How to interpret a standardized multiple regression coefficient

[Alycat]

How can I write an interpretation of the standardized multiple regression equation for both Age of Child and Number of Siblings in this model:

ToM^ = 0.68TELD – 0.11Age + 0.45Siblings

The dependent variable is Theory of Mind ̧ and the three independent variables are TELD (Test of Early Language Development) scores, the Age of Child, and the Number of Siblings.

Any help would be greatly appreciated!

 

[Asymptotically Unbiased]

Hi Alycat,

Standardized variables have a mean of zero and unit variance (SD=1). This means that a unit increase in the standardized variable is equivalent to a standard deviation increase in the unscaled variable.

On average, with all other things being equal, a SD increase of X is associated with a (beta) increase in Y. If Y is also standardized, a SD increase in X is associated with a (beta)*SD increase in Y. Since the variables have been scaled, those covariates with larger standardized regression coefficients have a larger effect on the response variable.

Standardized regression coefficients can also be less interpretable in some respects: In your example, a standard deviation increase in the number of siblings may not really be meaningful if the SD is something like 0.5 or 1.2. I would recommend centering age (subtracting its mean), and standardizing TELD, leaving the number of siblings unscaled. This will give the intercept an actual interpretable meaning (average value of TOM for a child with 0 siblings, average TELD score, and average age), and have regression coefficients that scale naturally: an increase of one sibling, an increase in one year of age, a SD increase in test score.

Hope that helps.

 

[Karabiner]

ToM^ = 0.68TELD – 0.11Age + 0.45Siblings

Theory of Mind actually decreases with increasing age,
number of siblings and TELD being equal?

 

[Alycat]

Thanks Asymptotically Unbiased and Karabiner. I wrote this following interpretation but realised the style was for interpreting an UNSTANDARDIZED multiple regression coefficient... is there a difference in style when interpreting standardized and unstandardized?

The partial regression coefficient for Age indicates that, for a unit INCREASE in scores on Age, we expect scores on the ToM to INCREASE by 0.11 units, holding constant scores on TELD and Siblings.
Likewise, the partial regression coefficient for Siblings indicates that, for a unit INCREASE in its scores, we expect scores on ToM to INCREASE by 0.45 units, holding constant scores on TELD and Age.

With the minus sign in front of AGE, I'm unsure whether it INCREASES or DECREASES

Thanks again for your help!

 

[amandarinorange]

The partial regression coefficient for Age indicates that, for a unit INCREASE in scores on Age, we expect scores on the ToM to INCREASE by 0.11 units, holding constant scores on TELD and Siblings.
Likewise, the partial regression coefficient for Siblings indicates that, for a unit INCREASE in its scores, we expect scores on ToM to INCREASE by 0.45 units, holding constant scores on TELD and Age.

With the minus sign in front of AGE, I'm unsure whether it INCREASES or DECREASES

Your units are in standard deviations, so your write-up should say something along the lines of "for every 1 standard deviation of increase in age, scores on ToM DECREASE by 0.11 standard deviations, controlling for TELD scores and number of siblings". Same idea for the interpretation of the coefficient for siblings - you're talking about increases/decreases associated with standard deviations. (Side note: I'm not quite sure why your data show an inverse relationship between ToM and age...this is very counterintuitive, at least in my mind...)