Standardized regression coefficients remove the unit of measurement of predictor and outcome variables. They are sometimes called betas, but I don’t like to use that term because there are too many other, and too many related, concepts that are also called beta.

There are many good reasons to report them:

- They serve as standardized effect size statistics.
- They allow you to compare the relative effects of predictors measured on different scales.
- They make journal editors and committee members happy in fields where they are commonly reported.

If you use a regression procedure in most software, standardized regression coefficients are reported by default. Or at least an easy option.

But there are times you need to use some procedure that won’t compute standardized coefficients for you.

Often it makes more sense to use a general linear model procedure to run regressions. But GLM in SAS and SPSS don’t give standardized coefficients.

Likewise, you won’t get standardized regression coefficients reported after combining results from multiple imputation.

Luckily, there’s a way to get around it.

A standardized coefficient is the same as an unstandardized coefficient between two standardized variables. We often learn to standardize the coefficient itself because that’s the shortcut. But implicitly, it’s the equivalence to the coefficient between standardized variables that gives a standardized coefficient meaning.

So all you have to do to get standardized coefficients is standardize your predictors and your outcome.

How?

### The Steps

Remember all those Z-scores you had to calculate in Intro Stats? It wasn’t the useless exercise you* thought* it was at the time.

Converting a variable to a Z-score is standardizing.

In other words, do these steps for Y, your outcome variable, and every X, your predictors:

1. Calculate the mean and standard deviation.

2. Create a new standardized version of each variable. To get it, create a new variable in which you subtract the mean from the original value, then divide that by the standard error.

3. Use those standardized versions in the regression.

Could this take a while? Yup.

But if that’s what the journal requires you report, just do it.

A nice advantage, is you can apply it, at least partially, even in regression models that can’t usually accommodate standardized regression coefficients.

For example, in a logistic regression it doesn’t make sense to standardize Y because it’s categorical. But you can standardize all your Xs to get rid of their units.

You can then interpret your odds ratios in terms of one standard deviation increases in each X, rather than one-unit increases.

{ 12 comments… read them below or add one }

Thanks for the above,

I was going to book an hour of consultation for this.

Your site and the workshops are really amazing.

Best wishes

Thanks, Aziz!

Thank you for post. However, if you have used the Multiple Imputation Method, SPSS will not produce the standardised beta weighs but ALSO it wont produce SDs for the pooled data….what is one to do in this situation? many thanks!

Hi Tamlyn, just standardize all Xs and Y BEFORE doing the multiple imputation.

I need to calculate scale scores after I complete the MI (e.g. total anxiety score), but then this becomes a predictor in my regression. This means I can’t standardize the variable prior to running MI, so I am still struggling with how to find the pooled SDs.

Hi I’m kind of late with this, but this is a great post! I have been wandering how I could determine the relative effects of my predictors. However, I am not understanding the process. I get lost at step 2 when you say subtract the mean from the original value. What original value? Could you show the process using actual numbers? Thanks!!!

Okay… so I just read how to calculate z-scores, which I understand completely. I guess my confusion is when you say “In other words, do these steps for Y, your outcome variable, and every X, your predictors”. What do you mean by outcome variable and predictors? Outcome variable as in the dependent variable? Predictors as in the independent variables/factors/predictors? In this case, I don’t understand how to calculate the z-scores for the predictors unless they’re numeric. In my case, my predictors are discrete.

Hi Delano,

Mathematically, you can still do it with dummy-coded predictor variables. The interpreation doesn’t make much sense, though, and therefore, it’s usually better to just keep those coded 0/1. Standardized coefficients aren’t really meaningful for categorical predictors.

Hi, should I use standardized variables for linear mixed effect models?

Thanks

One quick note about logit models. You correctly point out you shouldn’t standardize a dichotomous variable (I would probably argue not to standardize ordinal or categorical variables as well, as standardization implies continuous), and that you can standardize the X variables going into the model. Keep in mind that logit models are actually already standardized. See Williams (2009): http://www3.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf

… in logit and probit models, coefficients are inherently standardized. Rather than standardizing by rescaling all variables to have a variance of one, as in OLS, the standardization is accomplished by scaling the variables and residuals so that the residual variances are either one (as in probit) or π^2/3 (as in logit). If residual variances differ across groups, the standardization will also differ, making comparisons of coefficients across groups inappropriate.

Logit models can be very tricky to interpret when thinking about omitted variable bias (even if they are uncorrelated with your other independent variables) and when comparing across groups or samples.

Do you know if the coefficients output from excel data toolspack are standardised or unstandardised?

I need go the opposite direction. I have standardized scores but need to construct the corresponding prediction equation using raw variable readings.