Intuition tells me that using the mean of three measurements, which is characterized by a standard deviation already, will interfere with other statistics calculations and subsequently with fitting the model.
However I am not 100% sure which should I use. Better safe than sorry.
TL;DR: use the averages.
What you want to know is what one should (reasonably) expect when the experiment is replicated. Repeating the experiment means to use new experimental units. So the key thing to know is how variable are results between different experimental units. What is not interesting is the variability between repeated mesurements on one and the same experimental unit. This "technical" variabilty interferes with what you actually want to know.
When the technical variability is very small compared to the variability between experimental units, a single measurement is a sufficiently precise estimate of the value of that experimental unit. Variability between single measurements will (more or less) faithfully represent the variability between experimental units.
When the technical variability is large, a single measurement is not a good estimate. But errors will average out in replicate measurements. By using averages of multiple replicate measurements (taken on the same exp. unit), you will get better estimates.
Statistically, you usually also want to estimate some model parameters and provide uncertainty (or compatibility) intervals or p-values for these parameter estimates. This involves the standard errors, which are calculated based on the relevant "degrees of freedom" of the statistical model. These degrees of freedom depend on the number of experimental units in your study - not on the number of replicate readings per unit; these would not be statistically independent! Hence, if you use the averaged values, the model only sees only statistically independent values (as many as you have experimental units in your study).
Example: let the experimental units be human subjects and the experiment is to estimate how the body weight depends on the sex. As an extreme case, you can take one male and one female subject and mesaure their weights. Because the weight measurement is erroneous (or depends on many things you cannot control), you take 100 measurements from each subject (possibly on different days, day-times, etc.). If you want to estimate (or test) the mean difference, the test "sees" 2 x 100 values and assumes that they are all statistically independent. The standard error will thus be tiny and you will find a highly statistically significant maen difference which makes you concluse that, say, females are heavier than males. But this conclusion is not backed up by data. You have NO information how the weights would differ in different subjects and if the highliy significant difference you found is a precise estimate of an arbitrary difference between two random subjects or if this is attributable to a systematic sex effect. The only way to examing a systematic sex-effect is to have data from several (many) different subjects (from each sex). And it is ONLY the information per subject that will count. Replicate measurements can help to get more precise (average) values per subject.
You should use replication,it is usually not less than three!!. Regards
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