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Thread: Estimated Parameter as Dependent Variable

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    Estimated Parameter as Dependent Variable




    Hi,
    Would anybody be able to help me with the following problem? That would be great!!
    In my analysis I follow a two-step approach. In the first step, I model the effect of some beta on y while controlling for other variables. (Please note that I calculate the 1st step separately for 50 different brands).
    In the second step I then pool all estimated beta coefficients and try to explain their variance by some other variables. Thus, the estimated beta parameters, obtained from the first stage, represent the dependent variables in my second step
    Following this approach I neglect the error in the beta estimates. In order to account for the measurement errors in the betas I weight each variable with its inverse standard error.
    However, I am not sure whether this is sufficient. Is there another more sophisticated way to account for these errors? Is there a way to calculate both steps simultaneously? (Simply plugging the second equation into the first one is unfortunately not an option due to the high number of betas and other variables).
    Also I heard that bootstrapping might be a possible way to overcome this problem. I guess I would bootstrap the beta coefficients of the first regression, however I am not sure how to proceed further. I am bit lost. It would be really great if somebody could help me. Thank you soo much in advance.

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    Re: Estimated Parameter as Dependent Variable

    Can you describe the context, that may help us understand what you are doing. Are you using the same dataset for all the first step models, but just different independent and dependent variables?


    What is the purpose of your second step? I want to recommend MANOVA, but I don't know your purpose or what you are completely doing!
    Stop cowardice, ban guns!

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    Re: Estimated Parameter as Dependent Variable


    hi, first of all thank you.
    Let me be a bit more specific: I have two different datasets. My first dataset comprises weekly sales data for 50 brands and the corresponding marketing mix information such as price, promotions, and advertising spending for a period of T=300 weeks. First, I regress the marketing mix variables on sales (DV) using a general distributed lag model. I do so for each brand separately. My main goal from this first step is to acquire the effectiveness of brand’s promotions (sales response to different promotions).

    In the second step I try to explain the variance in promotion effectiveness by different context factors (type of promotion etc.). Therefore, I pool the betas on promotions (one brand can have more than one promotion) and explain them by different context variables that come from my second dataset. I hope this explains what I am trying to do

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