fixed effects/log transformations question
Gus Jespersen <jesper <at> u.washington.edu> writes:
Dr. Bolker, Thanks for the response. One last question with regard to negative t values when using log10 transformed data. I am assuming the correct interpretation of the following output is: if the t value is negative and you're using log10 data, to get the fixed effect CI, you must add your own negative sign to 10^(est.+1/96*SE), such that the backtransformed CI from the output below would be: ([1] "95 % REML Confidence interval" [1] -0.58261813 0.02578124 becomes -.295 -1.05 Is this correct,
No, but the interpretation is a little bit subtle. Here you
are working with (as far as I can tell) the back-transformed
confidence intervals on the effect of the treatment.
10^{-0.5826,0.02578} is {0.26,1.06} (where did you get 0.295??);
this says that the lower CI is that the proportional effect of
the treatment is to multiply by 0.26 (a 74% decrease); the upper
CI is a 6% increase (you can subtract 1 from the CI values if you
want to get it in terms of proportional changes).
If you were using the natural log (log_e) rather than the log10
scale, then you could interpret *small* (near zero) parameters as
being approximately equivalent to proportional changes (without
back-transforming), because exp(x)-1 is approximately x when
x is small ...
For what it's worth, this isn't an R question, or a mixed-model
question, any more, it's become a general statistical question -- you
might try asking similar questions on http://stats.stackexchange.com
...
Thanks again for the help
Gus
[1] "###############NH4 Results Year Two##################"
Data: data.sub
Models:
Mod.NH4.2.2: log10(NH4Nyeartwo) ~ 1 + (1 | pr)
Mod.NH4.2.1: log10(NH4Nyeartwo) ~ 1 + sitett + (1 | pr)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
Mod.NH4.2.2 3 26.427 29.700 -10.2136
Mod.NH4.2.1 4 25.243 29.607 -8.6216 3.1841 1 0.07436 .
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Linear mixed model fit by REML
Formula: log10(NH4Nyeartwo) ~ 1 + sitett + (1 | pr)
Data: data.sub
AIC BIC logLik deviance REMLdev
30.37 34.73 -11.18 17.24 22.37
Random effects:
Groups Name Variance Std.Dev.
pr (Intercept) 0.010942 0.10460
Residual 0.130473 0.36121
Number of obs: 22, groups: pr, 12
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.7305 0.1086 6.729
sitettToeAdditionsTreatment -0.2784 0.1552 -1.794
[1] "95 % REML Confidence interval"
[1] -0.58261813 0.02578124