Bioequivalence and Bioavailability Forum • Negative variance component

Negative variance component – Chow/Liu [Software]

posted by ElMaestro – Denmark, 2014-02-03 11:22 (4096 d 10:18 ago) – Posting: # 12319
Views: 27,944

Hi Detleffff,

❝ Ways out? Just to cite Chow and Liu (without the 'hat' above the σ²):

❝ "To avoid negative estimates a typical approach is to consider the following estimator

❝ σ²_S=max(0,σ²_S)

❝ σ²_e=σ²_e if MS_inter≥MS_intra

❝ σ²_e=σ² if MS_inter<MS_intra

❝ where σ² = (SS_inter+SS_intra)/(2*(n1+n2)

❝ The above estimators are known as restricted maximum likelihood (REML) estimators". End of citation.

Yes, indeed the holy scripture says so; I think much of the confusion hinges on eq.7.3.3 saying
E(V_inter)=V_e+2V_S
I think I do not follow it.

When PROC MIXED or R's LME/LER fit a true MM with REML, the Al Gore Rhythm does not derive the sigmas via any of these equations but from iterartively maximising the likelihoood of the V matrix with the fixed effects. It may be that the result ends up being these same as one of the REML estimators above. But are these estimates really "maximum likelihood"-related (however restricted they are), or are they just cheap ways out of an annoying situation?? After all, the residual of an LM/GLM (traditional ANOVA) is a decomposition of the entire variability into avialable factors, so if we e.g. set Ve=V as 7.3.3 suggests on the odd occasion then I think we are solving one problem in a quick and dirty fashion and at the same time doing something that appears very dubious. I guess my confusion boils down to something like "annoying negative values aside, where's the likelihood basis behind the idea of fiddling with the model's residual which truly is some kind of maximum likelihod estimator" ?
(and if we manually tweak V_e would we then reflect that in our calc. of the CI for "likelihood" reasons?)

If or when you test with PROC MIXED, can you paste the entire co-variance matrix (not the Z or the G)? It will be the one with 14 columns if you use the dataset above; I'd expect a common sigma sq. on the diagonal and a single beween-sigma sq. elsewhere in each row.

—
Pass or fail!
ElMaestro

Complete thread:

How to calculate intersubject variability in PHX WinNonlin zan 2014-01-29 23:58
- Negative variance component Helmut 2014-01-30 01:16
  - Negative variance component zan 2014-01-30 18:11
  - Negative variance component zan 2014-01-31 00:16
    - Negative variance component ElMaestro 2014-01-31 08:20
    - Negative variance component yjlee168 2014-01-31 10:26
      - Example data set Helmut 2014-02-01 16:03
        
        Example data set yjlee168 2014-02-01 17:40
        
        PHX build 6.3.0.395 / 6.4.0.511 Helmut 2014-02-02 02:04
        
        PHX build 6.3.0.395 / 6.4.0.511 yjlee168 2014-02-02 07:54
    - Negative variance component ElMaestro 2014-02-01 16:31
      - Negative variance component yjlee168 2014-02-01 17:47
        
        Just thinking loud ElMaestro 2014-02-01 19:02
        
        All models are wrong… Helmut 2014-02-02 02:31
        
        another book for linear model yjlee168 2014-02-02 08:07
      - References Helmut 2014-02-02 02:19
        
        References ElMaestro 2014-02-02 09:56
    - Negative variance component – Chow/Liu d_labes 2014-02-03 09:02
      - Negative variance component – Chow/LiuElMaestro 2014-02-03 10:22
        
        Variance components – Proc mixed d_labes 2014-02-03 11:58
        
        Variance components – Proc mixed ElMaestro 2014-02-03 12:58
        
        Variance components – Proc mixed 90% CIs d_labes 2014-02-03 13:16
        Variance components – Proc mixed Helmut 2014-02-03 14:14
        
        FDA code for non-replicate crossover? d_labes 2014-02-03 15:54
        
        Proc GLM rulez Helmut 2014-02-03 16:16
        
        Variance components – Proc mixed yjlee168 2014-02-03 20:43
        
        NOBOUND Helmut 2014-02-03 22:08
      - lm() or lme() for 2x2x2 study design? yjlee168 2014-02-03 20:22
        
        lm() or lme() for 2x2x2 study design? ElMaestro 2014-02-03 22:11
        
        lm() or lme() for 2x2x2 study design? yjlee168 2014-02-04 13:09
        
        bear for 2x2x2 study with negative variance components yjlee168 2014-02-05 19:12