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st: gllamm estimates vs likelihood ratio test


From   Subramanian Swaminathan <[email protected]>
To   [email protected]
Subject   st: gllamm estimates vs likelihood ratio test
Date   Mon, 25 Dec 2006 22:46:25 -0800 (PST)

Dear statalister,

I am trying to fit a mixed random effect model for a
clinical trial data in 
which the treatment was given once and the outcome was
measured at monthly 
interval for one year (repeated measure). Age, gender,
post_treatment time 
and pre-treatment measurement (coded as 0=low and
1=high) are my independent 
variables. I am interested to know whether response
varies between persons 
and also over time (i.e. heterogenity in response
between subjects over 
time).  The Table blow shows that a model with all
fixed effects along with 
a random intercept and slope for 'time' (model 4) was
found to be a better 
model than a model with all fixed effects but without
random slope (model 3, 
based on likelihood ratio test). But all the
coeffcients for the fixed part 
as well as random part in model 4 are not
significantly different from zero 
(based on z-test). However, with model 3, the
coefficients for some of the 
fixed effects (time, mf-density group*time) and the
random intercept are 
significantly different from zero. My questions are:

(1) If parameter estimates are not significant but the
LR test suggests that 
model 4 provides significantly better fit than model
3, which one of the two 
models (model 3 and model 4) is the most parsimonious?
(2) on what basis (LR test or z-test for the parameter
estimates)?

 Estimates of logistic regressions with and without
random coefficients for 
days post-treatment

      Covariate Model 1 Model 2 Model 3 Model 4
        Estimate SE Z Estimate SE Z Estimate SE Z
Estimate SE Z
      Fixed part: main effects
      Constant -0.7078 0.6126 -1.16 -1.5036 1.6155
-0.93 -1.8591 
1.3468 -1.38 -1.4780 2.1583 -0.68
      Age -0.0536 0.0202       -2.65 -0.0689 0.0536
-1.29 -0.0656 
0.0492 -1.33 -0.1258 0.0813 -1.55
      Sex (0=male; 1=Female) 0.0798 0.5977 0.13
-0.2241 1.3824 -0.16 -0.7612 
0.9792 -0.78 -0.9868 1.5981 -0.62
      Mf-density group: (0=low, 1=High)
      High -0.5180 0.7140 -0.73 -1.2402 1.5679 -0.79
      Time 0.0039 0.0020        1.97 0.0061 0.0026    
 2.34 0.0055 0.0019 
2.89 0.0054 0.0068 0.79
      Fixed part: interactions:
      Mf-density group � Time -0.0077 0.0045 -1.72
-0.0112 
       -2.01 -0.0132 0.0050       -2.62 -0.0234 0.0117
            -1.99
      Mf-density group � Female -1.3282 1.2179 -1.09
-0.7486 2.3540 -0.32
      Female � Time -0.0019 0.0028 -0.67 -0.0031
0.0037 -0.84

      Random part
      Variance of intercept (1)    5.4469 2.7907 
5.3062 2.5835  11.0471 
7.5482
      Variance of slope for time (2)          0.0003
0.0003
      Covariance of (2, 1)          -0.0222 0.0235
      r (intra class correlation)    0.6233   0.6171  
0.7704
      Log-likelihood -106.6     -87.4     -88.8    
-81.9


thanking you in advance

Subramanian Swaminathan
Vector Control Research Centre
(Indian Council of Medical Research)
Indira Nagar
Pondicherry - 605 006
INDIA 


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