Dear colleague, I came across a website/forum in which you talked about constraining the residual variance to zero (in LMEMs): http://permalink.gmane.org/gmane.comp.lang.r.lme4.devel/11418 I am aware that you suggested to use blmer. Has there been any development since 2013? Is there a way to fix sigma EXACTLY to zero now? Here is the problem. Like you, I teach statistics and linear mixed-effects models. My students and I frequently use lmer to analyze data with one or multiple sources of non-independence. However, I run into problems with designs that contain only dichotomous within-subject variables and only one data point per cell of the design per subject. In these designs, the residuals are zero (the level-1 models perfectly fit the data). I understand that technically, such a linear mixed-effects models are not identifiable. They would be identifiable, however, if I could fix the parameter for the variance of the residuals to zero. I can, of course, transform my data into wide format and analyze them with a GLM procedure (e.g., lm) but it seems bizarre to have to go through the tedious data restructuring process (dcast ...) and use different commands for a certain type of design that is in fact quite similar to other designs that can easily be analyzed with lmer. I tried a number of things (e.g., not including any random slopes, not including the random slope for the highest order interaction effect), but none of them gave me the ?right? values for the inferential statistics. Take a 2 x 2 within-subjects ANOVA with one data point per cell of the design from each participant. By transforming the data into wide format and using a standard GLM procedure I can obtain the ?right? F- and p-values. I have not found a way to obtain the same values with the data in long format (i.e., four lines per participant) and using lmer. It doesn?t matter which random effects structure I specify ? I am not getting the ?right? F- and p-values. The only trick I have found in lmer is to suppress the error message with control=lmerControl(check.nobs.vs.nRE="ignore"). But suppressing the error message is not the same as constraining sigma to be zero. Do you know how to fix the parameter for the variance of the residuals to zero? Thanks a lot for your insight. Best wishes, ? Markus ----------------------------------------------- Markus Brauer Professor Department of Psychology University of Wisconsin - Madison 1202 West Johnson St. Madison, WI 53706-1611 USA Tel. +1-608-890-3313 Cell +1-608-692-3468 Fax +1-608-262-4029 Office 417 Web Page: http://psych.wisc.edu/brauer/BrauerLab/
lmer: constraining sigma to 0
2 messages · Markus Brauer, Ben Bolker
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On 15-05-06 12:45 PM, Markus Brauer wrote:
Dear colleague, I came across a website/forum in which you talked about constraining the residual variance to zero (in LMEMs): http://permalink.gmane.org/gmane.comp.lang.r.lme4.devel/11418 I am aware that you suggested to use blmer. Has there been any development since 2013? Is there a way to fix sigma EXACTLY to zero now?
I believe nothing has changed since 2013. As I may have said in that message (I'm not bothering to check ...), and as Doug Bates has certainly said before, lmer's underlying parameterization is in terms of a *relative* covariance parameter Sigma -- that is, all of the random-effects (co)variances are expressed relative to the observation-level/residual variance. - From http://arxiv.org/abs/1406.5823 (hopefully coming to JSS any day now!) Section 3.4: We are now in a position to understand why the formulation in equations 2 and 3 is particularly useful. We are able to explicitly profile $\betavec$ and $\sigma$ out of the log-likelihood (Equation 25), to find a compact expression for the profiled deviance (negative twice the profiled log-likelihood) and the profiled REML criterion as a function of the relative covariance parameters, $\bm\theta$, only. Furthermore these criteria can be evaluated quickly and accurately. ======== I can understand the problem this presents for you, but I don't know how helpful I can be. Besides the aforementioned tricks (e.g. using blmer), I wonder if you could hack up a post-fitting summary that would combine the unidentifiable variance components into a single (identifiable) value ... ?
Here is the problem. Like you, I teach statistics and linear mixed-effects models. My students and I frequently use lmer to analyze data with one or multiple sources of non-independence. However, I run into problems with designs that contain only dichotomous within-subject variables and only one data point per cell of the design per subject. In these designs, the residuals are zero (the level-1 models perfectly fit the data). I understand that technically, such a linear mixed-effects models are not identifiable. They would be identifiable, however, if I could fix the parameter for the variance of the residuals to zero. I can, of course, transform my data into wide format and analyze them with a GLM procedure (e.g., lm) but it seems bizarre to have to go through the tedious data restructuring process (dcast ...) and use different commands for a certain type of design that is in fact quite similar to other designs that can easily be analyzed with lmer. I tried a number of things (e.g., not including any random slopes, not including the random slope for the highest order interaction effect), but none of them gave me the ?right? values for the inferential statistics. Take a 2 x 2 within-subjects ANOVA with one data point per cell of the design from each participant. By transforming the data into wide format and using a standard GLM procedure I can obtain the ?right? F- and p-values. I have not found a way to obtain the same values with the data in long format (i.e., four lines per participant) and using lmer. It doesn?t matter which random effects structure I specify ? I am not getting the ?right? F- and p-values. The only trick I have found in lmer is to suppress the error message with control=lmerControl(check.nobs.vs.nRE="ignore"). But suppressing the error message is not the same as constraining sigma to be zero. Do you know how to fix the parameter for the variance of the residuals to zero? Thanks a lot for your insight. Best wishes, ? Markus ----------------------------------------------- Markus Brauer Professor Department of Psychology University of Wisconsin - Madison 1202 West Johnson St. Madison, WI 53706-1611 USA Tel. +1-608-890-3313 Cell +1-608-692-3468 Fax +1-608-262-4029 Office 417 Web Page: http://psych.wisc.edu/brauer/BrauerLab/
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