Predictor Variables

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Variables believed to predict or correlate with the outcome variable.

Predictor variables in traditional regression models

It can be useful to distinguish between the following different types of predictor variables:[1]

  • Exposure of interest variables that are of direct interest when trying to understand the world. For example:
    • Price if predicting sales.
    • Educational level if predicting success in life.
  • Confounding variables which, if ignored, cause incorrect conclusions to be reached about the relationship between the exposure of interest variables and the dependent variable. For example:
    • If trying to understand the relationship between price and sales then 'out of stocks' (i.e., when the product is not available due to being sold out) is a confounding variable.
    • If trying to understand the relationship between educational level on success in life then parents' success in life is a confounding variable.
  • Precision variables are unrelated to the exposure of interest but explain some of the variability in the dependent variable and thus their inclusion in a model can allow more precise estimates of the relationship between the other predictor variables and the outcome variable (i.e., reduce standard errors and increase the power of any statistical tests). Precision variables are only worthwhile where they have a very strong relationship with the dependent variable.[2] Examples of precision variables include: blocks in some experiments, and alternatives in unlabeled choice experiments.
  • Concomitant variables, which are variables that are not of direct interest themselves, but which may moderate the relationship between the exposure of interest variables and the outcome variable. For example, in a study investigating how people respond to a new type of drug, differences in responsiveness may relate to gender, which makes gender a concomitant variable. The term 'concomitant variable' is not a standard term in data science, and various disciplines have different names for the same idea (e.g., covariate, moderating variable). Specific roles for concomitant variables in regression include:
    • Variables that are interacted with other variables.
    • Variables that are used to predict variance parameters.
    • Variables used to predict aspects of mixture distributions (e.g., a priori probability of class membership in a latent class model).

Also known as

  • Independent variables
  • Regressors
  • Explanatory variables
  • Explanators
  • Covariates
  • Factors
  • Attributes
  • Regression weights (although this name should be avoided, as it can too easily be confused with the weight variable).
  • Concomitant variables (in some contexts concomitant variables are a synonym for Supplementary Variables)

See also

References

  1. Lumley, T. (2010). Complex Surveys: A Guide to Analysis Using R (Wiley Series in Survey Methodology), Wiley.
  2. Lumley, T. (2010). Complex Surveys: A Guide to Analysis Using R (Wiley Series in Survey Methodology), Wiley.