Converting unstandardized regression coefficients to standard deviations / standardized effect size

[patrick handcock]

Hi there.

Apologies - this feel like an awfully simple question, but I've been struggling to find consistent answer online and have been going around in circles.

Basically I am looking at physical activity behaviours and their associations of 6 cardiometabolic risk biomarkers in a population level dataset. Lets take the example in this instance as walking time per hour (walkhr_12) and one biomarker - glucose (glu_12).

1) I have determined the subpopulation of interest and created an include variable for it.
2) I have generated decriptive means and sd's using the SVY command

svy, subpop(include): mean glu_12
estat sd

MEAN=5.343
SD= 0.6746407

3) I have run a regression and computed the unstandardized regression coefficients for association between walking and glucose.

svy, subpop (include): regress glu_12 walkhr_12 i.drsex_12 drage_12 i.educ_cat3 i.ethn3 i.occup_3 i.marital_cat2 i.alcohol_cat waist_12

Unstandardised b coefficient (95% CI) = -0.06 (-0.10, -0.03)

4) If I want to look at the 'standardized effect size’ (i.e. SD difference in glucose per hour/day walking so I can determine whether effect size is 'small', 'medium', 'large' - see quote at the end about the method) - is it just a matter of:

a) calculating a standardized walkhr_12 variable via...

gen glu_12_new1 = glu_12/0.6746407

OR

b) egen glu_12_new2 = std(glu_12)

...prior to running the regression:

svy, subpop (include): regress glu_12_new1 walkhr_12 i.drsex_12 drage_12 i.educ_cat3 i.ethn3 i.occup_3 i.marital_cat2 i.alcohol_cat waist_12

Both methods appear to give me the same result, but apparently not giving me the what I need (according to statistician).

Perhaps I am getting confused between ‘standardized regression coefficients’ with ‘standardized effect size’? Apparently it is the latter that I want... Finding it a bit confusing.

i.e. in methods section (for context):

Results are expressed in unstandardised (b) regression coefficients (for clinical interpretation), and sometimes also as partially standardised (β) regression coefficients (to facilitate comparison between the biomarkers). These coefficients respectively indicate the difference in biomarkers (in units and in standard deviations) per additional one h/day of context-specific walking time. Associations are described as very small (<0.2 SD), ‘small’ (0.2 SD), ‘medium’ (0.5 SD) and ‘large’ (0.8 SD) for a reasonable dose of walking time (here, 1 h/day) based on typical interpretations of standardised effect sizes.

What I ultimately want is to present the unstandardized regression coefficients (for clinical interpretation) AS WELL AS the SD difference results (for comparison between multiple biomarkers, as well interpretation of effect sizes - i.e. SD difference in biomarker)

Any help much appreciated! Hope I have given enough context...

Patrick

[Phil Bromiley]

In many cases, folks standardize both the iv and dv so they can talk about the influence of a 1 std change in iv on the dv measured in standard deviations. You can do the same thing simply by using the original variables and then looking at the predicted changes for a one standard deviation change in x (and you can turn that into std dev of y easily).

[Weiwen Ng]

In many cases, folks standardize both the iv and dv so they can talk about the influence of a 1 std change in iv on the dv measured in standard deviations. You can do the same thing simply by using the original variables and then looking at the predicted changes for a one standard deviation change in x (and you can turn that into std dev of y easily).

Continuing that point, if Patrick isn't already aware of

egen y_std = std(y)

then this is worth knowing.