---
title: "Protest: A moderation example"
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---

## Preamble

```{r}
#| label: setup
library(rccme)
library(modelsummary) # for model summary
```

Also install the `sandwich` package for robust standard errors, but you don't have to load it.

Summarise the dataset:

```{r}
summary(protest)
```

The goal is to fit the moderation model in Figure 10.2 of the 2017 Introduction to Process text by Andrew Hayes.

In this model, `sexism` interacts with both levels of `protest` to predict `liking`.

We already have scale average scores for `sexism` and `liking`.

We also gather construct reliabilities from table 1 in the paper:

```{r}
cons_rel <- list(
  "sexism" = .75, "liking" = .88
)
```

## Calibrating the scores

We calibrate the `sexism` score since it's the predictor. We pass the dummy variables for the two levels of protest since they are predictors that do not need calibrating.

```{r}
head(cov_lik <- model.matrix(~ factor(protest), protest))
cal_scores_for_lik_out <- rccme_calib_me(
  protest[, c("sexism")],
  rel_vec = cons_rel$sexism,
  z_mat = cov_lik[, -1] # remove intercept
)
head(cal_scores_for_lik_out)
protest$sexism_to_lik <- cal_scores_for_lik_out[, 1]
```

## Run the regression

```{r}
(fit_cal <- lm(
  liking ~ sexism_to_lik * factor(protest),
  protest
))
```

```{r}
(fit_no_cal <- lm(
  liking ~ sexism * factor(protest),
  protest
))
```

All coefficients are different.

```{r}
modelsummary(
  list(
    "Without Calibration" = fit_no_cal,
    "With Calibration" = fit_cal
  ),
  estimate = "{estimate} ({std.error})", statistic = "{p.value}",
  # Set standard error to HCSEs and omit distracting fit indices
  gof_omit = "IC|F|Log", vcov = "HC4",
  # Rename sexism_to_lik:
  coef_rename = c("sexism_to_lik" = "sexism")
)
```

## Original paper for dataset

Garcia, D. M., Schmitt, M. T., Branscombe, N. R., & Ellemers, N. (2010). Women’s reactions to ingroup members who protest discriminatory treatment: The importance of beliefs about inequality and response appropriateness. _European Journal of Social Psychology, 40_(5), 733–745. https://doi.org/10.1002/ejsp.644