Mixed Models in SAS and R
Everything here is true, or at least reasonable, but not related to the original question. 1. I believe the original question has identified (1) a potentially interesting question about differences between REML and ML estimation for a poorly posed model [alternatively one could say "it's poorly posed, I don't care how it works"] and (2) a potential problem/bug/infelicity where lmer fails to warn of the ill-posedness _on some platforms_. (The conversation is continuing on CrossValidated: https://stats.stackexchange.com/questions/328712/why-does-lmer-unlike-sas-output-a-non-zero-variance-of-random-effect-if-it-is/328845 ) 2. If you can figure out how to make lmer work with negative variances without completely breaking the linear algebra, I'd be interested to hear about it. (I don't think I can say for sure that I'd accept a pull request -- Doug and Martin might have perfectly reasonable philosophical reservations.) I suspect it will be very hard or impossible, although I'm happy to be proved wrong. 3. IMO the correct way to handle the case you've suggested is to allow for compound symmetric variance structures. I believe glmmTMB can do this, and the flexLambda branch of lme4 can do this, and it can certainly be hacked by someone who wants to do it. I would dearly like to find the time and energy to make the production version of lme4 capable of this, but holding your breath is not recommended.
On 18-02-15 04:07 PM, John Maindonald wrote:
The lme4 code, in a practice designed to preserve its vision of mathematical purity,
constrains the variance estimates to be non-negative. That makes sense if one
can be sure that the model is tuned to the circumstances that generated the data.
The negative variances that some of the other mixed modeling software allows can
be a useful diagnostic, indicating for example an inappropriate experimental design.
I have mentioned previously the example once mentioned to me, and which would
be easy to simulate, where blocks in a field block experimental design had been
laid out at right angles to a river bank. A negative block variance estimate was
required to give a variance-covariance matrix which had all the mathematical
respectability that anyone might want.
There are circumstances where it is useful to constrain the variance estimates to
be non-negative ? it would be useful to have a choice.
John Maindonald email: john.maindonald at anu.edu.au<mailto:john.maindonald at anu.edu.au>
On 16/02/2018, at 07:25, Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov>> wrote:
And this might be a very dumb question, but I thought that the Hessian was related to the variance estimates. SO if the Hessian has a negative eigenvalue, wouldn?t one of the variance estimates be negative?.....I thought that is what happens in SAS, and instead of reporting a negative variance estimate it bounds the estimate at 0.
But it has been a while since I have gotten deep into the theory behind these models, so I may be completely wrong.....and if so, we can just leave it at that.
-----Original Message-----
From: Baldwin, Jim -FS [mailto:jbaldwin at fs.fed.us]
Sent: Thursday, February 15, 2018 11:50 AM
To: Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov>>; Peter Claussen <dakotajudo at mac.com<mailto:dakotajudo at mac.com>>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: RE: [R-sig-ME] Mixed Models in SAS and R
Shows up for me at the very end of the summary. What version of R and lme4 are you using?
summary(l)
Linear mixed model fit by REML ['lmerMod']
Formula: y ~ (1 | site) + site
Data: fake_data
REML criterion at convergence: 49.7
Scaled residuals:
Min 1Q Median 3Q Max
-1.8662 -0.5452 -0.1016 0.7029 1.8630
Random effects:
Groups Name Variance Std.Dev.
site (Intercept) 4.5429 2.1314
Residual 0.7182 0.8475
Number of obs: 20, groups: site, 2
Fixed effects:
Estimate Std. Error t value
(Intercept) 6.171 2.148 2.872
site2 -2.808 3.038 -0.924
Correlation of Fixed Effects:
(Intr)
site2 -0.707
convergence code: 0
unable to evaluate scaled gradient
Model failed to converge: degenerate Hessian with 1 negative eigenvalues
Jim Baldwin, PhD
Station Statistician
Forest Service
Pacific Southwest Research Station
-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Bertke, Stephen (CDC/NIOSH/DSHEFS)
Sent: Thursday, February 15, 2018 8:46 AM
To: Peter Claussen <dakotajudo at mac.com<mailto:dakotajudo at mac.com>>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Mixed Models in SAS and R
I do not see any errors in R. What I posted is the entire output from running summary(). Is there something else I should be asking for?
From: Peter Claussen [mailto:dakotajudo at mac.com]
Sent: Thursday, February 15, 2018 11:15 AM
To: Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov>>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Mixed Models in SAS and R
I posted a response on stackexchange; I don?t think this is an R specific issue - SAS reports the same problem for your test data.
R is reporting a "degenerate Hessian with 1 negative eigenvalue", SAS reports that "final Hessian is not positive definite? - by definition, a positive definite matrix is a symmetric matrix with all positive eigenvalues.
