I've got repeated measures of hearing thresholds for a set of patients who each have a different inner ear measurement. This data is unbalanced, there are a varied number of measurements at varied intervals for each subject. My goal is to build a random-intercept random-slope (longitudinal) model that describes the impact of inner ear size (an unchanging value) and change in repeated measure over time, and I'm using
At the moment, I'm having difficulty choosing between two models. These models differ in how age is accounted for in the model.
The first model (M1) is written in R as:
M1 <- lmer(repeatedMeasure ~ innerEarSize + ageAtMeasurement + (1 + ageAtMeasurement | subjectName), data = data)
And the second model has age split into age at first repeated measure test, versus time since first repeated measure test.
To be clear, for each subject:
ageAtFirstMeasure = ageAtMeasurement - min(ageAtMeasurement)
timeSinceFirstMeasure = ageAtMeasurement - ageAtFirstMeasure
ageAtMeasurement = ageAtFirstMeasure + timeSinceFirstMeasure
I've written the second model in R as:
M2 <- lmer(repeatedMeasure ~ innerEarSize + ageAtFirstMeasure + (1 + yearsSinceFirstMeasure | subjectName), data = data)
Is this a reasonable specification for a longitudinal repeated-measures problem?
The second model accounts for
ageAtFirstMeasure as a fixed effect, and restricts the longitudinal component to the number of years after the first test. This teases out the effect of age on the repeated measure, while still accounting for increasing age.