Questions on the results from glmmPQL(MASS)

On Mon, Dec 8, 2008 at 3:29 PM, David Duffy  
<David.Duffy at qimr.edu.au> wrote:

On Mon, 8 Dec 2008, zhijie zhang wrote:

Do u mean the following method?
model0<-glmmML(y ~ trt + I(week > 2), cluster=ID, family=binomial,
data=bacteria)

model1<-glm(y ~ trt + I(week > 2), family=binomial, data=bacteria)
anova(model0,model1)

Error message occurred.

anova does not have a method for glmmML, but the deviances seem to be
calculated the same (see model0$cluster.null.deviance etc):.

model0 Residual deviance: 192.3  on 215 degrees of freedom       
AIC: 202.3
model1 Residual deviance: 199.18 on 216  degrees of freedom

LRTS = 6.88.  We will assume that the test statistic is distributed  
1/2
X2(0) and 1/2 X2(1), so P ~ 0.004.

1/2 X2(0) and 1/2 X2(1): ?? what do they mean?

X2 is chi-square. Because the test is on the boundary the test  
statistic is distributed as the weighted sum of chi-square rather than  
the usual chi-square. Verbeke and Molenberghs cover this in their books.

Simulation (parametric bootstrap) seems a better way of doing this.  
Information criteria (AIC or BIC) can also be used. Most usual  
justification for a random effect is that there is expected to be one,  
so provided it can be estimated it is included.
Comparing to a Wald test using the SE on the random effect SD, I get:

Z = 1.242/0.4024 = 3.08, P=0.001
Is this a "clerical error"? Based on your hints, it seems that p  
should be
0.003475077 .
dnorm(3.08)
[1] 0.003475077
  Thanks.

P value for z test is 2*dnorm(3.08) which is close enough to 0.001  
given that the test is only an approximation.

Ken

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

-- 
With Kind Regards,

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ZhiJie Zhang ,PhD
Dept.of Epidemiology, School of Public Health,Fudan University
Office:Room 443, Building 8
Office Tel./Fax.:+86-21-54237410
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Website: www.statABC.com
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Questions on the results from glmmPQL(MASS)

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