow -0.592 0.423
f_typncnflc -0.185 0.132 0.109
f_pwrhp:f_t 0.128 -0.170 -0.076 -0.694
f_pwrlw:f_t 0.082 -0.059 -0.144 -0.444 0.308
glmmPQL gives me:
summary(glmmPQL(fixed=accuracy~f_power*f_type, random=~1|subject,
family=binomial, data=syllogisms))
iteration 1
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
Linear mixed-effects model fit by maximum likelihood
Data: syllogisms
AIC BIC logLik
NA NA NA
Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev: 1.817202 0.8045027
Variance function:
Structure: fixed weights
Formula: ~invwt
Fixed effects: accuracy ~ f_power * f_type
Value Std.Error DF t-value p-value
(Intercept) 1.1403334 0.4064642 599 2.805496 0.0052
f_powerhp 0.0996481 0.5683296 83 0.175335 0.8612
f_powerlow 1.5358270 0.6486150 83 2.367856 0.0202
f_typenoconflict 3.0096016 0.4769761 599 6.309754 0.0000
f_powerhp:f_typenoconflict 0.1856061 0.6790046 599 0.273350 0.7847
f_powerlow:f_typenoconflict 0.0968204 1.0318659 599 0.093830 0.9253
Correlation:
(Intr) f_pwrh f_pwrl f_typn f_pwrh:_
f_powerhp -0.715
f_powerlow -0.627 0.448
f_typenoconflict -0.194 0.138 0.121
f_powerhp:f_typenoconflict 0.136 -0.182 -0.085 -0.702
f_powerlow:f_typenoconflict 0.089 -0.064 -0.153 -0.462 0.325
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-12.43735991 0.06243699 0.22966010 0.33106978 2.23942234
Number of Observations: 688
Number of Groups: 86
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?
Any help is very much appreciated.
Sam.
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