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Date User Name Chats
3/10/13 2:48 PM Jake okay, read the thread and posted in it
3/10/13 3:01 PM trinker Thank you both
3/10/13 3:04 PM trinker I I'm trying to connect this to what I already know via meta analysis. Does the fixed effect assume equal variances where as the random effects does not?
3/10/13 3:07 PM Jake they both assume equal within-cluster variance of y if that's what you mean
3/10/13 3:09 PM Jake one big difference is that fixed effects models analyze ONLY the within-cluster effects, whereas mixed models look at variance both within and between clusters. this is what gives mixed models their greater efficiency, however, it also means that you have to be careful to make sure the within-cluster effects are not too different from the between-cluster effects
3/10/13 3:09 PM Jake the paper i linked to in the thread talks about this issue in detail. its really quite a good paper
3/10/13 3:14 PM Dason random effects also puts a distributional assumption on cluster effects whereas fixed effects doesn't make any distributional assumption for those
3/10/13 3:15 PM Jake right. another source of efficiency for mixed models
3/10/13 3:18 PM Dason I don't work with mixed models as much as I think you do - I'm wondering how often, in practice, people check the distributional assumption of their random effects
3/10/13 3:18 PM Dason because I know there are complications associated with that
3/10/13 3:20 PM Jake i dont think too often really. in textbooks they usually go over checking that, but in practice i think people usually skip it. i usually skip it to be honest
3/10/13 3:20 PM Dason what do the textbooks offer as a way to check that assumption?
3/10/13 3:21 PM Jake e.g., assessing the alpha on a normal QQ plot
3/10/13 3:21 PM Dason using the blups as a plugin estimate I'm assuming
3/10/13 3:21 PM Jake right, by alphas i mean BLUPs
3/10/13 3:22 PM Dason because I've seen simulation evidence that even when you have normal errors and normal random effects that the qqplot doesn't quite look as nice as we would like
3/10/13 3:22 PM Dason one of the other grad students in the department I think is working on ways around this problem
3/10/13 3:23 PM Jake i find that the qqplot of residuals almost always looks funky, but i assume it is because really it comes from a mixture of many different normals
3/10/13 3:23 PM Jake as for qqplot of random effects, like i said, i usually don't even look at it =\
3/10/13 3:24 PM Jake my assumption is that the normality of random effects assumption matters less and less as number of clusters increases, similar to normality of errors in OLS
3/10/13 3:25 PM Dason Like I said I haven't done too much with this but it seems like most of the theory is derived under the assumption that we know the variance terms. In which case blups really are our best estimates and if we do know them and all the effects are normal then the distribution of the blups are normal... but in practice we estimate everything and it because a huge horrible nonlinear problem...
3/10/13 3:25 PM Jake i dont actually know that to be true though
3/10/13 3:26 PM Dason @Jake - That seems reasonable - I'm guessing the variance term estimates are consistent even if we make an incorrect distributional assumption and typically we just want that variance estimate to do actual inference
3/10/13 3:27 PM Jake yes typically. although there are some interesting cases where we want to do inference on the variance estimates too
3/10/13 3:27 PM Jake i like to talk about those cases when i present these models to my colleagues. its a whole new type of testing that we arent used to
3/10/13 3:27 PM Jake in my field that is
3/10/13 3:28 PM Dason I'm guessing the scaled variance estimates are asymptotically chi-squared as the number of clusters increases regardless of the distributional assumptions
3/10/13 3:29 PM Jake meh, sure ;)
3/10/13 3:29 PM Dason then again it's probably trickier than I imagine since we have to estimate a lot of quantities that we typically take as 'given' when deriving most of that theory...
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3/10/13 3:30 PM Jake yes removed i think so
3/10/13 3:31 PM Dason @removed - that's typically the case
3/10/13 3:31 PM Jake hglm?
3/10/13 3:31 PM Dason but it doesn't have to be that way.
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3/10/13 3:32 PM Dason well you can fit other models
3/10/13 3:32 PM Dason I think the hard part is trying to justify why you fit a different model
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3/10/13 3:33 PM Jake its hard for me to imagine a lot of cases where you have good reasons for strongly believing the random effects should be something other than normal
3/10/13 3:33 PM Dason especially since the main advantage of fitting the mixed model is that you're no longer treating everything as independent and are adequately modeling the covariance.
3/10/13 3:33 PM Dason I can think of cases where using something else might be reasonable
3/10/13 3:34 PM Dason I've even fit cases where we used something else
3/10/13 3:34 PM Jake like what
3/10/13 3:34 PM Dason gamma random effects for poisson response
3/10/13 3:35 PM Jake i see
3/10/13 3:36 PM Dason I can't remember the exact context but we had multiple counts from certain machines... or maybe it was missiles or something. It was real data though.
3/10/13 3:36 PM Jake poisson response usually uses log link function right?
3/10/13 3:36 PM Dason Well this was just a hierarchical model - no real need to fit a link function since we didn't have other covariates
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3/10/13 3:37 PM Jake okay, sure, but you could imagine that with a log link function you wouldnt need to assume a truncated distribution for the random effects, right?
3/10/13 3:37 PM Dason but sure we could have used a log link and fit normal random effects
3/10/13 3:38 PM Jake so with an appropriate choice of link function isnt it probably the case that a normal distribution of random effects is not much of a stretch?
3/10/13 3:39 PM Dason maybe
3/10/13 3:39 PM Dason for the most part the log-normal and the gamma can look fairly similar
3/10/13 3:40 PM Dason but there are some gammas that can't be considered to look similar to a log normal
3/10/13 3:40 PM Jake but those gammas probably are plausible distributions of poisson parameters, no?
3/10/13 3:40 PM Jake aren't* i mean
3/10/13 3:41 PM Dason They could be - I don't see why not.
3/10/13 3:41 PM Jake i guess i dont know what kind of gamma shape youre thinkin of
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3/10/13 3:49 PM Jake removed i looked on amazon and didnt see the book you mentioned. got link?
3/10/13 3:49 PM Jake found it -- glm with random effects
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3/10/13 3:53 PM removed removed
3/10/13 3:55 PM Dason @Jake - a gamma with alpha <= 1 isn't fit *too* well by a log normal. Probably adequately enough but it depends on what you're doing.
3/10/13 4:02 PM trinker Folks had to step out for an hour. Reading through your responses now.
3/10/13 4:09 PM removed removed
3/10/13 4:11 PM trinker @bg I want to sometimes test a package on various versions of R or see what a user experiences on that OS.
3/10/13 4:16 PM Jake dason, okay sure, there are some gamma shapes a log-normal can't emulate too great and probably vice versa. but in terms of having a better statistical model, is there any a priori, theoretical reason to believe that the model based on gamma random effects is in any way *better* than the log-normal model?
3/10/13 4:17 PM Jake removed, i often feel the same way about researchers wanting to have their pudding and eat it too when it comes to choosing fixed vs. random effects
3/10/13 4:18 PM Jake mainly the reason i am harping on this dason is that very often when i present these models to audiences in my field who are not familar with them, they bring up the issue of assuming normal random effects and seem to want to imply that it is a big limitation or restriction
3/10/13 4:19 PM Jake and i think, even setting aside the fact that we dont *have* to make that assumption, that really it is not a big limitation at all, in fact usually the assumption of normal random effects seems quite reasonable
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