Binary response ordering
On Wed, Aug 4, 2010 at 4:54 AM, John Haart <another83 at me.com> wrote:
Dear List, I have a quick question regarding the setup of my data for analysis with a glmm. ?I hope this is the appropriate list, i apologise if it is not. I have a response variable, TRUE or FALSE. I have coded this as 0 = False and 1 = TRUE in excel. I have 3 categorical factors with C,D and E I then read in the data frame and run the model as follows- lmer(trueorfalse~1+(1|A/B) + C + D+ E ,family=binomial) And this is the output Generalized linear mixed model fit by the Laplace approximation Formula: threatornot ~ 1 + (1 | A/B) + C + D+ ?E ,family=binomial) ?AIC ?BIC logLik deviance ?1410 1450 -696.8 ? ? 1394 Random effects: ?Groups ? ? ? Name ? ? ? ?Variance ? Std.Dev. ?family:order (Intercept) 6.7869e-01 8.2382e-01 ?order ? ? ? ?(Intercept) 7.8204e-11 8.8433e-06 Number of obs: 1116, groups: A:B, 43; B, 9
Apparently you altered the output at some point because the factors that were named A and B ended up as order and family in the random effects description.
Fixed effects: ? ? ? ? ? ?Estimate Std. Error z value Pr(>|z|) (Intercept) ?0.11281 ? ?0.42232 ? 0.267 ? 0.7894 C1 ? -0.02414 ? ?0.19964 ?-0.121 ? 0.9038 D2 ?-0.16482 ? ?0.38602 ?-0.427 ? 0.6694 E2 ? ? ? 0.95381 ? ?0.54316 ? 1.756 ? 0.0791 . E3 ? ? ?0.75733 ? ?0.87275 ? 0.868 ? 0.3855 E4 ? ? ? 0.03044 ? ?0.47328 ? 0.064 ? 0.9487 What i am unsure about is the inference, if a term is significant does this relate to TRUE or FALSE?
In this case it would be related to the probability of a TRUE response but, as this is simply 1 - P(FALSE) then the only change if you reversed the order would be to change the signs of the coefficients. The simple way to verify this is to fit glm(threatornot ~ 1) and check the value of the coefficient. It should be log(pHat/(1-pHat)) where pHat is the proportion of TRUE responses.
I.E E2 has a p value of 0.079, does this 0.079 relate to the probability of it resulting in a true or false response? Does it matter how i code the input i.e FALSE = 1, TRUE =2 for instance?
If there are two levels in the response then the model is fit according to the probability of the second versus the first. You can disambiguate the process if you convert the response to a factor with the levels specified explicitly. The bigger issue is that you shouldn't pay too much attention to a particular coefficient related to the levels of a factor like E because the coefficients are defined with respect to the contrasts in effect at the time the model was fit. Without knowing the contrasts being used and without prior knowledge that a particular contrast was important, those coefficients are not important by themselves. It is the cumulative effect of the variability amongst the levels of the factor that is important.
Maybe i am reading the output wrong? Thanks John
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