I have a data set where I estimated home range size using 10 estimators from 41 individuals. I wanted to test if these estimators were significantly different from each other so I fit a linear mixed-effects model with nlme as follows:
mod3fML1b<-lme(size~band*nobsS+Sex,random=~1|snake,data=HR.compare,weights=vf6,method='REML')
Size is home range size (log transformed to meet assumptions of normality), band is a factor with 10 levels representing my 10 estimators, nobsS is a measure of sampling intensity (number of individual locations standardized by number of sampling days), Sex is male/female, and snake is my random effect of individual. The summary output is as follows:
> summary(mod3fML1b)$tTable
Value Std.Error DF t-value p-value
(Intercept) 4.099809927 0.24824427 351 16.51522508 9.632758e-46
bandBPIdiagonal -0.344448847 0.05724340 351 -6.01726718 4.462854e-09
bandBPIfull -0.303881612 0.05593369 351 -5.43289002 1.038615e-07
bandHREFdiagonal -0.053639559 0.06749969 351 -0.79466377 4.273461e-01
bandHREFfull -0.131436107 0.06471844 351 -2.03089130 4.301931e-02
bandLCVdiagonal -0.186017321 0.11520159 351 -1.61471137 1.072717e-01
bandLCVfull -0.186017321 0.11520176 351 -1.61470908 1.072722e-01
bandLCVsingle -0.181687618 0.11940300 351 -1.52163366 1.290012e-01
bandSCVdiagonal -0.163761675 0.05816320 351 -2.81555466 5.144255e-03
bandSCVfull -0.120439828 0.05720672 351 -2.10534398 3.597148e-02
nobsS 0.406335759 1.16315897 38 0.34933811 7.287640e-01
SexMale 1.457327832 0.23373517 38 6.23495313 2.711438e-07
bandBPIdiagonal:nobsS -0.415077222 0.24845863 351 -1.67060896 9.569032e-02
bandBPIfull:nobsS -0.442855108 0.24277399 351 -1.82414559 6.898016e-02
bandHREFdiagonal:nobsS -0.143832274 0.29297492 351 -0.49093716 6.237777e-01
bandHREFfull:nobsS -0.007949556 0.28090319 351 -0.02829999 9.774390e-01
bandLCVdiagonal:nobsS -2.072417895 0.50001973 351 -4.14467228 4.270077e-05
bandLCVfull:nobsS -2.072417895 0.50002044 351 -4.14466640 4.270182e-05
bandLCVsingle:nobsS -2.171179830 0.51825545 351 -4.18940086 3.542319e-05
bandSCVdiagonal:nobsS -0.745834058 0.25245092 351 -2.95437248 3.344486e-03
bandSCVfull:nobsS -0.766847848 0.24829943 351 -3.08839960 2.172757e-03
The p-values indicate several levels are significantly different from the reference level and the patterns are consistent with what I expected based on the raw data. However, I wanted to display the mean log(home range size) with a 95% confidence intervals (not prediction intervals) to compare the effect sizes among different estimators. To do this I calculated predicted values using the predict.lme function and SE using code from a previous R thread at: https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q1/003320.html However, my 95% CI broadly overlapped, much more than I would have expected based on the p-values from my lme model. I have copied the values I obtained which shows the broad overlap in 95% CI:
data<-data.frame(band=c('BPId','BPIf','REFs','REFd','REFf','LCVs','LCVd','LCVf','SCVd','SCVF'),
log.mean.size=c(4.99,5.03,5.41,5.33,5.28,4.88,4.89,4.89,5.13,5.17),
lci=c(4.62,4.65,5.03,4.95,4.90,4.90,4.50,4.50,4.75,4.79),
uci=c(5.38,5.41,5.79,5.71,5.66,5.28,5.29,5.29,5.51,5.54))
Does anyone have suggestions for why the p-values are showing significant differences among estimator levels but the CI overlap? I apologize for not providing any data but I would be happy to email a copy of my raw data and full code if that would help.
Thanks, JBauder
