I have behavioral scores that I want to use in linear regression. Should I use the actual scores or standardized scores? The raw scores are approximately normally distributed. I have the actual standardized scores (Z-scores) for my subjects based on the original normative population; and of course I could compute the z-scores for just my sample of subjects as well.
Are there advantages or disadvantages of using a standardized score vs. the actual score values in linear regression? and if so, which z-score to use? And what if these behavioral scores are the outcome variable of interest---would it also be useful to use standardized scores in that case? Thanks for any insight -
Centering/scaling of variables help to interpret regression models. Standardization (which is both centering and scaling) helps cure multicollinearity and may be necessary when you have interaction or higher order terms. I added some links.
http://www.stat.columbia.edu/~gelman/research/unpublished/standardizing.pdf
https://stats.stackexchange.com/questions/29781/when-conducting-multiple-regression-when-should-you-center-your-predictor-varia
http://andrewgelman.com/2009/07/11/when_to_standar/
Centering/scaling of variables help to interpret regression models. Standardization (which is both centering and scaling) helps cure multicollinearity and may be necessary when you have interaction or higher order terms. I added some links.
http://www.stat.columbia.edu/~gelman/research/unpublished/standardizing.pdf
https://stats.stackexchange.com/questions/29781/when-conducting-multiple-regression-when-should-you-center-your-predictor-varia
http://andrewgelman.com/2009/07/11/when_to_standar/
I'm not a fan of standardizing. It can be very pernicious in some contexts.
Article Standardized or simple effect size: What should be reported?
Advantages, clearly!
Normative standardization for static designs can remedy some of the forms of Simpson's paradox:
- Yarnold, P.R. (1996). Characterizing and circumventing Simpson’s paradox for ordered bivariate data. Educational and Psychological Measurement, 56, 430-442.
Normative standardization conducted separately by sample also improves hold-out validity estimates for static designs:
- https://odajournal.com/2013/09/20/assessing-hold-out-validity-of-cta-models-using-unioda/
Ipsative standardization for dynamic designs can remedy some of the forms of Simspon's paradox, in multi-subject (a picture is worth a thousand words)
- https://odajournal.com/2013/10/23/ipsative-standardization-is-essential-in-the-analysis-of-serial-data/
- https://odajournal.com/2016/05/31/using-machine-learning-to-model-dose-response-relationships-via-oda-eliminating-response-variable-baseline-variation-by-ipsative-standardization/
and in single-case
- https://odajournal.com/2013/09/19/the-use-of-unconfounded-climatic-data-improves-atmospheric-prediction/
- https://odajournal.com/2013/11/07/ascertaining-an-individual-patients-symptom-dominance-hierarchy-analysis-of-raw-longitudinal-data-induces-simpsons-paradox/
designs. The latter article illustrates how to spot (and remedy) paradoxical confounding in various linear models, including regression and principal components analysis.
Dear Colleagues:
In my opinion the topic is this thread represents what is likely the most significant challenge to all of empirical research. In my view this is NOT a statistical issue, rather this IS a measurement issue.
A few Figures are worth a thousand words.
Please, if you have opportunity, can you explain the benefit of using raw scores (alternatively, of using standardized scores) in this brief, open access dose-response study involving lab rats?
Four figures (one using raw data) tell the story in this dynamic design...
- https://odajournal.com/2013/10/23/ipsative-standardization-is-essential-in-the-analysis-of-serial-data/
Here is a conceptually related thread concerning a static design:
- https://www.researchgate.net/post/NEGATIVE_CONFOUNDER_Im_analyse_adult_vaccination_association_with_demographic_and_primary_health_care_related_factors
The basic rule is always the same and is valid since the birth of the Statistic: when the variables in play are expressed in the same unit of measure and there are no outliers, there is no need to standardize; Otherwise, you need to standardize.
Science marches on: new statistical and measurement methods yield stronger results and correct prior misconceptions.
Common misconceptions about and misuse of transformations in measurement and statistical practice today are indeed ancient--and obsolete. To make matters even worse, common misconceptions about the assumptions underlying legacy methods are prevalent--for example, that data must be normally distributed for multivariable GLM methods.
If one’s data fail to meet (real or imaginary) distributional assumptions underlying a legacy statistical method, the prevalent reflex is to try using various types of post hoc (a posteriori) transformations, or combinations of types of transformations, in an effort to meet model assumptions (e.g., to eliminate or to reduce the influence of outliers in one’s sample).
Researchers rarely purposively use specific a priori data transformations which are theoretically motivated by the types of confounding that in principle can occur for the research design (a measurement issue), and that have been empirically found capable of eliminating prevalent statistical confounding (the most significant challenge to the validity of applied statistical findings).
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