Timeline for Can correlated random effects "steal" the variability (and the significance) from the regression coefficient?
Current License: CC BY-SA 3.0
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| Oct 9, 2014 at 10:17 | comment | added | Peter | In mixed models, you can test for presence of random effect. This translates to H0: $\sigma = 0$ vs HA: $\sigma > 0$. Failing to reject H0 means there is no evidence for the specific random effect and adding it to your model will generate extra noise. See this class note for a more technical explanation stat.wisc.edu/~ane/st572/notes/lec21.pdf | |
| Oct 9, 2014 at 9:12 | comment | added | Tomas | "is $\sigma$ significantly larger than zero?" Peter, well, I think $\sigma$ is always significantly larger than zero because it simply can't be negative... | |
| Oct 3, 2014 at 11:51 | comment | added | Peter | I agree with comment 1). In fact, I should read your index notation more carefully. Regarding your comment 2), when you fit your model, is $\sigma$ significantly larger than zero? Sometimes adding a random/fixed effect not strongly associated with outcome will add more noise rather than explaining variability in outcome. | |
| Oct 3, 2014 at 6:13 | comment | added | Tomas | Peter, 1) I am using random effects because the residuals of the model where correlated within years. This means there is some part of between-year population growth present over all sites which is not explained by $x_{i,j}$. This is not handled by the time series model. You speak of autocorrelation on the population size, while I speak of the autocorrelation of population growth, this is a different thing. 2) Sometimes it can happen that adding random effect will in fact enlarge the confidence intervals. | |
| Oct 2, 2014 at 16:44 | comment | added | Tomas | And you say $V$ is the "overall variance", don't you mean "overall residual variance" instead? | |
| Oct 2, 2014 at 16:43 | comment | added | Tomas | Peter, thank you for the answer! I have to go so I will have to look at your answer in more detail later. Now just a small comment - $\epsilon$ is not the only residual variability. $\epsilon$ is only the overdispersion - main residual variability is present within the $N_{i,j} \sim \mbox{Poiss} (\mu_{i,j})$ term. | |
| Oct 2, 2014 at 16:35 | history | answered | Peter | CC BY-SA 3.0 |