Timeline for How to fit a mixed model with response variable between 0 and 1?
Current License: CC BY-SA 3.0
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| Jan 5, 2018 at 23:29 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2017 at 13:01 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2017 at 12:55 | history | edited | amoeba | CC BY-SA 3.0 |
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| May 17, 2017 at 11:57 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 14, 2016 at 19:37 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 7, 2016 at 9:07 | vote | accept | amoeba | ||
| Sep 6, 2016 at 23:37 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 6, 2016 at 20:14 | comment | added | usεr11852 | @amoeba: I mostly mentioned it because you experienced issues with the glm to begin with. | |
| Sep 6, 2016 at 20:04 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 6, 2016 at 16:10 | answer | added | amoeba | timeline score: 30 | |
| Sep 5, 2016 at 22:30 | comment | added | amoeba |
@usεr11852: It's not balanced with respect to the levels of factors A, B, and C, if that's what you mean. Some factor combinations have many more trials than some other factor combinations. Complete separation is not an issue. Interesting idea about logistf, but it does not support random effects (?), so can't fully help me here in any case.
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| Sep 5, 2016 at 22:21 | comment | added | usεr11852 |
Only as a comment: You don't mentioned anything about how balanced your dataset is and whether or not you suspect issue with complete separation. If you use Firth logistic regression (logistf) do you still experience the same issue? (I tried it with some toy-data response and it seemed fine but clearly your experiment's design/complexity might be much more demanding)
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| Sep 5, 2016 at 18:28 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2016 at 15:30 | comment | added | amoeba | @fcop I am modeling their choices too (separately), but in this question I am concerned with modeling the confidences. | |
| Sep 5, 2016 at 15:28 | comment | added | user83346 | So they make a choice and you want to model their confidence in the choice made? You don't want to model the choice using their confidence as a weight? | |
| Sep 5, 2016 at 15:17 | comment | added | user83346 | Maybe, assuming that the variance is the same and that $p(1-p)/n$ is the formula for the variance, you may find something for $n$ and then use this to get numbers of successes. If you use weights then they should sum up to your number of observations else it is 'as if' you increase the sample size, hence the impact on standard errors. | |
| Sep 5, 2016 at 15:11 | comment | added | amoeba |
@fcop (1) Well, they would probably say that they are not "absolutely certain", but in the experiment they are asked to make a binary choice and to report their confidence (as a number); nothing else was recorded, that's the data I have. (2) It would be better not to make this assumption; I am adding a random intercept (1 | subject) which is basically allowing different subjects to be under-confident or over-confident. I don't know how to allow the variance for different subjects to be different, so I assume it's the same.
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| Sep 5, 2016 at 15:07 | comment | added | user83346 | And they are absolutely certain about their value like 0.9, or do they also have some ''error margin on it''? Can you assume that confidence reported by different subjects are equally precise? | |
| Sep 5, 2016 at 15:00 | comment | added | amoeba | @fcop Thanks. The problem is that I don't have the numbers of success/failures for each case; my response variable is not a fraction or a proportion. It's just a probability (confidence) reported by human subject, e.g. a person can report $0.9$ confidence in their choice, and I want to model that. | |
| Sep 5, 2016 at 14:57 | comment | added | amoeba |
@Aaron: I tried adding + (1 | rowid) to my glmer call and this yields stable estimates and stable confidence intervals, independent of my weight choice (I tried 100 and 500). I also tried running lmer on logit(reportedProbability) and I get almost exactly the same thing. So both solutions seem to work well! Beta MM with glmmadmb gives also very close results, but for some reason fails to converge completely and takes forever to run. Consider posting an answer listing these options and explaining a bit the differences and pros/cons! (Confidence intervals that I mention are all Wald.)
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| Sep 5, 2016 at 14:53 | comment | added | user83346 | I don' t know for glmer but for glm this may help: stats.stackexchange.com/questions/164120/…: | |
| Sep 5, 2016 at 14:32 | comment | added | amoeba |
Thanks. Yes, I can logit the DV and then use Gaussian mixed model (lmer), but this is also a kind of hack, and I've read that it's not recommended. I will try a random effect for each observation! At the moment, I am trying beta mixed model; lme4 cannot handle it, but glmmadmb can. When I run glmmadmb(reportedProbability ~ a + b + c + (1 | subject), myData, family="beta"), I get correct fit and reasonable confidence intervals, but a convergence failed warning :-/ Trying to figure out how to increase the number of iterations. Beta might work for me because I don't have DV=0 or DV=1 cases.
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| Sep 5, 2016 at 14:27 | comment | added | Aaron - mostly inactive | How about transforming the probabilities first? Can you get something that's closer to normally distributed with say, a logit transformation? Or the arcsin-sqrt? That would be my preference rather than using glmer. Or in your hack solution, you could also try adding a random effect for each observation to account for underdispersion due to your choice of weights. | |
| Sep 5, 2016 at 13:57 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2016 at 11:35 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2016 at 10:42 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2016 at 9:41 | history | edited | amoeba | CC BY-SA 3.0 |
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| Sep 5, 2016 at 0:14 | history | asked | amoeba | CC BY-SA 3.0 |