Mixed-Effects Modeling in R

• This tutorial introduces mixed-effects modeling and its implementation in R for researchers with basic statistical knowledge.

Accessibility

• Focuses on being approachable and avoids excessive mathematical terminology.
• References articles and textbooks for more details.
• Provides R code snippets with data and scripts available on OSF for readers to follow along.

Purpose of the Tutorial

• Equips researchers with tools to implement mixed-effects models in their own research.

Keywords

• Mixed-effects modeling, R, language, speech perception, open data.

Data Collection

• Researchers often collect data from participants responding to multiple trials in experimental psychology.

Traditional Analysis Method

• Repeated measures analyses of variance (ANOVAs), which assess differences in means while accounting for correlations within individuals.

Independence Assumption

• Observations in a dataset must be independent, but observations within individuals are often correlated.

Shortcomings of Repeated Measures ANOVAs:

• Can model either participant- or item-level variability, but not both simultaneously.
• Observations collapsed across items or participants lead to lost information and reduced statistical power.
• Misses single observations via listwise deletion, reduces sample size, and inflates standard error estimates.
• Requires a continuous dependent variable and categorical independent variables.
• Makes modeling nonlinear relationships difficult.
• Primarily indicates effect significance without information on magnitude or direction.

Benefits of mixed-effects modeling:

• Examines conditions of interest and also accounts for the variability within and across participants and items simultaneously.
• Handles missing data and unbalanced designs effectively.
• Participants/items with more missing cases also have weaker influences on parameter estimates.
• Extreme values get shrunk toward the mean.
• Does not cause problems with continuous predictors, and the fitted model provides coefficient estimates for effects of interest.
• Can handle a variety of response variables via generalized linear mixed-effects models.
• Makes the transition to Bayesian modeling easier.
• More flexible analytic tool than ANOVAs.

Disclosures

• Data and R script for models are available via OSF.

Data Explanation

• Examples come from perception in human speech, and the information applies beyond psychology.
• In social psychology, participants might evaluate videos. In clinical psychology, participants might read narratives.
• Goal of the text is to introduce conducting linear mixed-effects modeling.
• The text provides snippets of R code using dummy data.
• The example data comes from a speech-perception study.
• 53 participants were each presented with 553 separate words.
• Either in the auditory condition or with the accompanied video.
• Participants listened and repeated each word.
• Response time was simultaneously measured. The data is available from a previous, modified experiment for pedagogical purposes.
• Accuracy data was not modified but variables were removed.

Fixed Effects

• Represent population-level effects persistent across experiments.
• Condition effects are typically fixed effects.

Random Effects

• Model the extent to which trends vary.
• Random effects are clusters of data from the same higher-level group.
• It is included in mixed-effects models to account for differing participants/items

Modeling Participants/Words

• Participants model random effects in hypothetical experiments because they are randomly sampled. Wanting to account for variability.

How including items/participants resolves problem of nonindependence

• Accounts for response-time variability across people.

Random Intercepts

• Random deviations from average
• Model estimates mean for condition
• Random intercepts allow model to take into account each participant's variance

Including random intercepts for items

• Allows model to account for variance within each item
• Reflects facts that some words are responded to more quickly

Multiple Regression analysis

• Regression line applied to all, leads to inaccurate prediction
• Residual error tends to be larger

Mixed Modeling

• Fixed-intercept estimate in mixed modeling is the average intercept
• Random intercepts allow deviance from average
• Such deviations follow normal distribution and the model estimates

Random Slope in Mixed Modeling

• Can account for fact that a fixed effect have influence on items or participants
• Can model differences in response times
• For research, the model estimates effect is 83 millisecond
• Means participants were 83 milliseconds slower, but some are more than others and same with other people
• Individual deviations are modeled via random slopes

Effects

• Fixed is the effect, if it is assumed, would exist on different participants
• Modality is a fixed effect because it is a common modality on response times accross items and participants