5.7 Overview of Ordinal DVs

• If you are considering using linear regression for ordinal outcomes, consider y* standardized coefficients from the ordinal model as an alternative
  • Unlike multinomial logit, only requires estimating J – 2 more parameters than linear regression (for the thresholds τ). So, relatively efficient model
• Before using ordinal models, consider:
  1. Is there a clear y* latent metric underlying the observed categories of your dependent variable? If not, ordinal models may not be the best choice
     • If yes, and the latent y* is of substantive interest, the ordinal model can greatly simplify interpretation
  2. Whether your DV is ordinal as Stevens defined it:
     • Categories are ranked on a single dimension
  3. Consider whether the relationship between your predictor and outcome variable is likely ordered in nature
• If either (b) or (c) are violated, the ordinal model can lead to biased conclusions
  • Even if you think (c) is likely to hold, always do a sensitivity analysis using a nominal model before accepting the results of an ordinal model

Extensions of the ordinal model

• Even if you don’t use the ordinal model much in your work, it is the foundation for other useful models. E.g.,
  • Graded response item response theory (IRT) models are based on ordinal logit
  • The y* derivation of the ordinal model is used for the derivation of nonlinear factor analysis models for ordinal items
    • These are methods used to scale continuous latent variables from ordinal observed items
    • More appropriate than factor analysis (which assume interval level latent variables and interval level items)
• Both IRT and nonlinear factor analysis (actually the same underlying model) are very useful scaling techniques
  • Covered extensively in the Item Response Theory section of my Latent Variable Modeling course