I am a medical doctor and definitely not an expert in statistics, although I think I do okay and I am familiar with R.
I have discussed the following issue with a statistician but I am still not sure whether we came up with the right solution. I hope one of you can help.
I want to estimate the precision (repeatability) of a continuous variable measured on x-rays (PT) and evaluate the influence of different raters by specifying the variance between and within raters (inter- and intra-rater variance).
I have had 4 raters measure the continuous variable on 67 x-rays twice, thus each x-ray has been measured 8 times in total.
THE DATA (Pre):
'data.frame': 536 obs. of 4 variables: ID : Factor w/ 67 levels Rater : Factor w/ 4 levels Time : Factor w/ 2 levels PT : num 40.4 29.3 36 58.8 40.5 ...
THE MODEL we came up with was a linear mixed effect fit:
a <- lmer(PT~ (1|ID) + (1|Rater:ID), data=Pre)
From exploring the web I found that ":" is rarely used and that the model is equivalent to:
b <- lmer(PT~ (1|ID/Rater), data=Pre)
THE RESULT of either model a or b is:
Linear mixed model fit by REML ['lmerMod'] Formula: PT ~ (1 | ID/Rater) Data: Pre REML criterion at convergence: 2729.2 Scaled residuals: Min 1Q Median 3Q Max -5.7958 -0.2266 -0.0165 0.2214 4.8076 Random effects: Groups Name Variance Std.Dev. Rater:ID (Intercept) 4.630 2.152 ID (Intercept) 97.178 9.858 Residual 2.695 1.642 Number of obs: 536, groups: Rater:ID, 268; ID, 67 Fixed effects: Estimate Std. Error t value (Intercept) 18.611 1.214 15.34
THE INTERPRETATION according to the statistician was that:
The residual variance represents the intra-rater variance and the inter-rater variance is the sum of Rater:ID and residual variance.
Are these interpretations valid?
My concern is especially if the residual variance is truly an expression of the intra-rater variance or if I should somehow include the "Time" variable in the model to specify the variance between the first and second measurements within raters within subjects.