Meta Analysis with Several Regression Studies

[quantumdude]

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!

 

[Stephen Tashi]

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?

 

[quantumdude]

Hi Stephen, thanks for replying.

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?)

I'm dealing with multivariate least squares regression models.

Are x1 and y1 the only random variables with a given estimated covariance ? - or do all pairs xj, yj have an estimate covariance?

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!