In the notes, it is stated that we obtain the same multiplier from both representations of the model (Complete and Marginal interactions). However, in the marginal interactions case, the multiplier for Factor 1 Level B, Factor 2 Level X and the interaction terms between Factor 1 Level B and Factor 2 Level X, are zero. Therefore for the case of Factor 1 Level B and Factor 2 Level X, the total multiplier is zero, which is not equal to the Multiplier obtained from the Complete Interactions of multiplier 1.00. Can someone please explain why is this the case? Thank you.
Hi Purple, You're looking at the base level combination, which has multipier 1. So Factor 1 Level B and Factor 2 Level X gives a multiplier of 1 x 1 x 1, which is the same as the complete interations representation of the model. Kind regards, Katherine.
In the attached pdf, I have produced two sets of Marginal interactions multipliers, namely Case A and Case B. Why is it that for the case of Marginal interactions, the multipliers are as given in Case A and not Case B which produces overall relvativity which is equivalent to the relativities for the complete interactions? What do the multipliers actually mean? What is the difference between the two examples of marginal interactions? Thank you.
Dear Purple, Case A and Case B are the same. You've made an error in your spreadsheet, so no wonder it's confusing. The overall relativities presented in your top right table are incorrect. For example, the multiplier for the combination of X and D should be 1 x 1 x 1.2 = 1.2, however your answer is a dash, meaning 1. You have given the correct overall relativities for both Case A and Case B in the bottom right table. I think you're getting confused by the dash. Remember that a dash denotes the base level 1.
Thanks Katherine. If dash equal to 1, does that mean that we can either express the base multipliers as dashes or ones? And can the multipliers for complete interactions be presented as below? Does it mean the same as when the BX multiplier for complete interactions is expressed as one? A B C D W 0.72 0.80 0.88 0.96 X 0.90 - 1.10 1.20 Y 0.97 1.20 1.45 1.66 Z 1.26 1.40 1.85 2.10 Thank you.
I think the answer to all three of your questions is yes. In the table at the top of page 42 of Chapter 16, dashes are being used instead of ones for certain entries to highlight the fact that no parameter is required corresponding to these entries. Counting up the entries which are not dashes, you should get 15 corresponding to the 15 parameters needed. A dash is being used in the row of X and column of B because the combination of B and X is the base level. You would not use a dash in place of a 1 for the interaction term between A and W for example.
