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Meta Analysis with Several Regression Studies

  1. Jan 28, 2015 #1

    Tom Mattson

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    I have come across a problem that I need to solve, and it isn't your garden variety regression problem. It isn't even covered in any of my books, of which I have many. I need either a book title or an online PDF that covers this material.

    Suppose we have a response variable [itex]z_1[/itex] that depends on predictor variables [itex]x_1,x_2,...,x_n[/itex]. Further suppose that we have another response variable [itex]z_2[/itex] that depends on predictor variables [itex]y_1,y_2,...,y_m[/itex].

    There are 4 studies to be synthesized.

    In Study 1 a regression model [itex]z_1=\alpha_0+\alpha_1x_1+\alpha_2x_2+...+\alpha_nx_n[/itex] is obtained.
    In Study 2 a regression model [itex]z_2=\beta_0+\beta_1y_1+\beta_2y_2+...+\beta_my_m[/itex] is obtained.
    In Study 3 a correlation between [itex]z_1[/itex] and [itex]z_2[/itex] is obtained.
    In Study 4 a correlation between [itex]x_1[/itex] and [itex]y_1[/itex] is obtained.

    The goal is to synthesize these studies to model [itex]z_1[/itex] as a function of [itex]x_1[/itex] and [itex]y_1[/itex] only.

    What's a good read to get going on this? Thanks!
     
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  3. Jan 28, 2015 #2

    Stephen Tashi

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    Are these regression models fit by considering both the z-variable and x-variables to be random variables? (e.g. total least squares regression as opposed to least squares regression?)

    Are x1 and y1 the only random variables with a given estimated covariance ? - or do all pairs xj, yj have an estimate covariance?
     
  4. Jan 28, 2015 #3

    Tom Mattson

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    Hi Stephen, thanks for replying.

    I'm dealing with multivariate least squares regression models.

    It's just the one pair of predictor variables for which I have an estimated covariance. But leaving that aside, what I really want to know is if there is a comprehensive reference from which I could learn how to combine regression models. It would be a bonus if both cases in your question were covered. Thanks!
     
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