Interpreting effect size

[Adeola Kolade]

Dear all,

I will please like to know how to discuss the result of a regression analysis
e.g.
Ols produces results below

reg education overobesity i.soclass age

Source | SS df MS Number of obs = 706
-------------+---------------------------------- F(6, 699) = 52.62
Model | 818.018761 6 136.33646 Prob > F = 0.0000
Residual | 1811.13846 699 2.59104215 R-squared = 0.3111
-------------+---------------------------------- Adj R-squared = 0.3052
Total | 2629.15722 705 3.72930103 Root MSE = 1.6097

------------------------------------------------------------------------------
education | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
overobesity | -.2752897 .1358245 -2.03 0.043 -.5419626 -.0086168

i know this produces a negatively significant result. My question is how to interpret the effect size (-0.275) to know if they are big or not relative to the mean value of the outcome. How is this calculated?

Lets also assume we get the same result in a probit analysis, how will i also interpret the effect size in regards to the outcome (a binary variable e.g no education (0) and education (1)). I will really appreciate a reply. Many thanks.

[Felix Bittmann]

First, this is not the effect size but the beta coefficient you are talking about (-0.275). To get the effect size, type:

estat esize

For interpretation it is crucial to know what overobesity is here: a binary variable or a continuous one? If the latter, a histogram is useful to get an impression of this variable and then talk about effects. Same for education, how is this measured?

[Carlo Lazzaro]

Adeola:
unless you wanted to run a linear probability model, I fail to get the role of -regress- here (as your regressand seems to be a binary variable).
If -overobesity- is categorical, being overobese (coded 1) reduces education achievement and significantly so.
As far as -probit- coefficients (and related interpretation) are concerned, please see https://stats.idre.ucla.edu/stata/ou...it-regression/.
That said, at its face-value your model may suffer from two different forms of endogeneity:
1) reverse causation: it may well be that, other things being equal, low education causes overobesity;
2) latent variable: family disposable income (embedded in residuals) may well be correlated to both overobesity (other things being equal, on average low income comes with a higher probability of eating junk food) and education attainment (other things being equal, on average low family disposable income maean lower education levels).

[Adeola Kolade]

Many thanks for your replies and for the extensive comments by @ Carlo. The regression result shown is actually from a probit analysis but lets also assume we obtain similar results from OLS using BMI. See below

Probit

probit education overobesity i.soclass age
------------------------------------------------------------------------------
education | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
overobesity | -.2752897 .1358245 -2.03 0.043 -.5419626 -.0086168

OLS

reg test score BMI i.soclass age
------------------------------------------------------------------------------
test score | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
BMI | -.2752897 .1358245 -2.03 0.043 -.5419626 -.0086168

education= has no education (0) and has an education (1)
overobesity = not overweight/obese (0) and overweight/obese (1)
test score= continuous variable ranging from score 1-160 with a mean score of 90 in my data
BMI= continuous variables with mean value of 26

My question is how do i interpret the coefficient , so i know for the OLS example that an increase in BMI will lead to a 0.275 point decrease in test scores.
1. How do i know if the magnitude of the coefficient is big or small relative to the mean value of the outcome (test score)
2. How do i interpret this coefficient in terms of economic significance i.e will a 0.275 decrease in test score be important

and how do i also interpret this for the probit result. I will really appreciate a response.

[Carlo Lazzaro]

Adeola:
0) for both regression models, it does not make sense to consider each coefficient separately, as they're adjusted for the other ones;
1-2) if the men value of the test is 90 points, a reduction of 0.275, other things being equal, sounds as negligible (but what at 0) still holds).
An aside, the potential endogeneity-related issues still hold.

[Adeola Kolade]

Many thanks, i have addressed the endogenity issues using a fixed effect and IV, however, my supervisor says i have to interpret the magnitudes of the coefficient obtained from OLS and Probit. He said "Comment on the magnitudes of the coefficients too. Are they big or not relative to the mean values of the outcome variables?" That's the reason for my question. In some papers i see that they address the coefficient (0.275) in relations to the outcome by some calculations but i am not sure how this is done.

For example a paper reads "Prolonged breastfeeding reduces the BMI of a child by 0.17 BMI points (0.17 is the coefficient obtained from OLS). Although this does not sound like a large reduction, at this young age this is a relatively high percentage (4.23%) of the average BMI and is likely to lead to larger differences later in childhood."

In the paper quoted above how was 4.23% obtained?

[Carlo Lazzaro]

Adeola:
I really can't say, as I do not know the paper you're referring to.