Variable types

0.1 Continuous variables

  • The variable can take on any positive and negative real number, including 0: Gaussian (aka normal) distribution.

    • There are very few truly Gaussian variables, although in some cases one can speak of “approximate” or “assumed” normality.
    • This family is fitted by default in lm(), lme4::lmer() and brms::brm().

  • The variable can take on any positive number only: Log-normal distribution.

    • Duration of segments, words, pauses, etc, are known to be log-normally distributed.
    • Measurements taken in Hz (like f0, formants, centre of gravity, …) could be considered to be log-normal.
    • There other families that could potentially be used depending on the nature of the variable: exponential-Gaussian (reaction times), gamma, …

  • The variable can take on any number between 0 and 1, but not 0 nor 1: Beta distribution.

    • Proportions fall into this category (for example proportion of voicing within closure), although 0 and 1 are not allowed in the beta distribution.

  • The variable can take on any number between 0 and 1, including 0 or 0 and 1: Zero-inflated or Zero/one-inflated beta (ZOIB) distribution.

    • If the proportion data includes many 0s and 1s, then this is the ideal distribution to use. ZOIB distributions are somewhat more difficult to fit than a simple beta distribution, so a common practice is to transform the data so that it doesn’t include 0s nor 1s (this can be achieved using different techniques, some better than others).

0.2 Discrete variables

  • The variable is dichotomous, i.e. it can take one of two levels: Bernoulli distribution.

    • Categorical outcome variables like yes/no, correct/incorrect, voiced/voiceless, follow this distribution.
    • This family is fitted by default when you run glm(family = binomial), aka “logistic regression” or “binomial regression”.

  • The variable is counts: Poisson distribution.

    • Counts of words, segments, gestures, f0 peaks, …

  • The variable is a scale: ordinal linear model.

    • Likert scales and ratings, language attitude questionnaires.
    • Ordinal linear models, a.k.a. ordinal logistic regression, can be fitted with the ordinal and the brms package.