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st: Interpreting gllamm


From   Malin Lundberg Rasmussen <[email protected]>
To   "'[email protected]'" <[email protected]>
Subject   st: Interpreting gllamm
Date   Tue, 13 Nov 2012 15:41:08 +0100

Dear statalist

I hope you can help me and my lack of statisticcally/STATA knowledge. And have patience; there are questions in the end ;o)

I have a group of patients and have studies their eyes (dependent variables). I want to see if a finding in 1995 can predict an outcome in 2011. 
The covariate (ma1995) I am investigating is consisting of continuus data (1-10), the outcome (ret_2011) is a grading level/categorical (level 10-85 (12 levels in all)). And since I am dealing with eyes my data is not independent. 
And just a view of my variates: 
tab ma1995

     ma1995 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |          1        0.95        0.95
          1 |         49       46.67       47.62
          2 |         20       19.05       66.67
          3 |         12       11.43       78.10
          4 |          9        8.57       86.67
          5 |          5        4.76       91.43
          6 |          5        4.76       96.19
          7 |          2        1.90       98.10
         10 |          1        0.95       99.05
         21 |          1        0.95      100.00
------------+-----------------------------------
      Total |        105      100.00

. tab ret_2011

   ret_2011 |      Freq.     Percent        Cum.
------------+-----------------------------------
         20 |         17       16.19       16.19
         35 |         34       32.38       48.57
         43 |         15       14.29       62.86
         47 |          3        2.86       65.71
         61 |         22       20.95       86.67
         65 |          9        8.57       95.24
         71 |          1        0.95       96.19
         75 |          3        2.86       99.05
         85 |          1        0.95      100.00
------------+-----------------------------------
      Total |        105      100.00

I was told I could use the STATA command gllamm, but I have a problem interpreting the outcome...
I write 

gllamm ret_2011 ma1995, i(inr_) 

And get the following results: 

Iteration 0:   log likelihood = -440.63147  (not concave)
Iteration 1:   log likelihood = -440.45372  
Iteration 2:   log likelihood = -416.91371  (not concave)
Iteration 3:   log likelihood = -414.37278  
Iteration 4:   log likelihood = -410.47618  
Iteration 5:   log likelihood = -410.22201  
Iteration 6:   log likelihood = -410.22191  
Iteration 7:   log likelihood = -410.22191  
 
number of level 1 units = 105
number of level 2 units = 73
 
Condition Number = 8.5127997
 
gllamm model 
 
log likelihood = -410.22191
 
------------------------------------------------------------------------------
    ret_2011 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      ma1995 |   .5467041    .171913     3.18   0.001     .2097609    .8836473
       _cons |    40.5618   .6920948    58.61   0.000     39.20532    41.91828
------------------------------------------------------------------------------
 
Variance at level 1
------------------------------------------------------------------------------

  16.905984 (2.8159187)
 
Variances and covariances of random effects
------------------------------------------------------------------------------

 
***level 2 (inr_)
 
    var(1): 156.99649 (9.1764146)
------------------------------------------------------------------------------

My questions are:
1) What does 'not concave' mean? 
2) What is the "Condition Number"? 
3) I have read that the Coef. is the average score - but this doesn't seem to fit (see tab ma1995 above)
4) What is statistically significant (p=0.001)?? - that there is a connection, between ma1995 and the outcome? And if so, can I see what the connection is (e.g. the higher ma1995, the higher ret_2011)
5) and last; what does the last outcome say (variance at level 1 and level 2)??

I am very sorry for my ignorance!

Hoping for some help

Best regards
Malin


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