Cheers,
On Feb 15, 2018, at 9:56 AM, Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov><mailto:inh4 at cdc.gov>> wrote:
Sorry for all the emails, but I have edited/simplified my question to what I believe is the root issue as well as posted simulated data to test with:
https://stats.stackexchange.com/questions/328712/lmer-vs-proc-mixed-output
-----Original Message-----
From: Bertke, Stephen (CDC/NIOSH/DSHEFS)
Sent: Wednesday, February 14, 2018 2:25 PM
To: 'Thierry Onkelinx' <thierry.onkelinx at inbo.be<mailto:thierry.onkelinx at inbo.be>>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: RE: [R-sig-ME] Mixed Models in SAS and R
I posted the question on stackoverflow here:
https://stackoverflow.com/questions/48794651/lmer-vs-proc-mixed-output
This will hopefully make reading my code and output easier.
I would expect a 0 variance since I am in essence fitting a model with both the site variable in the fixed and random part of the model. I actually went ahead and fit that "dumb" model in both SAS and R and once again, all results are nearly identical except SAS estimates a 0 variance and R estimates a relatively large positive variance. However, R now gives an error/warning at the bottom of the results indicating an issue with this very dumb model. Again, those results are in the above link.
-----Original Message-----
From: Thierry Onkelinx [mailto:thierry.onkelinx at inbo.be]
Sent: Wednesday, February 14, 2018 11:39 AM
To: Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov>>
Cc: r-sig-mixed-models at r-project.org<mailto:r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Mixed Models in SAS and R
Dear Stephen,
The list removes all HTML formating, making your post hard to read.
Please use only plain text when posting.
You'll need to make sure that you fit exactly the same model in SAS as in R. Not everyone here speaks SAS. Providing the math equation for the SAS model would help.
Also please elaborate why it makes sense that the variance of site should be zero. We cannot verify that statement based on the information you provide.
Best regards,
ir. Thierry Onkelinx
Statisticus / Statistician
Vlaamse Overheid / Government of Flanders INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND FOREST Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance thierry.onkelinx at inbo.be<mailto:thierry.onkelinx at inbo.be> Havenlaan 88 bus 73, 1000 Brussel www.inbo.be<http://www.inbo.be>
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2018-02-14 17:07 GMT+01:00 Bertke, Stephen (CDC/NIOSH/DSHEFS) <inh4 at cdc.gov<mailto:inh4 at cdc.gov>>:
Hello everyone. I have just joined this mailing list so I wanted to introduce myself as well as ask a question.
My name is Steve Bertke and I am a researcher at the National Institute for Occupational Safety and Health (NIOSH) which is one of the centers within the Centers for Disease Control and Prevention (CDC). I am a long-time SAS user but have been slowly finding myself using and liking R. I have found the support community for R very helpful and rewarding and am looking forward to contributing my part.
On to my question.
I have ran the same model (I think) in both SAS (proc mixed) and R (lmer) but have gotten different results for the random terms.
A quick background, we took 2 personal air samples for 127 people at 15 different factories for a total of 252 samples (after dropping 2 samples). We are trying to model various factors of the factory on the air samples. To do so, we need to control for the repeated measure of the person (nested within factory) as well as the random factory effect.
You can see below for the exact code and exact results, but in short, when I run the models in R and SAS without any fixed effects, I get the same results for the random effects. When I enter in the fixed effects, I get a different result for the Site variance...but all other results are the same (both the fixed effects and the other random effects).
There is another methodological issue with the model I am running. I am entering in 17 fixed effects that describe the 15 sites. Therefore, the model is over-specified. As a result, SAS gives a variance estimate of 0 for site (which, in hindsight, makes sense) however, R does not. That is a separate issue that we are dealing with, but I would expect that R and SAS would give the same result. Or maybe at least a warning.
Below is my code and output. I hope the formatting remains so that it is easily readable for everyone. I may also be able to share the data too, but I need to get some approval for that first.
Details
I ran the following code in SAS and R without any fixed effects and both give the same results:
proc mixed data=dat;
class NewSiteID NIOSHID;
model ln_i = ;
random NewSiteID NIOSHID(NewSiteID);
run;
Covariance Parameter Estimates
Cov Parm
Estimate
NewSiteID
6.3433
NIOSHID(NewSiteID)
0.7465
Residual
2.5256
mixedidsite <- lmer(ln_i ~ (1 | NewSiteID/NIOSHID),
data = Modeling_Database_Final)
summary(mixedidsite)
Random effects:
Groups Name Variance Std.Dev.
