Comparing Sets of Variables

[Serena Menny]

Dear members,

I am currently studying the determinants of sustainable investment and have identified four sets of variables for this purpose. The breakdown of these variables is as follows:

The first set contains 2 variables.
The second set contains 3 variables.
The third set contains 3 variables.
The fourth set contains 2 variables.

To analyze these variables, I am employing marginal effects from probit regressions.

I am seeking advice on the best approach to determine which set of variables most effectively explains sustainable investment (the contribution of each set of variable). Applying Δpseudo-R² values is a little complicated.

Thank you,

[Carlo Lazzaro]

Serena:
see -estat gof-.

[Rich Goldstein]

I think it depends heavily on what you mean by "most effectively explains sustainable investment (the contribution of each set of variable)" - are you asking which (sub)set does the "best" job of prediction or something else? if something else, what? (e.g., maybe you have some theory and you want to know which set matches the theory most closely?)

added in edit: or maybe you are concerned with predictions or other results for certain subgroups?; finally, at least for now, maybe you are interested in whether some variables "dominate", in a specific sense, others; if so, see the user-written "domin" - use -search to find and download (and link to an SJ article with lots of cites)

[Serena Menny]

I think it depends heavily on what you mean by "most effectively explains sustainable investment (the contribution of each set of variable)" - are you asking which (sub)set does the "best" job of prediction or something else? if something else, what? (e.g., maybe you have some theory and you want to know which set matches the theory most closely?)

I would like to know which set of variables does the "best" job of prediction yesss.Specifically, I aim to classify the four sets of variables based on their effectiveness in explaining the decision to invest in green funds.

[Rich Goldstein]

in your first sentence in #4 you say you want the set the does the best job of prediction but in your second sentence you say you want to classify the sets of variables based on their effectiveness in explaining .... - to me these are different things; you might want to look at Shmeuli, G (2010), "To explain or to predict?", Statistical Science, 25(3): 289-310

[George Ford]

Do you intend on interpreting the coefficients/marginal effects, or just best predicting the outcome? In the latter case, you don't care much about bias or standard errors.

[Serena Menny]

in your first sentence in #4 you say you want the set the does the best job of prediction but in your second sentence you say you want to classify the sets of variables based on their effectiveness in explaining .... - to me these are different things; you might want to look at Shmeuli, G (2010), "To explain or to predict?", Statistical Science, 25(3): 289-310

The goal is to determine the contribution of each set of variables. In this regard, I would like to identify the set that explains the best, followed by the second, third, and finally the fourth.
Thank you for the reference!

[Serena Menny]

Do you intend on interpreting the coefficients/marginal effects, or just best predicting the outcome? In the latter case, you don't care much about bias or standard errors.

I interpreted the marginal effects for the sub-variables within each set of variables for individual models. However, in the final model where all sets of variables are combined, I would like to determine how each set of variables predicts the outcome. Specifically, I want to know which set predicts the outcome best, which one is second, and so on.

[Rich Goldstein]

I'm still not sure I understand, but look at the user-written -domin-, its associated SJ article (citation in help file) and other cites in the help file or the article

[George Ford]

sysuse auto, clear

global X1 mpg weight
global X2 displacement length turn
global X3 mpg length turn
global X4 weight turn


eststo e1: probit foreign $X1
eststo e2: probit foreign $X2
eststo e3: probit foreign $X3
eststo e4: probit foreign $X4

forv i = 1/4 {
    qui estimates restore e`i'
    local r2 : di %5.3f e(r2_p)
    qui estat classification
    local class : di %5.3f r(P_corr)
    qui lroc
    local area : di %5.3f r(area)
    di "Model with X`i' :  r2 = `r2'   , class = `class' , lroc = `area'"
}

[Serena Menny]

sysuse auto, clear

global X1 mpg weight
global X2 displacement length turn
global X3 mpg length turn
global X4 weight turn


eststo e1: probit foreign $X1
eststo e2: probit foreign $X2
eststo e3: probit foreign $X3
eststo e4: probit foreign $X4

forv i = 1/4 {
qui estimates restore e`i'
local r2 : di %5.3f e(r2_p)
qui estat classification
local class : di %5.3f r(P_corr)
qui lroc
local area : di %5.3f r(area)
di "Model with X`i' : r2 = `r2' , class = `class' , lroc = `area'"
}

Thank you so much for this!!