[R-sig-ME] fixed effects/log transformations question

[Gus Jespersen]

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,

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

Gus Jespersen <jesper <at> u.washington.edu> writes:

>
> Thank you Thierry,
> I have looked through the glht function in multcomp, and have two
> further questions:
>

 [snip]

> Yet I get the following error message:
>
> Error in parse(text = ex[i]) : <text>:1:20: unexpected symbol
> 1: sitettMossAddition Treatment
>                                        ^
> Any ideas on what I'm doing wrong here?

  It is very likely that the glht function is having trouble
with the spaces in your level names.  I would strongly suggest
that you reformulate them as legal R variable names: something like

     levels(mydata$myfactor) <- make.names(levels(mydata$myfactor))
should work.

>
> (2) As you can see, I am working with a log10 transformed response
> variable.  I'd like to stay with this for homog. of variance reasons,
> and for reporting the "Treatment -Control" CI previously mentioned,
> I'd like to report the backtransformed limits of the CI.  At what
> point in this process should the back-transformation happen?  When
> attempting this calculation without glht, I am uncertain of where in
> the process to back-transform as well.  I had been hoping to simply
> use 10^ for each fixed effect and its SE, as well as each element of
> the vcov matrix, but I fear I am overlooking some basic math here.

  Yes, you are.  You need to back-transform the confidence intervals,
not the elements and their standard errors.  The basic math you
are thinking about is

  10^(est+1.96*stderr) !== 10^est+10^(1.96*stderr)

If you back-transform first, the RHS is what you will be doing;
you want the LHS (this is for the upper CI, the obvious parallel
applies for the lower CI)


-- 
R. Gus Jespersen
PhD Candidate
College of Forest Resources
University of Washington
Box 352100
Seattle, WA 98195-2100
(206) 543-5777
jesper at u.washington.edu