Moderation analysis

Overview

A moderator is a variable that changes how strongly, or in which direction, one variable affects another. Moderation is tested as an interaction: the product of the predictor and the moderator enters the regression next to both of them 2401.12247 §3.3.3. The paper judges each moderation hypothesis by its interaction coefficient, read from the model that adds the interaction terms 2401.12247 tab. 5. Only one card uses the statistical sense, so the page describes one method in detail. A second card carries this slug but uses "moderation" for platform content moderation; see Not the same sense.

Variants

Blocked OLS with mean-centred interaction terms

Predictors and the moderator are mean-centred, their products are formed, and ordinary least squares (OLS) regression is run in blocks: controls first, then main effects, then interaction terms. The authors add the blocks in that order and report the coefficients per model in one table 2401.12247 §3.3.3 tab. 5. Card: Exploring consumers response to text-based chatbots in e-commerce: The moderating role of task complexity and chatbot disclosure.

The paper reports two moderators, task complexity and chatbot disclosure, each tested against two predictors (perceived empathy and friendliness). Of the four predicted interactions, two are supported; the other two are not, and one of those is significant in the direction opposite to the prediction 2401.12247 §3.3.3 tab. 5. The authors describe the entry as stepwise, but the selection criteria are not stated 2401.12247 §3.3.3.

Not the same sense

Platform research also uses "moderation" for the actions a site takes on user content. 1610.08914 §5.2 is filed here, but it does not test a moderator. It labels personal attacks in 63M Wikipedia talk comments and reports how often an attack was followed by a warning or a block within 7 days: 7.7%, 7.0% and 11.3% for either 1610.08914 §5.2. The statistical methods above do not apply to that analysis. For the labelling method, see toxicity-detection.

When to use which

The paper supports one variant, so the choice below is limited to its constraints.

Implementation sketch

The steps below follow the paper's blocked procedure. The paper does not say how construct scores were computed, so the scoring step is a choice you must make and report.

# Blocked moderation regression  [arxiv:2401.12247 §3.3.3]
# Input:  one row per respondent, construct scores, controls
# Output: coefficients per block, including interaction terms

def moderation_blocks(data, outcome, controls, predictors, moderators):
    # Score each construct; the paper does not state the method  [§3.3.3]
    scores = build_construct_scores(data)
    # Mean-centre the scores before forming products  [§3.3.3]
    centred = subtract_means(scores)
    # Block 1: controls only  [tab. 5, Model 1]
    block_1 = ols(outcome, controls)
    # Block 2: add the predictors and moderators  [tab. 5, Model 2]
    block_2 = ols(outcome, controls + predictors + moderators)
    # Block 3: add each predictor times each moderator  [tab. 5, Model 3]
    products = [p * m for p in predictors for m in moderators]
    block_3 = ols(outcome, controls + predictors + moderators + products)
    return block_1, block_2, block_3

Contradictions

• Direction of one predicted moderation. The authors predicted that disclosure would strengthen the effect of empathy on trust. The interaction is significant but negative (−0.154, p < 0.05). The text calls the hypothesis "not supported" 2401.12247 §3.3.3 tab. 5. Read it as an effect in the opposite direction, not as a null result.
• Sign of one main effect. The friendliness main effect in Model 3 is printed as 0.275 in the rotated table, while the model figure shows −0.275 2401.12247 tab. 5 fig. 2. The text does not resolve this, so check the source before copying the sign.

Papers

• Exploring consumers response to text-based chatbots in e-commerce: The moderating role of task complexity and chatbot disclosure: a survey of 299 shoppers that tests two moderators of chatbot trust with blocked OLS and interaction terms.
• Ex Machina: Personal Attacks Seen at Scale: labels attacks in Wikipedia talk comments and reports platform moderation outcomes. It uses "moderation" in the content sense; see Not the same sense.