z score as outcome

[Gianfranco Di Gennaro]

Dear Stata users,
I have two questions. Thanks in advance for your opinion.

One: Is there a command to directly get the z scores of a variable?

Question number two: I have a set of predictors and four different outcomes (four different measurement scales).
Would it make sense to you to transform each outcome value into a z score using the mean for that outcome, and then use a single multilevel model to model the z scores?

Thanks again.

[Ken Chui]

Can help with Q1: I believe there is a -zscore- program that you can download (use -help zscore- and start from there). But actually it's rather easy to compute it in two lines:

sum your_var
* quietly sum your_var // use this if you don't want to see the output
gen your_var_z = (your_var - r(mean))/r(sd)

[Joro Kolev]

I do not think that transforming to unitless measures is a good idea.

But if you want to do it anyways, check the user written -center-

net describe center, from(http://fmwww.bc.edu/RePEc/bocode/c)

or the egen function -egen, std()-

If you have multiple outcomes with the same predictors this sounds like a Multivariate regression exercise see -mvreg-.

[Dirk Enzmann]

I would respond to #3 that it depends (as always): Transforming to unitless measures (and other alternatives such as z/2-scores or percent-of-maximum-possible (POMP) scores) can be a good idea -- perhaps less so in econometrics and more so in psychometrics. Illuminating discussions can be found in Cohen et al. (1999), Gelman (2008), and Smithson & Verkuilen (2006) (see below).

If you want to transform variables into z-scores (or z/2-scores), think about the issue of listwise deletion of cases with missing values -- it may be that your regression model will use a different subset of cases depending on the missing values in some of the model's variables which will result in a mean and a SD of z-scores different from 0 and 1 in the subset of cases actually used (you can control this with the help of -mark- and -markout- and the -if- qualifier when transforming your variables).

An .ado-program that offers many different methods of transforming variables (e.g. to z-scores, z/2-scores, POMP-scores, etc.) and simultaneously allows for listwise deletion of missing values (with the -if- qualifier over cases, but also over a user-specified number of variables when calculating scores "row-wise") is -scores- on SSC.

References:

• Cohen, P., Cohen, J., Aiken, L.S., & West, S.G. (1999). The problem of units and the circumstance for POMP. Multivariate Behavioral Research, 34, 315-346.
• Gelman, A. (2008) Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine, 27, 2865-2873.
• Smithson, M. & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological Methods, 11, 54-71.