I have a very large data set with repeated measurements of same blood value (co) (1 to 7 measurements per patient). Each measurement is coupled with time which is the time interval between surgical operation and blood level measurement.
My aim is to show that this blood value correlates positively with time.
Blood level measurements are highly skewed to right and hence I am using a log-transformation and linear mixed effect regression model (lmer in lme4 package).
I have constructed a null model:
Model 2 includes time as independent variable:
Id is the patient number in th dataset.
By using the anova() function I see that fit2 is significantly better than fit1:
> anova(fit1,fit2) refitting model(s) with ML (instead of REML) Data: ASR Models: fit1: lgco ~ (1 | id) fit2: lgco ~ time + (1 | id) Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) fit1 3 342.77 357.50 -168.39 336.77 fit2 4 320.64 340.27 -156.32 312.64 24.135 1 8.983e-07 ***
However I have other data which suggests that the correlation between time and blood value might even more profound, for example quadratic. This would be Model 3.
I tried the following: first I took the square root of the blood value and after that I made the transformation using log.
My question is that can I compare models 2 and 3 in anyway now after the dependent variable has two different transformations in these models. In fit1 and fit2 the transformation is identical, only the independent is added. I assume that with different dependent variable transformation the use of anova() is not allowed:
anova(fit2,fit3) refitting model(s) with ML (instead of REML) Data: ASR Models: fit2: lgco ~ time + (1 | id) fit3: lgsqrtco ~ time + (1 | id) Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) fit2 4 320.64 340.27 -156.32 312.64 fit3 4 -1065.66 -1046.03 536.83 -1073.66 1386.3 0 < 2.2e-16 ***