I wish to analyse a simple lab experiment. I have 8 fish. Four are fed on diet A, and four on diet B. I measure their Nitrogen (N) over 5 time periods (so 5 repeated measures per fish). I wish to know 3 pieces of information:
1) On diet A, does N change with time (i.e. a true slope different from zero)?
2) On diet B, does N change with time (i.e. a true slope different from zero)?
3) Do slopes of A and B differ from one another?
Thus I have run a simple mixed model in R, of the form:
Nitrogen ~ Time * Diet + (1|replicate)
Replicate is used as a random effect to control for repeated mesaures per individual fish.
I have compared this model to a simpler model without an interaction term, using analysis of deviance:
Nitrogen ~ Time + Diet + (1|replicate)
The model with the interaction explained signifcantly more variance and thus the better model.
Based on this interaction model, I have the following output table with the parameter estimates, and I wondered if I can use this table to answer my three questions? (I have calculated confidence intervals for these parameter estimates to determine if effects are real).
Fixed effects: Estimate Std. Error t value +95% CI -95% CI (Intercept) 15.8624 0.2332 68.0300 16.3194 15.4053 time 0.0069 0.0009 7.7600 0.0086 0.0051 dietB -0.1948 0.3298 -0.5900 0.4515 -0.8411 time:dietB -0.0066 0.0013 -5.2800 -0.0042 -0.0091
I understand the "Intercept" is value of N when time = 0 for diet A (R software works alphabetically so dietA before dietB), while "dietB" + Intercept is intercept for dietB when time = 0.
However, to answer my 3 questions I need to better understand how to interpret the slope information and how to report it. My current understanding is:
"time" gives me a real slope value (0.0069) to report for diet A, and having calculated confidence intervals, I can see they do not cross zero in this instance meaning diet A is a true slope (i.e. different from a slope of zero). So this is Question 1 answered, I hope?
"time:dietB" tells me that slope of dietB is 0.0069("time") + -0.0066, which gives me a slope value to report for diet B (0.0069 + - 0.0066 = 0.0003). As I currently understand it, the Std. Error for "time:dietB" is associated with this comparative slope value (-0.0066), and not on slope B's real value (0.0003), and consequently, confidence intervals also refer to this comparative value (-0.0066), and thus as confidence intervals do not pass through zero, this means that slope B is different from slope A. So this means Question 3 is answered, I hope?
If this is the case, then how do I answer my Question 2 - that slope B is different from a slope of zero? Can I get confidence intervals to answer this question, and/or do I need them?! Or is this information already contained within this summary table? Or instead, do I need to conduct a subsequent / entirely different analysis?