NIOSHID:NewSiteID (Intercept) 0.7465 0.864
NewSiteID (Intercept) 6.3434 2.519
Residual 2.5256 1.589
However, when I add in the fixed effects, I get different results. SAS gives an estimate of 0 for Site while R does not. All other results are the same:
proc mixed data=dat;
class NewSiteID NIOSHID F_mass_handled_or (ref=first); model ln_i = F_High_Exp F_Mat_Type_SW F_Mat_Type_CNF F_Mat_Form_Dry F_Mat_Form_Liq F_Mat_Form_Comp F_Hybrid F_Primary F_Coatings F_mass_handled_or F_adequate F_inadequate F_emp_sc F_diam_sc/solution; random NewSiteID NIOSHID(NewSiteID); run;
Covariance Parameter Estimates
Cov Parm
Estimate
NewSiteID
0
NIOSHID(NewSiteID)
0.6954
Residual
2.5372
Fit Statistics
-2 Res Log Likelihood
961.8
AIC (Smaller is Better)
965.8
AICC (Smaller is Better)
965.9
BIC (Smaller is Better)
967.3
Solution for Fixed Effects
Effect
F_mass_handled_or
Estimate
Standard
Error
DF
t Value
Pr > |t|
Intercept
-139.29
83.6162
92.1
-1.67
0.0991
F_High_Exp
-180.24
102.72
92.6
-1.75
0.0826
F_Mat_Type_SW
470.30
261.53
92.1
1.80
0.0754
F_Mat_Type_CNF
-636.35
347.99
92.1
-1.83
0.0707
F_Mat_Form_Dry
662.26
368.75
92
1.80
0.0758
F_Mat_Form_Liq
-583.14
318.54
92
-1.83
0.0704
F_Mat_Form_Comp
598.77
331.85
92
1.80
0.0745
F_Hybrid
-1197.69
658.23
92
-1.82
0.0721
F_Primary
-639.93
352.80
92
-1.81
0.0730
F_Coatings
92.7949
50.7416
92.1
1.83
0.0707
F_mass_handled_or
F2
134.91
77.2496
92
1.75
0.0841
F_mass_handled_or
F3
-1235.37
677.42
92
-1.82
0.0715
F_mass_handled_or
F4
137.71
75.9370
92
1.81
0.0730
F_mass_handled_or
F1
0
.
.
.
.
F_adequate
139.45
76.5607
92
1.82
0.0718
F_inadequate
1395.04
767.40
92
1.82
0.0723
F_emp_sc
-1259.21
691.98
92
-1.82
0.0721
F_diam_sc
-20.1875
9.9710
89.5
-2.02
0.0459
mixedidsite <- lmer(ln_i ~ (1 | NewSiteID/NIOSHID) + F_High_Exp + F_Mat_Type_SW +
F_Mat_Type_CNF + F_Mat_Form_Dry + F_Mat_Form_Liq + F_Mat_Form_Comp +
F_Hybrid + F_Primary + F_Coatings + F_adequate +
F_inadequate + F_emp_sc + F_diam_sc,
data = Modeling_Database_Final)
summary(mixedidsite)
REML criterion at convergence: 961.8
Scaled residuals:
Min 1Q Median 3Q Max
-2.3019 -0.5248 -0.1668 0.3511 4.7091
Random effects:
Groups Name Variance Std.Dev.
NIOSHID:NewSiteID (Intercept) 0.6954 0.8339
NewSiteID (Intercept) 1.5932 1.2622
Residual 2.5372 1.5929
Number of obs: 252, groups: NIOSHID:NewSiteID, 127; NewSiteID, 15
Fixed effects:
Estimate Std. Error t value
(Intercept) -139.292 83.702 -1.664
F_High_Exp -180.239 102.778 -1.754
F_Mat_Type_SW 470.297 261.537 1.798
F_Mat_Type_CNF -636.352 347.993 -1.829
F_Mat_Form_Dry 662.263 368.761 1.796
F_Mat_Form_Liq -583.142 318.541 -1.831
F_Mat_Form_Comp 598.774 331.856 1.804
F_Hybrid -1197.691 658.229 -1.820
F_Primary -639.928 352.811 -1.814
F_Coatings 92.795 50.804 1.826
F_mass_handled_orF2: 10 - 134.912 77.291 1.746
F_mass_handled_orF3: 101 -1235.372 677.423 -1.824
F_mass_handled_orF4: >1 k 137.714 75.958 1.813
F_adequate 139.446 76.582 1.821
F_inadequate 1395.036 767.413 1.818
F_emp_sc -1259.213 691.979 -1.820
F_diam_sc -20.188 9.971 -2.025
Again, the SAS results make sense...that there is 0 variance left over from the fully specified fixed effects. I am fairly certain the combination of the fixed effects uniquely identifies each facility. However, why doesn't R give a 0 variance? What is different between the two methods?
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