Thank you Rolf, >> Using the analysis of co-variance example from MASS (fourth edition, p >> 142), what is the correct notation for the formula "Gas, ~ Insul/Temp > There shouldn't be a comma after ``Gas'' in that formula. >> - 1"? Obviously, if we fit it as two separate models (as in the >> example above it), we would have something like y_i = \beta x_i for >> each of the two models. > No. y_i = alpha + beta x_i . Clearly you need an intercept. > Do you really expect gas consumption to be nil when the average > external temperature is 0 degrees C ? Right, of course... both silly mistakes, my apologies! >> So my question is, when we have a single model >> with a k-level factor interaction term as in the equation above, what >> is the correct/standard statistical (LaTeX style) notation? > The model is simply > y_ij = alpha_i + beta_i x_ij > where i = 1 (before) or 2 (after). I.e. you are allowing a different slope > and intercept > for each of the scenarios (before and after). > But this is the ``deterministic'' part of the model. You should really > include the random part: > y_ij = alpha_i + beta_i x_ij + E_ij > where the E_ij are independent random variables with mean 0 and common > variance sigma^2. (Often the E_ij are assumed to be Gaussian, mainly > because if all you have is a hammer, then everything looks like a nail). Perfect! Thanks for the clarification. I think I was previously trying to be a bit more clever than necessary (and as a result not being very clever at all :-p)
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