Extracting R2 from multiple regressions and using them as a variable after logit transformation-interpretation

[Ahmad]

Hi i have estimated a large number of equations, i have extracted the R2 from the regressions and am using it as a dependent variable in another regression.

Literature tells that i should do a logistic transformation of R2 before using it as a dependent variable in a regression as it is bounded between 0 and 1 .

hence i perform the following transformation: y= ln ( R2 / 1-R2)

then i conduct the regression.

There are following problems: number 1 ) my new variable Y is all in negative

                                                           2) i get unusually high beta coefficients which are like 100 or 115, which make no economical sense.

Can anyone please suggest how to interpret the coefficients or what am i doing wrong??

thanking you in anticipation

[Reeza]

Well, for

1) it means that R2 is always less than 0.5 (easy enough to check)

2) No idea

Not very helpful, hopefully others have more idea.

[SteveDenham]

Reeza answered the first point, and the second depends on the independent variables and how they are scaled.  When working with logits, recall that the beta coefficients relate to changes in the log odds ratio per unit change in the independent variable, and not to changes in R2.

Steve Denham

[Ahmad]

steve that i understand but how to intrpret coefficients , which make an economical sense?

[Reeza]

I don't think we can state that without knowing way more about your model. How are they doing it in the literature that's telling you to use this method in the first place?

[Ahmad]

my model is simple,

i regress individual stock liquidity on market liquidity for 500 stocks using following equation

IL = a + b1 ML +e

i regress it for every stock for every month over a period of 7 years,

i extract the R2 from the above equations for every stock in every month, calculate the cross sectional average every month. hence i have a time series monthly R2 for a period of 7 years, which represent the liquidity commonality of the market.

as R2 is bouded between 0 and 1, i perform a logit transformation. i understand that the values obtained from logit transformations are all negative because most of the values of orignal R2 are between .04 and .2

now i want to regress this using OLS , on the monthly market returns, abs + monthly market returns, and abs negative monthly market returns.

monthly market returns have mostly the value between 0.1 and .2,

but i get coefficients like 100 and 22

which make absolutely no economic sense.

I dont know how to interpret the coefficients, or if i am doing something wrong while estimating the last equation.

Thanks

but i ge