mvn imputation - able to get unstandardized?

[Cherish Michael]

I use the mi estimate syntax for my mvn imputations. I find that they always provide standardized coefficients.

Is there an option for unstandardized?

Here is an example of the syntax I am referring to (that always provides standardized coefficients):

mi estimate, dftable: reg HEALTHPLAN1 AGE AGE2 woman2 nonhispblack other hisp SEX2 college_2 continc OWNRENT2 SELFRATED PHYS_ABLE AbilityMean AGEID LONGLIVE prevmarr widowed nevermar faminter_score friendsinter_score

I use this coding to obtain the R-square:

mibeta HEALTHPLAN1 AGE AGE2 woman2 nonhispblack other hisp SEX2 college_2 continc OWNRENT2 SELFRATED PHYS_ABLE EYES HEAR PAIN AbilityMean AGEID LONGLIVE prevmarr widowed nevermar faminter_score friendsinter_score

[daniel klein]

What makes you think that mi estimate : regress reports standardized coefficients?

[Cherish Michael]

daniel klein Another post clarified that they are standardized and when I use this with ", beta" it provides the same exact coefficients.

[daniel klein]

Please post a link to that other post.

To be clear here: mi estimate : regress does not produce standardized coefficients by default. It produces the very same coefficients that regress produces. It does so for all m imputed datasets, then reports the arithmetic mean of the coefficients.

[Cherish Michael]

I’ll try to track that down. In the meantime, is there a way to standardize using the syntax I use?

[daniel klein]

In the meantime, is there a way to standardize using the syntax I use?

So you want standardized coefficients? I ask because your question implies that you do not.

Anyway, there is no general agreement on how to obtain standardized coefficients in multiply imputed data (see, e.g., van Ginkel, 2020). mibeta (from http://www.stata.com/users/ymarchenko/) pools standardized coefficients from the m datasets. From a quick glance at the code, I'd say that it obtains results that you would get from the beta option of regress. Personally, I do not like this approach for categorical variables. I find them hard to impossible to interpret. For example, how do you internet a standard deviation of gender? I prefer using standardized continuous variables (including the outcome) and leaving categorical variables untransformed in the regression models. However, this is technically a bit cumbersome in multiply imputed data. Also, you seem to be willing to assume a multivariate normal distribution for the imputation model so you might not have a problem with standardized categorical variables either.


van Ginkel, J.R. 2020. Standardized regression coefficients and newly proposed estimators for R2 in multiply imputed data. Psychometrika, 85:185--205.

[Cherish Michael]

Actually I would like both standardized and unstandardized- I have been asked to provide both. To clarify, the mibeta syntax provides the standardized coefficients?

[daniel klein]

Well, the output that mibeta provides below the standard coefficient table of mi estimate says:

Standardized coefficients and R-squared

So, yes; the coefficient table shows the unstandardized coefficients that you would get from mi estimate : regress and the additional table shows the mean (i.e., pooled) standardized coefficients, R2, and their distribution.

[Cherish Michael]

Thank you - one more thing. How do I know if they are significant or not? I do not see the p values for these. Do they maintain the same significance between standardized and unstandardized?

[daniel klein]

How do I know if they are significant or not? [...]Do they maintain the same significance between standardized and unstandardized?

By "they", you mean the standardized coefficients, right? The t-tests for standardized and unstandardized coefficients are the same in a single dataset. This is why the beta option of regress does not provide standard errors and t values.

mibeta does not provide standard errors and t values for standardized coefficients. However, as discussed in the literature that I have cited in #6, the standard errors and t values for standardized coefficients in multiply imputed data will generally differ from their unstandardized counterparts -- at least if we follow the so-called "standardize-then-combine" approach, which is (probably) what mibeta does.* This is one more reason why I prefer using standardized variables over transforming the coefficients.

If you want the standard errors and t-values for standardized coefficients with the "standardize-then-combine" approach, create standardized versions of your variables then plug them into the regression models. Here is the basic approach to that:

u_mi_assert_set flong

mi query
local M = r(M)

foreach var in varlist_to_standardize {
    
    generate double z_`var' = .z
    
    forvalues m = 1/`M' {
        
        summarize `var' if _mi_m == `m'
        replace z_`var' = (`var'-r(mean))/r(sd) if _mi_m == `m'
        
    }
    
}

where varlist_to_standardize is the list of variable names that you want to standardize; do not forget to standardize the outcome (dependent) variable.

I have mentioned before that there are some technical pitfalls to this approach. First, your data must be saved (or converted to) mi flong style. Second, the standardized variables must not be registered imputed. Both requirements are necessary because the standardized variables will be super-varying; that is: their values will vary over imputed datasets even for observations with non-missing values. The reason is that the imputed values will generally lead to different means and standard deviations across datasets. Registering the variables imputed will cause the mi machinery to replace the values in the non-missing observations to match the observed values. This is not what you want. Last, you cannot use factor-variables; instead, you need to create indicator variables manually. But, as I have pointed out, I would not recommend standardizing categorical variables in the first place.


* mibeta uses the undocumented and built-in _ms_display to obtain standardized coefficients. Because I cannot look into the code, I am not sure what it does, exactly.